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HP 39gs Master Manual

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hp 39gs and hp 40gs graphing calculators

Mastering the hp 39gs & hp 40gs

A guide for teachers, students and other

users of the hp 39gs & hp 40gs

Edition 1.0

HP part number F2224-90010

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Summary of Contents for HP 39gs

  • Page 1
    39gs and hp 40gs graphing calculators Mastering the hp 39gs & hp 40gs A guide for teachers, students and other users of the hp 39gs & hp 40gs Edition 1.0 HP part number F2224-90010…
  • Page 2
    Notice REGISTER YOUR PRODUCT AT: www.register.hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED «AS IS» AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE.

  • Page 3: Table Of Contents

    What is the HOME view? …18 Exploring the keyboard …19 Angle and Numeric settings …28 Memory Management …30 Fractions on the hp 39gs and hp 40gs …33 The HOME History …37 Storing and Retrieving Memories …39 Referring to other aplets from the HOME view…40 A brief introduction to the MATH Menu …41…

  • Page 4
    The Statistics Aplet — Univariate Data…114 The Expert: Simulations & random numbers…120 The Statistics Aplet — Bivariate Data…123 The Expert: Manipulating columns & eqns…133 The Inference Aplet …141 The Expert: Chi tests & Frequency tables …147 The Linear Solver Aplet …150 Example 1 …150 Example 2 …150 Example 3 …151…
  • Page 5
    Deleting downloaded aplets from the calculator …250 Capturing screens using the Connectivity Kit …251 Editing Notes using the Connectivity Software…252 Programming the hp 39gs & hp 40gs …255 The design process …255 Planning the VIEWS menu …257 The SETVIEWS command …259 Example aplet #1 –…
  • Page 6
    Rectilinear Motion…321 Limits…321 Piecewise Defined Functions …322 Sequences and Series …322 Transformations of Graphs …323 Appendix C: The CAS on the hp 40gs …324 Introduction …324 Using the CAS …327 Examples using the CAS …341 The CAS menus …358 On-line help …361 Configuring the CAS…362…

  • Page 7: Introduction

    This book is intended to help you to master your hp 39gs or hp 40gs calculator but will also be useful to users of earlier models such as the hp 39g, hp 40g and hp 39g+. These are very sophisticated calculators, having more capabilities than a mainframe computer of the 1970s, so you should not expect to become an expert in one or two sessions.

  • Page 8
    39g which would ‘convert’ it into an hp 40g and activate the CAS. This is not the case with the hp 39gs & hp 40gs: the internal chips are different and there is no way to ‘convert’…

  • Page 9: Getting Started

    The sketch below shows most of the important keys. As can be seen on the previous pages, the keyboards for the hp 39gs and hp 40gs are exactly the same except for the different color schemes. These keys are the ones which control the operation of the calculator – most others are simply used to do calculations once the important keys have set up the environment to do it in.

  • Page 10: Some Keyboard Examples

    — used to graph the function. PLOT (The PLOT SETUP key is used to choose which aplet is active. There are 12 APLET aplets provided with the calculator and more can be downloaded from the internet. view sets the axes.)

  • Page 11: Keys & Notation Conventions

    & & There are a number of types of keys/buttons that are used on the hp 39gs and hp 40gs. The basic keys are those that you see on any calculator including scientific ones, such as the numeric operators and the trig keys. Most of these keys have two or more functions, with the second function accessed…

  • Page 12
    The Screen keys A special type of key unique to the hp 39gs, hp 40gs and family is the row of blank keys directly under the screen. These keys change their function depending on what you are doing at the time. The easiest way…
  • Page 13
    (see image). In case you symbol comes from the divide key HOME The calculator also comes with an immense number of mathematical functions. They can all be obtained via menus through the from the keyboard. Try pressing the find your screen looks like the screen shot left.

  • Page 14: Everything Revolves Around Aplets

    A built in set of aplets are provided in the and hp 40gs. This effectively mean that it is not just one calculator but a dozen (or more), changing capabilities according to which aplet is chosen. The best way to think of these aplets is as “environments” or “rooms” within which you can work. Although…

  • Page 15
    The Sequence aplet (see page 99) Handles sequences such as recursive and non-recursive sequences. The Solve aplet (see page 105) Solves equations for you. Given an equation such as variable if you tell it the values of the others. The Statistics aplet (see page 114 & 123) Handles descriptive statistics.
  • Page 16
    The standard aplets will cover all of your normal requirements in mathematics. However one of the great strengths of the hp 39gs and hp 40gs is their ability to “download” additional aplets from other calculators and from the Internet. See page 245.
  • Page 17
    Once an aplet is transferred onto any calculator from the PC, transferring it to another takes only seconds using the built in infra-red link at the top of each calculator on the hp 39gs or using the mini-serial cable on the hp 40gs.

  • Page 18: The Home View

    HOME • Exploring the Keyboard Angle and numeric settings • Memory management • Fractions on the hp 39gs & hp 40gs • History • HOME • Storing and retrieving memories • Referring to other aplets from the •…

  • Page 19: Exploring The Keyboard

    The first step in efficient use of the calculator is to familiarize yourself with the mathematical functions available on the keyboard. If we examine them row by row, you will see that they tend to fall into two categories — those which are specific to the use of aplets, and those which are commonly used in mathematical calculations.

  • Page 20
    Internet written by other programmers. Once these are downloaded into your calculator they can also be accessed via the later in this section, and the chapter entitled “Programming the hp 39gs & hp 40gs” on page 255. The SYMB, PLOT and NUM keys When working mathematically there are three ways that we view functions: •…
  • Page 21
    VIEWS from the Internet. When a programmed aplet is created for the hp 39gs or hp 40gs, a menu is provided by the programmer to let you control and use it. During the programming this menu is tied to the…
  • Page 22
    “The MATH Menus” on page 165. As is usual with all calculators, most of the keys have another function above the key. The hp 39gs and hp 40gs get twice the action from each key by having this second function.
  • Page 23
    ALPHA right of most keys. Pressing SHIFT ALPHA Calculator Tip If you press and hold down the although this doesn’t work for lower case. Many people use this to type in functions by hand rather than going through the views, such as the Notepad, also offer a screen key function that lets you lock either upper or lower case alpha mode.
  • Page 24
    Of course, the Scientific calculator’s idea of scientific notation may not be the same as yours. Since the calculator has no way of displaying powers as superscripts, a result of 3 203 ×10…
  • Page 25
    Moving back to our tour of the keyboard, the next key is key. This is used as an all purpose “I’ve ENTER finished — do your thing!” signal to the calculator. In situations where you woul d normally press the ‘…
  • Page 26
    The negative key Another important key is the hp 39gs and hp 40gs do not treat a negative as being the same as a subtract. If you want to calculate the value of (say) − − − before the 2 and the 9 rather than the subtract key. If you press the subtract key twice, entering ‘subtract, subtract 9’…
  • Page 27
    ‘super delete’ key. For example, if pressing CLEAR would erase one function only in the Calculator Tip Another use for the if you move back into the then pressi in the CLEAR entries.

  • Page 28: Angle And Numeric Settings

    It is critical to your efficient use of the hp 39gs and hp 40gs that you understand how the angle and numeric settings work. For those few who may be upgrading from the original hp 38g released in the mid ‘90s this is particularly important, since the behavior is significantly different.

  • Page 29
    It even resulted in users returning their hp 38g to dealers as being ‘faulty’! Hence the change, which was first made in the hp 39g and hp 40g.

  • Page 30: Memory Management

    One of the major complaints about the original hp 38g was its memory — mainly the lack of it at only 23Kb, but also the inability to easily control or manage it. This problem has been addressed on the hp 39gs and hp 40gs in two ways.

  • Page 31
    Connectivity Kit, or which are supplied to you by your teacher via the infra-red link on an hp 39gs or the cable on an hp 40gs, then you need to bear in mind that most of them have ‘helper’ programs that aid them in performing their tasks.
  • Page 32
    ‘helper’ programs. Calculator Tip Because of the amount of memory available on the hp 39gs & hp 40gs, the Memory View is not one that you will normally need to worry about unless you store a tru y amazing number of Notes. It is probably of more interest to programmers.

  • Page 33: Fractions On The Hp 39Gs And Hp 40Gs

    Most calculators opt for the easy option of switching to a decimal answer in any mixture of fractions and decimals. When making the hp 39gs and hp 40gs HP took a very different approach. Once you select including any decimals.

  • Page 34
    The second point to remember involves the method the hp 39gs and hp 40gs use when converting decimals to fractions, which is basically to generate (internally and unseen by you) a series of continued fractions which are approximations to the decimal entered. The final fractional approximation chosen for display is the first one found which is ‘sufficiently close’…
  • Page 35
    0.666, while adding one more 6 (to take the decimal beyond 4 d.p.) will give the desired result of other words, so long as you understand the approach taken by the hp 39gs and hp 40gs it is capable of producing results which are closer to what was probably intended by the user in entering 0.66666.

  • Page 36: Fraction Setting

    Generally it is not a good idea to go below the default setting of . In fact, a Fraction 4 Fraction 6 A new feature of the hp 39gs and hp 40gs is the setting of in the view. Fraction MODES The results of this new setting can be seen in the image to the right.

  • Page 37: The Home History

    SHIFT CLEAR regularly, since the history uses memory that may be needed for other things, even with the immense amount of user memory the hp 39gs & hp 40gs have. You can number of different lines in building your new expression.

  • Page 38
    . This key will display an expression the way you would write it on the page rather than in the somewhat difficult to read style that is forced on the calculator when it must show the whole expression on one line. This works anywhere the label appears, not just in .

  • Page 39: Storing And Retrieving Memories

    X and then for re-evaluation. Clearly, if the expression is complex, this can be very helpful. Calculator Tip 1. The memory to store the current cursor position in the access it in other places. Values stored in next time you use the 2.

  • Page 40: Referring To Other Aplets From The Home View

    The results shown will, of course, depend on your settings in the view. The reason for the QUOTE(X-2) would tell the calculator to use the value currently stored in memory while tells it to use the symbol. The QUOTE(X-2) available through the menu under Symbolic (see page 181).

  • Page 41: A Brief Introduction To The Math Menu

    menu holds all the functions that are not used often enough to be worth a key of their own. There MATH is a very large supply of functions available, many of them extremely powerful, listed in their own chapter beginning on page 165. When you press the key you will see the pop up screen shown MATH…

  • Page 42: Resetting The Calculator

    Thi s method is provided in case the calculator is locked up to the point that the keyboard no longer responds. On the back of the calculator is a small hole. Poke a paper clip or a pin into this hole and press gently on the switch inside.

  • Page 43
    This type of reset will always cause complete loss of data. If you find that the screen fills with garbage, or if the calculator’s in-built diagnostic routine starts to run, then it is just that you have not released them in the right order.
  • Page 44
    If so, clean them carefully, being careful not to get moisture inside the calculator. Have you recently dropped the calculator or spilled liquid on it? If so, this is not good. It is probably • permanently dead. Did you need a very expensive paperweight? Check the USB and Serial ports at the top of the calculator.

  • Page 45: Summary

    • simply putting the letter in the expression in place of the number. You can easily reboot the calculator if it locks up, generally without loss of memory. Make sure you • know how to do this in case it happens during a test or an examination.

  • Page 46: The Function Aplet

    The Function aplet is probably the one that you will use most of all. It allows you to: graph equations • find intercepts • • find turning points (maxima/minima) • find areas under curves find areas between curves • find gradients •…

  • Page 47
    This is the Notice that the screen title is supplied so that you will know where you are (if you didn’t already). Calculator Tip Pressing ENTER Whenever there is an obvious choice pressing produce the desired effect.
  • Page 48
    One of the easiest ways to set up the axes properly for a function whose shape is not known in advance is to let the calculator suggest a suitable scale using the Auto Scale option in the menu covered on the next VIEWS page.

  • Page 49: Auto Scale

    See “The Expert” chapter beginning on page 62 for more information on how to find good choices for axes. The Auto Scale function is also covered on page 89. key. Use the arrow keys to scroll . The calculator will adjust the y view. If you look PLOT SETUP keys you will see the word setting that removes the ‘thick’…

  • Page 50: The Plot Setup View

    SHIFT PLOT the right. The highlight should be on the first value of XRng. Enter the value -4. Calculator Tip Don’t use the subtract key to enter a negative. You MUST use the negative key labeled subtract. For example, Type in 4 for the other…

  • Page 51
    Simultaneous The first option controls whether each graph is drawn separately (one after the other) or whether they Simult are all drawn at the same time, sweeping from left to right on the screen. My preference is to turn this off. I find that if there are more than two functions defined then drawing them all at the same time can be confusing.

  • Page 52: The Default Axis Settings

    In any of these modes the up/down arrows move the cursor from function to function, while the left/right arrows move along the currently selected function. Calculator Tip Pressing SHIFT directly to the right or left side of the screen.

  • Page 53: The Menu Bar Functions

    In the examples and explanations which follow, the functions and settings used are: Trace is quite a useful tool. The dot next to the word means that it is currently switched on. If yours shows underneath to turn it on. Leave it on for now. Press the left arrow 5 or 6 times to see a similar display to that shown right.

  • Page 54
    Calculator Tip example, jump to a value such as e intersection, then jumping to a value of to that point.
  • Page 55
    The Zoom Sub-menu The next menu key we’ll examine is pops up a new menu, shown right. The list which follows covers the purpose of the first nine options shown right, down to “Set Factors”. The four final options which follow these are also on the and are covered on page 85 as part of the detailed examination of the menu.
  • Page 56
    As you move the cursor to a position at the diagonally opposite corner of a rectangle, the selection box will appear on the screen. Pressing expands the box to fill the screen. You’ll notice that the scale has been disrupted so that the labels are no longer very helpful.

  • Page 57: The Fcn Menu

    In this case that means moving it past the turning point. Calculator Tip If you are working with a function which has asymptotes then make sure the cursor is positioned on the same side of the asymptote as the root.

  • Page 58
    X axis, or the other function are shown right. F2(X) Calculator Tip When you find an intersection or a root the value of the x coordinate is stored in the memory . If you immediately change to the and type See “The Expert”…
  • Page 59
    If you now press again to accept the end point, the hp 39gs or ENTER hp 40gs will calculate the signed area and display the result at the bottom of the screen. Calculator Tip It should be c early understand that although the label at the…
  • Page 60
    As you do the area will be shaded by the calculator. The current position is shown at the bottom of the screen. When you reach the end point you are looking for, press the and the area will be calculated as before.
  • Page 61
    Extremum from the menu. You should find that the cursor will jump to the position of the maximum. Calculator Tip If your graph has asymptotes then make sure that the cursor is positioned on the side of the asymptote containing the extremum before initiating the process.

  • Page 62: The Expert: Working With Functions Effectively

    Part of the answer is to know your function – this is why we still expect you to learn mathematics instead of expecting the calculator to do it all! If you know, for example, that your function is hyperbolic then that immediately gives information about what to expect.

  • Page 63
    Change into the view and scroll through the window from zero to 100. As you do so, take note of the values that the function takes. From the display it seems that the function peaks around y=30 and then declines steadily. Change into the view and enter an x axis of 0 to 100 PLOT SETUP…
  • Page 64
    If the highlight is now positioned on each of these in turn, and the performed. The result is shown in the right hand snapshot. Notice that the calculator is smart enough to realize in not, unfortunately, smart enough to keep track of the implications for the domain, which are that be defined only for non-negative x.
  • Page 65
    These functions can all be graphed but the speed of graphing is slowed if you don’t press internally re-evaluated for each point graphed. The hp 39gs and hp 40gs are fast enough that the result is still satisfactory but if you have an old 39g or 40g they are slowed to the point of being unusable.
  • Page 66
    Differentiating There are different approaches that can be taken to differentiating, most of which are best done in the SYMB The syntax of the differentiation function is: ∂X ( function ) where function is defined in terms of X. The function can be already defined in the in the screen shot above.
  • Page 67
    Algebraic differentiation is most easily handled in the your function as and its derivative as F1(X) Calculator Tip Doing your differentiation in the Function aplet is much easier and offers the additional advantage of being able to graph the two functions. Circular functions There are two issues that influence the graphing of circular functions, both related to the scale chosen.
  • Page 68
    This is shown in the second snapshot above. The reason for this is that when the calculator draws the graph it does so by ‘joining the dots’. For the default scale of -6.5 to 6.5 this is not a problem since the edges of the two half circles at -3 and 3 fall on a pixel. This means that the last segment of the graph plotted extends is from 2.9 to 3 and the circle reaches right down to…
  • Page 69
    0, 0.0923077, 0.1846154… In particular, near x=3 the pixel values are 2.953846 and 3.046154. This means that the calculator can’t draw anything past 2.953846 because the next value doesn’t exist, being outside the circle. This is what causes the gap in the circle. There’s nothing to join to past that last point.
  • Page 70
    Retaining calculated values When you find an extremum or an intersection, the point is remembered until you move the cursor even if it is not actually on a value that would normally be accessible for the scale you have chosen. For example, if you find an intersection and then immediately return to menu and choose Slope, the slope calculated will be for the intersection just found rather than for the nearest pixel point.
  • Page 71
    Automatic vs. Build Your Own Looking at the view you will see an entry called NUM SETUP The alternative to Automatic is the setting of Build Your Own. Under this setting the waiting for you to enter your own values for Typing in the values of (for example): 3 ENTER (-) 2 ENTER 5 ENTER In this situation the function values are being calculated as you input the…
  • Page 72
    Integration: The definite integral using the The situation for integration is very similar to that of differentiation. As with differentiation, the results for algebraic integration are better in the Function aplet. The The syntax of the integration function is: ∫ ( , , a b function name ) where: a and b are the limits of integration…
  • Page 73
    — 1, X ) This is shown above, together with the results of highlighting the answer and pressing result may seem odd but is caused by calculator assuming that other variable and integrating accordingly as a ‘partial integration’. While mathematically correct, this is not what most of us want.
  • Page 74
    ‘+c’! Calculator Tip There are strict limits to what the hp 39gs can integrate. For example, on the hp 39gs if you try to evaluate able to do it.
  • Page 75
    Integration: The definite integral using PLOT variables As was discussed earlier, when you find roots, intersections, extrema or signed areas in the view, the results are stored into variables for PLOT later use. For example, if we use Root to find the x intercept of −…
  • Page 76
    Suppose we want to find the area between f x − 2 and ( ) = x ( ) 0.5x −1 from x = -2 to the first positive intersection of the two g x = graphs. From the hand shaded screenshot shown above right it can be seen that to find the area we need to split it into two sections, with the boundaries being -2 and the two intersections.
  • Page 77
    Piecewise defined functions It is possible to graph piecewise defined functions using the Function aplet, although it involves literally splitting the function into pieces. ⎧ x + 3 ⎪ For example: f x ( ) = ⎨ x ⎪ 3 − x ⎩…
  • Page 78
    ‘Nice’ scales As discussed earlier, the reason for the seemingly strange default scale of -6.5 to 6.5 is to ensure that each dot on the screen is exactly 0.1 apart. There are other scales, basically multiples of these numbers, that also give nice values if you want to along the graph.
  • Page 79
    Use of brackets in functions One problem commonly encountered by new users is misinterpretation of brackets. The hp calculator will correctly interpret F1(X) = X (X+1) but will not understand .
  • Page 80
    ) instead of the true situation of the bottom being roughly twice size of the top. This error is most likely to happen with limits involving power functions as they will overflow for smaller values of x. The hp 40gs can instead evaluate limits algebraically using the CAS (see page 324). An example is shown right to illustrate the results.
  • Page 81
    There are naturally a whole range of numbers which will all round off to the same value of 1.00000000003, so that (for that range of numbers) the expression (1+ 1 / X ) X is equivalent mathematically (on the HP) to 1.00000000003 X . This produces a short section of an exponential graph, which only looks linear because you don’t see enough of it.
  • Page 82
    39gs to numerically evaluate limits. Because of the CAS on the hp 40gs this situation is less likely to be a problem for that model. The solution to all problems of this type is to simply be aware of their existence and to allow for them rather than simply accepting the results shown in view.
  • Page 83
    Gradient at a point as the limit of the slope of a chord The true gradient at a point is available in a number of ways. For example, via the view or via the δ differentiation operator. For students first being introduced to calculus a common task PLOT is to investigate the slope of the chord joining two points as the length of the chord tends towards zero.
  • Page 84
    This method works equally well for complex roots. See page 309 for details on finding roots of real and complex polynomials using the CAS on the hp 40gs. Calculator Tip This trick is particularly helpful if you are working with complex roots.

  • Page 85: The Views Menu

    It may seem odd to devote an entire chapter to what might appear to be an inconsequential key. In fact, however, this button is very useful to the effective use of the calculator, and crucial if you intend to use aplets downloaded from the internet.

  • Page 86
    Plot-Detail Choosing Plot-Detail from the menu splits the screen into two halves and re-plots the graph in each half. The right hand side can now be used to without affecting the left screen. The idea is that you the left screen and the result appears on the right screen. For example a Box zoom shows the result on the right allowing easy comparison of ‘before’…
  • Page 87
    Plot-Table The next item on the menu is Plot-Table. This option plots the VIEWS graph on the right, with the Numeric view on the right half screen. Using the left/right arrow keys moves the cursor in both the graph and the numeric windows.
  • Page 88
    Nice table values What makes this view even more useful is that the table keeps its ‘nice’ scale even while the usual tools are being used. As you can see in the screenshot left, the table is automatically repositioned to show the closest pixel value to that of the extremum found.
  • Page 89
    Auto Scale Auto Scale is an good way to ensure that you get a reasonable picture of the graph if you are not sure in advance of the scale. After using Auto Scale you can then use the It is important to understand two points about how Auto Scale works. 1. Auto Scale uses the X-axis range that is currently chosen in range to include as much of the graph as possible.
  • Page 90
    The example right uses zoom factors of 2×2 with Recenter: Calculator Tip In the graphs above the cursor is at x = . The coordinates at the bottom of the screen should show F1(X)=0 but doesn’t due to the fact that the value of π…

  • Page 91: Downloaded Aplets From The Internet

    The most powerful feature of the hp 39gs & hp 40gs is that you can download aplets and programs from the internet to help you to learn and to do mathematics. Two quick examples of aplets that are available are shown here.

  • Page 92: The Parametric Aplet

    T range to that of the X and Y ranges. Calculator Tips The default setting for TStep is 0.1. In my experience this is too large and can result in graphs that are not sufficiently smooth. It is worth developing the habit of changing it to 0.05…

  • Page 93
    The effect of TRng The X and Y ranges control the lengths of the axes. They determine how much of the function, when drawn, will be visible. See the examples below. Notice that in both cases, followed by an ordered pair giving (X,Y). Unlike &…
  • Page 94
    Calculator Tip Decreasing ƒ graphing process without smoothing the graph any further. 0.05 is generally enough. Since trig functions are often used in parametric equations, one ƒ should always be careful that the angle measure chosen in MODES As usual, the view gives a tabular view of the function.

  • Page 95: The Expert: Vector Functions

    Apart from the normal mathematical and engineering applications of parametric equations, some interesting graphs are available through this aplet. Three quick examples are given below. Example 1 Try exploring variants of the graph of: = 3sin 3t x t = 2sin 4t Example 2 Try varying the values of A and B in the equations: x1(t) = ( A B)cos(t…

  • Page 96: Vectors

    The Parametric aplet can be used to visually display vector motion in one and two dimensions. Example 1 A particle P is moving in a straight line. Its velocity v (in ms ( ) = 2t − 5t + 2t − 3 Enter the motion equation from (v) as X(T) and enter Y(T)=T.

  • Page 97
    Example 2 Two ships are traveling according to the vector motions given below, where time is in hours and distance in kilometers. Illustrate their motion during the first ten hours. ⎛ x  = ⎜ Ship A : ⎝ ⎛ ⎜…

  • Page 98: The Polar Aplet

    This aplet is used to graph functions of the type where the radius r is a function of the angle the Parametric aplet, it is very similar to the Function aplet and so the space devoted to it here is limited mainly to the way it differs.

  • Page 99: The Sequence Aplet

    This aplet is used to deal with sequences, and indirectly series, in both non-recursive form (where T function of n) and implicit/recursive/iterative form (where T Recursive or non-recursive Examples of these types of sequences are: (explicit/non-recursive) T = 3n − 1 … 2, 5,8,11,14,…

  • Page 100
    U1(1) The value of will be ignored in the U1(2) calculator automatically in the Convenient screen keys provided There are a number of very convenient extra buttons provided at the bottom of the screen when entering sequences. Two of these — moves onto the line (see right).
  • Page 101
    view offers more useful features. Change to that view NUM SETUP now and change the value to 10. If you then swap back to NumStep view you will see (as right) that the sequence jumps in steps of 10. In case you don’t realize… ⋅…

  • Page 102: The Expert: Sequences & Series

    Defining a generalized GP and the sum to n terms for it. If we define our GP using memory variables then it becomes far more flexible. The advantage of this method is that you now need only change the values of in the change the sequence.

  • Page 103
    Population type problems are also easily dealt with in this way. For example, “A population of mice numbers 5600 and is growing at a rate of 12.5% per month. How long will it be until it numbers more than one million?” Pressing (above ) clears out the existing expressions, and…
  • Page 104
    Modeling loans Suppose that I need to see the progress of a loan of $10,000 at a compound interest of 5.5% p.a. calculated each quarter, starting Jan. 1 1995, with a quarterly repayment rate of $175. This problem can be modeled by a sequence. To do this, set up as shown above.

  • Page 105: The Solve Aplet

    This aplet will probably rival the Function aplet as your ‘most used’ tool. It solves equations, finds zeros of expressions involving multiple variables, and even involving derivatives and integrals. Equations vs. expressions To ensure that we are using the same terminology, let’s define our terms first. An equation includes an = sign, and can usually be solved: ⎫…

  • Page 106
    Suppose you had the problem: “What acceleration is needed to increase the speed of a car from 16 67 m/s (60kph or ~38mph) to 27 78 m/s (100kph or 60mph) in a distance of 100m (~110 yd)?” ⋅ We’ll assume that you have already entered the equation into Solving for a missing value If you press to change to the…
  • Page 107
    Multiple solutions and the initial guess Our first example was fairly simple because there was only one solution so it did not much matter where we began looking for it. When there is more than one possible answer you are required to supply an initial estimate or guess.
  • Page 108
    (eventually) of 2.4495. The delay is caused by the repeated integrations as the calculator searches for better solutions. It is important to remember that the calculator does not use algebra in Solve – it uses an algorithm which is essentially a more sophisticated version of “guess, check & improve”.
  • Page 109
    Example 4 “Let X be a random variable, representing the heights of basketball players. If X is normally distributed, with the tallest 5% of players.” function which allows you to work with the normal distribution is MATH gives the upper-tailed probability. The syntax is In the Solve aplet, set P=UTPN(M,V,X) Enter the…
  • Page 110
    The result is a quadratic intersecting a line and the reason for this lies in how Solve interprets your equation. When you select by highlighting it, the calculator substitutes the supplied values in the other variables except and graphs the left and right sides of the equation as two separate graphs. This may not always be obvious because the substitution may produce graphs which aren’t visible on the default scale.
  • Page 111
    Now press and you will see the calculator find the nearest solution to your guess. Finish by pressing is valid. See page 106 for more information regarding this. Obviously the next step is to change back to the cursor near to the second intersection and…
  • Page 112
    16 67 When you press there are a number of possible positive responses. They are: Zero — The calculator tried to find a value of • shown above, it is reporting that it succeeded. Sign reversal — This also indicates a correct solution, since normally one expects to find an •…

  • Page 113: The Expert: Examples For Solve

    Easy problems Have you ever thought “There has to be an easier way!” when confronted in a test with something like: x −1 3 − x − = − If you’re sure there is only one answer to a problem, as there is in this case, then solving it is simply a matter of entering the equation into the Harder problems When you know or suspect that there is going to be more than one…

  • Page 114: The Statistics Aplet — Univariate Data

    One of the major strengths of the hp 39gs & hp40gs is the tools they provide for dealing with statistical data. The Statistics aplet and its companion the Inference aplet provide very powerful yet easy to use tools with which to analyze statistical data.

  • Page 115
    As you can see in the screens above right, the calculator gives not only the standard statistics that any scientific calculator would give, but also the minimum and maximum values, the median and the upper and lower quartile cutoffs.
  • Page 116
    Registering columns as ‘in use’ Change into the SYMB view and edit yours so that it looks like the one on the right. You must make sure that checked columns will show in the Note that a screen key is provided to give you the letter having to use the key.
  • Page 117
    If you use the left/right arrows and look at the bottom of the screen you’ll see that the frequencies and ranges are listed. It is probably worth tidying up this graph up a little by going into second page) setting the value to be 5 instead of 1.
  • Page 118
    50 — 59 As with most calculators, the hp 39gs & hp 40gs provide only limited methods to deal with data of this form. Summary statistics can be obtained by entering the mid-points of the intervals as the data values but these will only be approximations, as nature of the data itself does not allow calculation of exact values.
  • Page 119
    variable controls the width of the HWidth columns, with the initial starting value and end value set by . In the frequency HRng table on the previous page the interval width was 10. By setting to 10 in the HWidth view as shown right we can PLOT SETUP produce the graph shown below.

  • Page 120: The Expert: Simulations & Random Numbers

    New columns as functions of old You have already seen the use of one trick when we created a new column view. This can be used to create new columns as functions of any number of others. For example, HOME a set of data that you suspect is exponential could be ‘straightened’…

  • Page 121
    Simulation of a normal die Similarly the expression INT(RANDOM*6+1) die. This means that MAKELIST(INT(RANDOM*6+1),X,1,500,1) simulate 500 rolls of a normal die. We therefore need only store the resulting list into a Statistics aplet column to analyze and graph it. This is shown in the series of screen shots to the right.
  • Page 122
    Its mean turned out to be 2.067 (3 decimal places.). Yours will be different of course — after all, that’s the point of using random numbers! Calculator Tip RANDOM computer. If you use the calculators just out of the box then you wil see the same set of numbers…

  • Page 123: The Statistics Aplet — Bivariate Data

    As mentioned in the Univariate section, one of the major strengths of the hp 39gs & hp 40gs is the tools they provide for dealing with statistical data. Unlike the others, the Statistics aplet begins in the offers easy input and editing of values, while the data and which ones frequencies, as well as for indicating pairing of columns for bivariate data.

  • Page 124
    The which to choose, or you can use the name. Entering data as ordered pairs Calculator Tip You can enter the x enter it as ordered pairs in brackets. i.e. as Returning to the data from the previous page, having entered it into the and Auto Scale to produce a plot (this generally produces very satisfactory results), but let’s have a look at the PLOT SETUP screen instead.
  • Page 125
    The cursor If you now press you will see the result shown right. If you look at PLOT the screen you will see a small cross and, at the bottom of the screen, a listing of . This is telling you that the cross is currently on the S1[1]: 1,5 first point in data set whose value is…
  • Page 126
    User Defined — discussed on the following page. Calculator Tip If you want the value of L calculated automatically for the Logistic model then store a value of zero into known, you can store a positive real value into memory L prior to the curve fit and this will be used.
  • Page 127
    When you set the model to user defined it means that you are expected to supply the complete equation, including the values of any coefficients. The calculator will not calculate the values of any variables you include. For example, if you were to supply an equation of use the values of currently in memory.
  • Page 128
    Calculator Tip If you have trouble seeing the small dots that the calcu ator uses in its scatter-graphs by defau t then you will be interested in the settings circled on the ri set you are using and press below from which you can choose a different mark. The contrast is illustrated below.
  • Page 129
    PLOT SETUP From the view, press the Calculator Tip Make sure that your data set is defined and view before you try to obtain these results. Results are only SETUP given for data sets that are defined and…
  • Page 130
    As long as you press from whatever you had previously chosen to User Defined instead.
  • Page 131
    There are two methods of dealing with this. The first is to use another measure of goodness of fit. The second is to ‘linearize’ the data (discussed on the next page). The calculator provides an alternative measure of goodness of fit via the…
  • Page 132
    The curve which results in the PLOT the equation comes out as Y = ⋅ EXP (0.693147 X ) This “ “ is the calculator’s notation for Y = ⋅ e EXP( which then changes to Y = 2 Checking the key shows that the correlation is unchanged at
    0.9058 even when the new equation clearly fits the data perfectly.

  • Page 133: The Expert: Manipulating Columns & Eqns

    ‘multiply the mean by 3.5’ is not hard. The values shown on the screen can also be retrieved for use on the calculator relatively easily. For example, the set of data below contains a suspected outlier (erroneous value). In this case one might suspect a missing comma between the last two values.

  • Page 134
    People often find it easier to simply type HOME them. You can obtain the summation sign in Calculator Tip The values of the mean and standard deviation retrieved are those of last set calculated If you have more than one set of data in the…
  • Page 135
    Obtaining coefficients from the fit model The function from PREDY MATH This means that you must use the make sure is set to the correct fit model, and also use the SYMB SETUP ensure that your set of data was the last one graphed and that it has had its curve of best fit displayed. Until the curve has been displayed, the coefficients are not available or, worse, might belong to another data set.
  • Page 136
    (unlike the correlation) changes as the independent and dependent variables swap roles and can’t be simply algebraically reversed in this way. It should not be thought that the hp 39gs & hp40gs are unusual in this odd interpretation. Most calculators’ equivalent of the function behave in the same manner.
  • Page 137
    While the value of S will not change if the roles of independent and dependent columns are reversed, the value of on the bottom means that this formula will give a different value if you change which column is regarded as x (independent) and which as y (dependent). This different value for b will also mean a different value for a and these will not be the values which would result from the simple inverse function.
  • Page 138
    Now position the highlight on column screen (shown right) enter SORT SETUP column. This will have the effect of pairing columns then sorting column into ascending order, re-arranging column retain the existing data pairings. When ready, press of this sort are shown right. The final column has not been re-arranged.
  • Page 139
    eg. 2 A population of bacteria is known to follow a growth pattern governed by the equation N = N e colonies of bacteria and also that at t = 10 hours there are 10 000 colonies. i. Find the values of ii.
  • Page 140
    (iii) Find t so that N = 2N The value of is the y intercept of the line of best fit. These values from the curve of best fit are not directly accessible but can be retrieved using the function (see page 135). This is shown in the screen PREDY shown right.

  • Page 141: The Inference Aplet

    This aplet is a very flexible tool for users investigating inference problems. It provides critical values for hypothesis testing and confidence intervals, and does this not only quickly but in a visually helpful format. It will be assumed in the explanations that follow that the reader is familiar with the concepts of hypothesis testing.

  • Page 142
    Change now to the NUM SETUP Rather than entering them by hand, press the more than one copy of the Statistics aplet (under other names) then you will be presented with a list of aplets from which to choose. Once you have chosen the aplet, you need to nominate the column from which to import the data.
  • Page 143
    µ Confidence interval: T-Int 1- In the previous example we found that the evidence of our sample indicated that the mean number of matches in the boxes was not 50. Suppose we now want to know, at the 95% confidence level, within what range of values the true population mean lies.
  • Page 144
    µ µ Hypothesis test: T-Test A farmer compared the 15-day mean weight of two sets of chicks, one group receiving feed supplement A and the other supplement C. Twenty two chicks only one day old were assigned randomly to the two groups. To distinguish between the two groups of eleven, which were caged together to minimize other influences, the heads of the chicks were stained red and purple respectively with a harmless vegetable dye.
  • Page 145
    view shows the critical values. We can see that the probability of obtaining a test student-t value of 3.38 is 0.0015 and this is well below the permitted test level of 1%. view also shows that the vertical line representing the value of PLOT −…
  • Page 146
    The hypotheses are: The sample is drawn from a population whose mean is the same as the standardized population The sample is drawn from a population whose mean is larger than that of the standardized population Change to the view, you can use the NUM SETUP import facility to import the summary statistics from the Statistics aplet.

  • Page 147: The Expert: Chi 2 Tests & Frequency Tables

    We will start with a small digression to look at a simple inferential problem which can be solved using only the Statistics and Solve aplets. Using the Chi test on a frequency table “Four coins are tossed 400 times and the number of heads noted for each toss. The results are shown below.

  • Page 148
    In the menu, Probability section (see page 208), there is a MATH function called (Upper-Tailed Probability Chi-squared) which will UTPC give the critical X probability for a supplied number of degrees of freedom and a value. In this case we would like the value for a given probability so we will enter the formula into the Solve aplet.
  • Page 149
    Bear in mind that if you use this program to create a column containing hundreds or even thousands of values then the program will take a long time to complete. In the case of thousands of values you may even exceed the calculator’s memory in the MAKELIST…

  • Page 150: The Linear Solver Aplet

    As you may be able to see, this is a pair of parallel lines and so has no solution. To see this on the calculator we must first change to the 2×2 view, meaning 2 equations in 2 unknowns. At the bottom of the screen…

  • Page 151: Example 3

    ‘spindle’ of planes in 3-space as shown in the diagram above right. This situation allows infinite solutions anywhere along the line of intersection of the three planes. As you can see right, the calculator has correctly indicated the situation.

  • Page 152: The Triangle Solve Aplet

    This aplet allows you to solve for missing sides and angles in a triangle, either right angled or not. Unlike most aplets it does not have a view but only the dual view discussed below. PLOT When you first start the aplet you will be presented with one of two views.

  • Page 153: Example 2

    Since this is not a right triangle, the first step is to ensure that α β δ the three angles can be used to represent the 115 δ In this case I will use for no other reason than that it is at the top of the illustration, just as it is in the diagram of the triangle.

  • Page 154: Example 3

    Solve the triangle shown right. This is an example of a triangle that has two possible solutions, generally referred to as “The Ambiguous Case”. The calculator will give both possible solutions. Begin by setting the calculator into Change into the…

  • Page 155: The Finance Aplet

    For example, that a dollar invested today can generate more money than the same dollar invested later. The calculator manual contains a lengthier explanation including cash flow diagrams for those who need it, as does any high school or college textbook.

  • Page 156
    (positive) and no payments (withdrawals) are made during the period of the investment. Five years of monthly payments means that is 60. The view on the right shows the problem on the calculator. The button has been pressed to give a future value…
  • Page 157
    Annuities An engineer retires with $650,000 available for investment. She invests the money in a portfolio which is expected to have an average return of 5% per annum. She wants to have the account pay a monthly income to her and asks the accountant to assume that the income must last for 20 years.
  • Page 158
    Amortization The second page of this aplet allows amortization calculations in order to determine the amounts applied towards the principal and interest in a payment or series of payments. Suppose we borrow $20,000 at an interest rate of 6.5% and make monthly payments of $300.

  • Page 159: The Quad Explorer Teaching Aplet

    Rather than being a multi-purpose aplet, this is a teaching aplet specialized to the single use of exploring graphs of quadratics. As such it does not have the normal multi-purpose view. Objectives Using the Quadratic Explorer aplet, the student will investigate the behavior of the graph of y as the values of a, h and v change.

  • Page 160
    ‘step size’ of the movements on the screen. Possible values for the increment are 0.5, 1 and 2. Pressing on the calculator, or the screen key labeled SYMB change the emphasis from the graph to the equation in the right hand half of the screen.
  • Page 161
    If you go to HP’s website you can download a worksheet for use with your class. It takes the student through the process of deducing the effects of each of the coefficients on the shape of the graph, requiring them to…

  • Page 162: The Trig Explorer Teaching Aplet

    Rather than being a multi-purpose aplet like most of the others covered so far, this is a teaching aplet specialized to the single use of exploring the graphs of trigonometric functions. As such it does not have the normal SYMB PLOT have meanings but not the normal ones.

  • Page 163
    The operation of the two modes is summarized below. The PLOT mode The underlying concept in PLOT equation. The user has control of the graph via two manipulation points (see above and below) and any changes to the graph are reflected in the equation at the top of the screen.
  • Page 164
    The c coefficient is shown as a multiple of coefficient is highlighted and can be changed using the up/down arrow keys in increments of 0.1 for the coefficients a, b and d. π The default increment for c is π π…

  • Page 165: The Math Menus

    ‘unknown user function’ error. Since they are not relevant for both calculators, the CAS commands are covered in the section on the CAS for the hp 40gs. key. MATH…

  • Page 166: Accessing The Math Menu Commands

    The mechanics of accessing the MATH illustrate the process using the Polynomial function an extremely useful one. Change into the key. MATH When you do you will see the screen on the right. The menu always first appears with the Real functions highlighted. We could use the arrow keys to scroll down to the Polynomial functions but it is far faster to simply press the key labeled with the letter ‘…

  • Page 167
    39gs & hp 40gs. If you need the higher level commands then consult the manual.

  • Page 168: The Phys Menu Commands

    menu is divided up into three sections by learning area. PHYS These sections are: Chemistry • • Physics • Quantum Physics The contents are simply the numerical values of various physical constants that are useful in calculations and formulae. Chemistry Avogadro’s number •…

  • Page 169: The Math Menu Commands

    — functions used in probability calculations. Some of these functions have little application at school level and will not be covered here. Others will be covered to varying depths. Anyone needing those not covered will find them in the manual that comes with the calculator.

  • Page 170: The ‘Real’ Group Of Functions

    ‘ ’ ‘ ’ CEILING(<num>) This is a ‘rounding’ function but different in that it always rounds up to the integer above. Mainly of interest to programmers. Eg. CEILING(3.2) = 33 CEILING(32.99) CEILING((12+ 6)/7) Note: = -2 not -3. The CEILING(-2.56) to the next integer above, which is -2.

  • Page 171
    FNROOT(<expression>,<variable>,<guess>) This function is like a mini version of the Solve aplet. If you feed it an algebraic expression and an initial guess it will start from your guess and find the value which makes the expression zero. Don’t bother. It’s a lot easier to use the Solve aplet.
  • Page 172
    This function works with time and angles. It converts degrees, minutes and seconds to degrees, and also hours, minutes and seconds to decimal time. The calculator can convert a value such as the form 45.2317 and then use the ′ ′′…
  • Page 173
    INT(<num>) This function is related to the FLOOR those two, which consistently move down or up respectively, the function simply drops the fractional part of the number. Eg. INT(3.786) = -5 INT(-5.84) See also: FLOOR CEILING ROUND MANT(<num>) This function returns the mantissa (numerical part) of the number you feed it when transformed into scientific notation.
  • Page 174
    MIN(num1,num2) As with , this function is used mainly by programmers. It returns the smaller of the two numbers entered. Eg. MIN(3,5) See also: <num> MOD <divisor> For those not familiar with modulo arithmetic, it will suffice to say that this function gives you the remainder when one number is divided by another.
  • Page 175
    %CHANGE(<num1>,<num2>) This function calculates the percentage change moving from the formula . It can be used to calculate (for example) 100(Y-X)/X percentage profit and loss. Eg. I buy a fridge for $400 and sell it for $440. What is my profit as a percentage? Use: %CHANGE(400,440) I sell a toy for $5.95 that normally sells for $6.50…
  • Page 176
    ROUND(<num>,<dec.pts>) This function rounds off a supplied number to the specified number of decimal places (d.p.). Eg. Round 66.65 to 1 d.p. Use: ROUND(66.65,1) Round 34.56784 to 2 d.p. Use: ROUND(34.56784,2) This function is also capable of rounding off to a specified number of significant figures (s.f.).
  • Page 177
    TRUNCATE(<num>) This function operates similarly to the the extra digits instead of rounding up or down. It is somewhat similar in effect to the function but the FLOOR any number of decimal places or significant figures instead of always dropping to the nearest lower integer value. TRUNCATE(3405.6375,-6) TRUNCATE(32.889,1) See also:…

  • Page 178: The ‘Stat-Two’ Group Of Functions

    If these conditions are satisfied then the function produce a predicted y (dependent) value for the x (indep.) value of Calculator Tip The line of best fit used in the function last plotted. It is up to you to ensure that this is in fact the one you want…

  • Page 179: The ‘Symbolic’ Group Of Functions

    = sign is simply used in exactly the way that you would expect it to be, mainly in the Solve aplet. It’s easier to obtain the = sign directly from the keyboard. The reason that it is found in the calculator, the hp 38g, had less keys on the keyboard and had no room for it. It was added in later models. ISOLATE(<expression>,<var-name>) This function will rearrange a formula so that its subject is another variable.

  • Page 180
    − ± − 4 ac to give both ’ formal variable to represent the where were memory values, in order to tell the calculator that the active variable was ± = 5 or −1 tools. ± 4 − 6…
  • Page 181
    If you are fortunate enough to have an hp 40gs rather than an hp 39gs then you can do all this far more easily in the CAS.

  • Page 182: The ‘Tests’ Group Of Functions

    These two groups of functions cover the Trigonometry functions, plus others, which are less commonly used and which have consequently not been given their own keys on the face of the calculator. Use them in the same way as the normal…

  • Page 183
    Some further functions are available in the Hyperbolic group of functions. They are duplicates of functions available on the face of the calculator but give more accurate answers. They would primarily be of use to those people, such as architects and engineers, for whom high accuracy is paramount. These are: EXP(<num>)

  • Page 184: The ‘Calculus’ Group Of Functions

    LNP1(<num>) As in the previous function, this is supplied to supplement the function and gives a more accurate value when x is near zero. Again, this is not something which would normally be of concern at school level. ‘ ’ ‘…

  • Page 185
    The <expression> supplied is approximated with respect to <var_name> by terms of a polynomial up to <num> power. The screen shot on the right shows the calculator deriving the Taylor polynomial for sin(x) up to the 7 approximated by taking terms from the polynomial: sin( x) = −…

  • Page 186: The ‘Complex’ Group Of Functions

    ‘ ’ Complex numbers on the hp 39gs & hp 40gs can be entered in either of two ways. Firstly, in the same way as they are commonly written in mathematical workings: a + bi. Secondly, as an ordered pair: (a,b).

  • Page 187
    In addition to the trig functions, there are other functions that take complex arguments. ABS(<real>) or ABS(<complex>) The absolute function, which is found on the keyboard above the left bracket key, returns the absolute value of a real number. returns a value of 3. ABS(-3) When you use the absolute function on a complex number a + bi it returns the magnitude of the complex number as…
  • Page 188
    As mentioned earlier, a very useful function ( on the keyboard as the function for SHIFT number in (r, ) form as shown right, then the calculator will display it in θ θ the form r cos( ) + r sin( ) from, and as an (a,b) ordered pair.

  • Page 189: The ‘Constant’ Group Of Functions

    , are far more easily obtained via the keyboard. π The first, , is available via a key on the face of the calculator above the 3 key. The other two , easily obtained as lowercase letters via the ‘…

  • Page 190: The ‘List’ Group Of Functions

    ‘ ’ ‘ ’ CONCAT(< list1>, <list2>) This function concatenates two lists — appending one on to the end of the other in the order that you specify. Lists must be enclosed in curly brackets unless list variables are used. L 1={2,5,-2,10,3.75} L2={1,2,3,4,5} = {2,5,-2,10,3.75,1,2,3,4,5}…

  • Page 191
    Eg. 1 MAKELIST( X2,X,1,10,2) L1 produces { 1, 9, 25, 49, 81 } as X goes from 1 to 3 to 5 to … and also stores the result into Eg. 2 MAKELIST(RANDOM,X,1,10,1) in this case serves only as a counter since it does not appear in the expression. Eg.
  • Page 192
    SIZE(<list>) or SIZE(<matrix>) This function returns the size of the list or matrix specified. Since normal users would probably know anyway, and could find out easily via the list catalog, this is clearly another of those functions which are of more use to programmers (who won’t know when they write their program just how long the list you will ask it to deal with will be when you eventually run the program).

  • Page 193: The ‘Loop’ Group Of Functions

    ‘ ’ ‘ ’ This is a group of functions that may be of use for students studying discrete functions and sequences but are primarily of use to programmers. ITERATE(<expression>,<var_name>,<num>,<num>) This function evaluates an expression in terms of a variable, starting with a supplied initial value, for a specified number of iterations.

  • Page 194
    ‘i’, ‘j’ & ‘k’ are simply the letters traditionally used in mathematical problems involving summation. When working in the hp 40gs CAS it is not possible to use ‘i’ because the CAS will interpret it as i rather than as a variable name.

  • Page 195: The ‘Matrix’ Group Of Functions

    ‘ ’ ‘ ’ This group of functions is provided to deal with matrices. The scope of functions & abilities covered in this group is in fact vastly greater than would be required by the average high school student or teacher. In many cases supplying an explanation in more detail than the manual of what the function is used for would occupy many pages to no real useful gain.

  • Page 196
    DET(<matrix>) This function finds the determinant of a square matrix. See page 213 for an example of its use in finding an inverse matrix. ⎡ 2 3 ⎤ A = ⎢ then find det(A). ⎥ ⎣ − 1 5 ⎦ Ans: det (A) = 2×5-3x(-1) = 13…
  • Page 197
    Some people write the inverse matrix as a fraction (one over the determinant) multiplied by a matrix, so as to avoid decimals and fractions within the inverse matrix. The calculator does not do this. If you want the matrix with the determinant factored out,…
  • Page 198
    LSQ(<matrix1>,<matrix2>) The least squares function displays the minimum norm least squares matrix (or vector). LU(<matrix>) This Decomposition function is similar to the into three matrices, returning them in the form of a list variable. {[[lower triangular]],[[upper triangular]],[[permutation]]} The upper triangular has ones on its diagonal. The matrices can be separated in the same method outlined for the function.
  • Page 199
    ROWNORM(<matrix>) Finds the row norm of a matrix: the maximum, over all rows contained in the matrix, of the absolute values of the sum of the elements in each row. ⎡ ⎢ Eg. For the matrix M 1 ⎢ ⎢ ⎣…
  • Page 200
    For example, suppose we use the system of equations below, in which the third equation is a linear combination of the first two but the constant is not consistent with this — ie no solution. If we solve this in the same way as before, the matrix ⎧…
  • Page 201
    SVD(<matrix>) This function performs a Singular Value Decomposition on an m × n matrix. The result is two matrices and a vector: {[[m × m square orthogonal]],[[n × n square orthogonal]],[real]}. SVL(<matrix>) This function returns a vector containing the singular values of the supplied matrix. TRACE(<matrix>) This function finds the trace of a square matrix.

  • Page 202: The ‘Polynomial’ Group Of Functions

    ‘ ’ ‘ ’ This group of functions is provided to manipulate polynomials. We will use the function shown right to illustrate some of the tools in the Polynomial group. Its equation is: ( ) = − 2)(x + 3)(x −1) = POLYCOEF([root1,root2,…]) This function returns the coefficients of a polynomial with roots x x x vector form means in square brackets.

  • Page 203
    POLYFORM(<expression>,<var_name>) This is a very powerful and useful polynomial function. It allows algebraic manipulation and expansion of an expression into a polynomial. The expected parameters for the function are firstly the expression to be expanded, and secondly the variable which is to be the subject of the resulting polynomial.
  • Page 204
    As you can see in the screen shot, the roots of 2, -3 and 1 have been correctly found. See page 309 for details on finding roots of real and complex polynomials using the CAS on the hp 40gs. − 7x + 6 we can enter the coefficients as…

  • Page 205: The ‘Probability’ Group Of Functions

    ‘ ’ ‘ ’ This group of functions is provided to manipulate and evaluate probabilities and probability distribution functions (p.d.f.’s). COMB(<n>,<r>) This function gives the value of Eg. Find the probability of choosing 2 men and 3 women for a committee of 5 people from a pool of 6 men and 5 women.

  • Page 206
    It is important to realize that the values produced by the Inside the calculator is a mathematical procedure (an algorithm) which uses a ‘seed’ number to produce them. Unfortunately, when taken straight out of the box, two calculators will produce exactly the same sequence of “random”…
  • Page 207
    UTPN(<mean>,<variance>,<value>) This function, the ‘Upper-Tail Probability (Normal)’, gives the probability that a normal random variable is greater than or equal to the value supplied. Note that the variance must be supplied, NOT the standard deviation. Eg. 1. Find the probability that a randomly chosen individual is more than 2 meters tall if the population has a mean height of 1.87m and a standard deviation of 10.4cm σ…
  • Page 208
    SYMB key is provided in the SYMB Final answer… 47.06% and 82.94% are the cut-offs. Calculator Tip The normal order for the arguments in the UTPN(mean, variance, value) probability. probability instead. Fortunately the function can easily be adapted for this.

  • Page 209: Working With Matrices

    The hp 39gs & hp 40gs deal very well with matrices. They offer many powerful tools as well as a special with full editing facilities. MATRIX Catalog The MATRIX Catalog is entered by pressing (located above MATRIX Catalog MATRIX the 4). It allows storage of ten matrices ( ) which can be M1,M2,..M9,M0…

  • Page 210
    Enter the numbers 4, 5 and 6 and you will find that the calculator automatically drops down to row three without the need to use the down arrow key again, since it now knows how many columns the matrix is to contain.
  • Page 211
    The method for doing this on the calculator is as follows… Step 1. Enter the MATRIX Catalogue matrices if desirable.
  • Page 212
    The third option is actually identical to the first. The original hp 38g only had the later models.
  • Page 213
    Finding an inverse matrix Eg. 2 Find the inverse matrix The first step is to store the matrix A into inverse into you will find, depending on the determinant, that the result is probably a collection of decimal values (see right). This answer is correct and we could stop there.
  • Page 214
    This substitutes to give a solution of: On the calculator, the functions magnitude respectively, when fed with vectors. The calculator writes vectors as row matrices. a = (3, 4) For example would be written as The calculations are shown in the two screen shots on the right.

  • Page 215: Working With Lists

    A list in the hp 39gs or hp 40gs is the equivalent of a mathematical set. As with a set, it is written as numbers separated by commas and enclosed with curly brackets. {2,5,-2,10,3.75} The list variables Using the view these lists can be stored in special list variables.

  • Page 216
    Lists can be sent from one calculator to another using the infra-red link on the hp 39gs or using the supplied mini-serial cable with the hp 40gs. The procedure is the same as that for sending aplets from one calculator…

  • Page 217: Working With Notes & The Notepad

    The hp 39gs & hp 40gs provide access to Notes which can either be attached to an aplet or exist independ­ ently. The notes belonging to the standard aplets are blank unless you add to them, but copies you transfer from a computer or another calculator may have had notes added to them as instructions on how to use them.

  • Page 218
    An example is shown above right of a sketch from one of the aplets available from HP’s web site called ‘Periodic’. If you installed this aplet on your calculator then this sketch could be viewed via the…

  • Page 219: Independent Notes And The Notepad Catalog

    These notes can be sent to (received from) another calculator or from a computer via the 39gs this is done via the infra-red link. On the hp 40gs there is no infra-red capacity and the transfer is done via the supplied mini-serial cable shown right. More information on cables and their use can be found on page 237.

  • Page 220: Creating A Note

    ) and you will see the an existing Notes to or from another calculator (or a computer). A key will delete all Notes in the catalog. SHIFT CLEAR menu. However, if the CHARS key.

  • Page 221
    The original hp 38g only had the function INVERSE(…) and the added for convenience sake in the hp 39g, released in 2000. To do this the creators had to borrow one of the existing unused characters, the…

  • Page 222: Working With Sketches

    Facilities provided in the Sketch view are good for a bit of fun, but very primitive when you try to do anything at all complex. This is not meant as a criticism of the calculator. It does an extremely good job at what it was designed for — working with numbers — but it was never designed to compete with a computer drawing package.

  • Page 223: The Draw Menu

    There are two font sizes available via the size being large. If you press the . Although there is no apparent change when you are typing in the text, the font will become smaller when it appears in the window. Only uppercase is available in this small font.

  • Page 224
    CIRCLE The circle command is similar to the box command. You should position the cursor at the center of the proposed circle. Pressing the cursor outwards from the center, forming a radius. As you do so you will see a small arc appear, giving you an indication of the curvature of the circle.
  • Page 225
    If you’re intending to do this to produce a set of ‘cheat notes’ for your next test or exam, you would do better to spend the time studying! Calculator Tip The screen capture facility demonstrated here can be used to capture…

  • Page 226: Copying & Creating Aplets On The Calculator

    No programming is necessarily required at the lowest level and so, unless you want to learn about the programming language of the hp 39gs & hp 40gs, there is no reason to worry about it unless you want to produce highly enhanced aplets.

  • Page 227: Different Models Use Different Methods To Communicate

    39gs. The mini-serial port is still present though because it is anticipated that it may be used in the future to connect to data-loggers and other possible peripherals.

  • Page 228: Sending/Receiving Via The Infra-Red Link Or Cable

    Any aplet, note, program, matrix or list can be copied from one calculator to another via the infra-red link at the top of the calculator on an hp 39gs or via the supplied cable on an hp 40gs. A sketch can be transferred by sending the aplet to which it belongs.

  • Page 229
    The process is essentially: • Press the key on the sending calculator and the • Choose the option for your particular calculator. On an hp 39gs this will be “HP39 (IrDA)” and on an hp 40gs it will be “HP39/40 (Ser)”. • Press on both calculators and the transmission process will begin.

  • Page 230: Creating A Copy Of A Standard Aplet

    In either of those two cases, the solution is to make a copy of the aplet concerned. You can make as many copies of any of the standard aplets as you wish. The only limit is the calculator’s memory. Depending on what you put in them the calculator’s memory is normally sufficient to store anything from 30 to 100 aplets.

  • Page 231
    This saved aplet can now be downloaded to all the students’ calculators using the infra-red link in the case of an hp 39gs or using the cable in the case of the hp 40gs. This ensures that each student has exactly the required data sets, with views pre-set to the teacher’s needs.

  • Page 232: Some Examples Of Saved Aplets

    The Triangles aplet In the view, the Solve aplet and APLET name of “Triangles”. Now The theta character can be obtained from the keyboard on the zero button using . Change into the ALPHA use another mode). By changing into the Some users choose to use the letter The Prob.

  • Page 233
    Use it by substituting whatever function is in use for the one currently entered. As this formula involves the integration function, each use of the solve process will require the calculator to perform multiple integrations. Because of this the solving process will be relatively slow.
  • Page 234
    Equation This equation gives P a ≤ ≤ calculate P x a just find P x a ≥ Equations Finally, equations concern the Normal distribution, with giving P a allowing calculation of questions such as “what distance either side of the ≤…
  • Page 235
    So… how does this aplet work? The formulas in the view form the key to the process by allowing SYMB the calculator to fetch values from the matrices, with the values fetched being determined by the settings in the For example, as runs from…
  • Page 236
    TRange values in the use a shapes that is highly symmetrical, like a square, as it makes it harder to recognize transformations. Calculator Tip It is probably faster to have the class set it up themselves instead of sending it via cable or infra-red.

  • Page 237: Storing Aplets & Notes To The Pc

    PC and is safe from accidental loss. In addition to this, one of the nice features of the hp 39gs and hp 40gs is that when you switch it on it resumes operation in exactly the state you left it. Not all calculators will do this and it is clearly highly desirable but it also has its downside.

  • Page 238: Software Is Required To Link To A Pc

    The connectivity software for the hp 39gs and hp 40gs was being rewritten at the time when this book was being published. The version on the CD which came with your calculator may not be the most recent version. For the latest version of the software for your calculator you should consult Hewlett Packard’s web site (http://www.hp.com/calculators) or the author’s website at…

  • Page 239: Sending From Calculator To Pc

    This mini-USB cable is used for communication with a PC and the same cable is used for both the hp 39gs and the hp 40gs via the USB cable on the PC.

  • Page 240
    Before beginning you should install the Connectivity software. This can be found on the CD that came with your calculator but it is best to download a fresh version from the web so as to obtain the most recent version (see page 237).
  • Page 241
    PC. This can be one of the standard ones or one that you have saved under another name. Press the button on the calculator to see the view shown right, which lists the choices on an hp 39gs. On an hp 40gs the “ HP39+ (IrDA) Ensure that the “…
  • Page 242
    The reason for the contraction is that the original hp 38g from which the hp 39gs and hp 40gs are derived was released for an earlier version of Windows that did not allow long filenames. This has never been changed on later models.
  • Page 243
    The HP HOME view (at http://www.hphomeview.com). Normally you do not need to worry about this, since the calculator knows they belong with the aplet and will automatically transmit them with it. This can greatly increase the transmission time and it is important that you don’t interrupt the process early.

  • Page 244: Receiving From Pc To Calculator

    The process of retrieving objects that have been stored to the PC is almost identical to that of sending them in the first place. Connect the calculator, run the software and choose the folder in which the aplets, notes, or other objects are stored. Then press the button and again choose the “…

  • Page 245: Aplets From The Internet

    The Hewlett-Packard site is one possible starting point and can be found at http://www.hp.com/calculators. From that point you can follow the links to collections of material for the hp 39gs and/or hp 40gs as well as to software and utilities. Other sites can be found that have been created by enthusiasts. One of the most extensive is that of the author, The HP HOME view, found at http://www.hphomeview.com.

  • Page 246
    You may notice separate download icons for the 38G and for the 39G, 40G and 39g+ with no mention of the new hp 39gs and hp 40gs. This will change as the sites update the contents to reflect the new models.
  • Page 247
    Having downloaded an aplet from the web to the computer, we now have the task of transferring it from the computer to the calculator via the HP Connectivity Software. To do this, of course, you need the mini-USB cable that came with your calculator (see page 239) plus some software.
  • Page 248
    The process of transferring the newly downloaded aplet from the PC to the calculator is exactly the same as it is for an aplet which you have saved to the PC yourself. The instructions for this can be found on page 244.

  • Page 249: Using Downloaded Aplets

    It is worth reading the information contained in Appendix B: Teaching or Learning Calculus on page 314. key on your hp 39gs or hp 40gs then menu VIEWS . When you delete the…

  • Page 250: Deleting Downloaded Aplets From The Calculator

    “Coin Tossing”. .COIN Simply position the highlight on each of the programs in turn and press key. If your calculator only contains one aplet with programs linked, then it is faster to use SHIFT CLEAR once.

  • Page 251: Capturing Screens Using The Connectivity Kit

    Once the image is captured it can be copied to the clipboard and pasted into another application. The software also allows it to be saved as a .BMP image file. All the images of calculator screens in this book were captured in this way.

  • Page 252: Editing Notes Using The Connectivity Software

    Software will also allow you to edit it once it is on the PC. On previous models this was done using a separate piece of software called the ADK but with the release of new software with the hp 39gs and hp 40gs this ability was integrated into one program.

  • Page 253
    The changes you make are automatically saved as you type, just as they are on the calculator itself. When you’ve finished editing you can use the Connectivity Software to transfer the result back to the calculator.
  • Page 254
    The names used to record the Notes on the PC are not terribly imaginative, as can be seen to the right. You must not change these names! files HP39DIR.CUR and HP39DIR.000 and the calculator will expect to find them under those names. Highlighting an existing Note and pressing the Copy button will produce a copy of the existing Note with the title “Copy of …………”.

  • Page 255: Programming The Hp 39Gs & Hp 40Gs

    Although you can choose to simply create programs, it should be remembered that the whole point of working on the hp 39gs or hp 40gs is to use aplets. Working with an aplet means that you inherit its abilities such as…

  • Page 256
    To use this software you must be able to send to and receive from a computer, and for models before the hp 39gs & hp 40gs this means buying a cable. For the hp 39gs & hp 40gs the mini-USB cable required is included in the package with the calculator.

  • Page 257: Planning The Views Menu

    When the ‘helper’ program terminates the calculator drops into whatever view you as the designer choose. For example, a ‘helper’ program might set up axes based on the data entered and then drop the user into the view.

  • Page 258
    Another example of an existing aplet is shown right. It is called “Tangent Lines” and it draws a tangent line onto a graph and then lets the user move it around, displaying the gradient as it does so. This aplet has the Function aplet as its parent because of the need to graph functions.

  • Page 259: The Setviews Command

    Part of the job of the ‘helper’…

  • Page 260
    Special entries in the SETVIEWS command In addition to the lines which form the menu for your aplet, there are some special entries which are treated differently. If you include entries called “Start” or “Reset”, then the ‘helper’ programs associated with those •…
  • Page 261
    Shown below is a program which illustrates this for an aplet with Function as its parent… SETVIEWS The behaviour will be: • Choose “ ” Opt. 1 • Choose “ ” Plot-Table • Choose “ ” Auto Scale • Choose “ ”…

  • Page 262: Example Aplet #1 — Displaying Info

    This example uses the SETVIEWS totally useless) aplet, which illustrates a few of the concepts useful in programming the hp 39gs or hp 40gs. We’ll call it the ‘Message’ aplet and create it as a child of the Function aplet. Change into the…

  • Page 263
    ERASE a message on lines 4 DISP and 5 of the screen. The calculator then s waiting learning a new language! FREEZE for a key to be pressed. .MSG.FN This is the most complex of the programs.
  • Page 264
    Having created all of the programs that make up the aplet ‘Message’, we can now run the program , severing the aplet’s link to its current .MSG.SV aplet, and substituting this new menu. Before you do this, check that you are still in the correct aplet. Press key and check that the title at the top still says “…
  • Page 265
    The next option in the menu is ‘Input value’. Choosing this option will create an input screen. The statement controlling this was: INPUT N; «MY TITLE»; «Please enter N..»; «Do as you’re told.»; 20: Examine the snapshot on the right and notice the connection between the various parts of the statement and their effect.
  • Page 266
    The final option is ‘Show function’. The program this runs is a little more complex than the ones shown so far and illustrates a useful technique. The line: ‘((X+2)^3+4)/(X-2)’ x + 2 stores the expression Notice the way the function is in single quotes so that the algebraic expression itself is used rather than its value when evaluated using the current contents of memory X.
  • Page 267
    Finally the commands commands are used to draw an oblique line across the screen and a LINE box near the center. LINE Xmin; Ymin; Xmax; Ymax: BOX 3; 3; -2; -2: Notice the use of Xmin Xmax maximum limits of the current PLOT appear the same even if the screen were to be re-sized in the hand, would change size if the screen size were to be changed in…

  • Page 268: Example Aplet #2 — The Transformer Aplet

    Xmin and then changes it back. In the original version the user had to press draw. This technique fools the calculator into thinking that view. PLOT SETUP and therefore forces a re­ draw without the need to press a key. It also re- ed and ready for use.

  • Page 269
    .TRANSF.SHAPE (continued…) Since the default contents of any variable is zero and there is no zero’th option on a list this means a program bug waiting to happen unless you preset the value. Options 1 and 2 load preset matrices while option 3 allows the user to edit their own.

  • Page 270: Designing Aplets On A Pc

    Connectivity Kit” but this too may have changed. Look for the latest version on HPs website or on The HP HOME view (at http://www.hphomeview.com). In the next example we will use The Connectivity Kit to create small program and then to re-create the same ‘Transformer’…

  • Page 271
    So… if there is a “Save” button or an option on the File menu of “Save” then use this now to save your code. If there’s no such option then go on to the next step. Change back to the Folders/Transfers and download your program to the calculator for use. The result is shown in operation below.

  • Page 272: Example Aplet #3 — Transformer Revisited

    – – Run the Connectivity Kit and use the File menu to create a new folder called “Transformer”, and highlight that folder to hold your aplet. In my experience it is a very good idea to store each aplet in a separate folder but this is not strictly necessary.

  • Page 273
    As you enter each triplet, the boxes will blank ready for the next menu item to be added. You can construct the entire menu at one time OR you can edit the code for the program before proceeding. In many ways it is better to design the entire menu structure before beginning to code but that may not be the way you prefer to work.

  • Page 274: Example Aplet #4 — The Linear Explorer Aplet

    As can be seen in the example below, CHARS there is no attempt to place line breaks at the end of words. The view on the calculator will certainly not match that on the PC so why bother?

  • Page 275
    If you have done this correctly then your menu have three entries VIEWS shown right when it is transferred to the calculator. The text for the ‘helper programs’ associated with each menu entry is shown below:…
  • Page 276
    It will probably be easier to understand how the aplet works if you see it in action first so you may wish to download the aplet from The HP HOME View The first option on the menu plots a set of axes and must be VIEWS chosen first.
  • Page 277
    The second and third lines insert a function into done, of course, if the parent aplet is parent is another aplet then the code will still execute but the function will be inserted into the real Function The reason for inserting this particular function is that we need a function when the axes are plotted or the normal error message will be displayed (see above right).
  • Page 278
    Still referring to the code on the previous page, you will see that it refers to . The sketches in the PageNum calculator’s view are numbered 1, 2, 3…etc. Sketch number 1 is always present but after that only SKETCH sketches that have been created are available and the program will crash if you try to access one that does not exist.
  • Page 279
    Any labels off the edge of the screen will be ignored by the calculator so you don’t need to check for that in the program. This is a very nice feature of the HP.
  • Page 280
    This aplet illustrates most of the commonly used programming techniques. If you would like to gain experience then I suggest that you do as I did when I first began programming the HP — download aplets and pull them apart to see how they work.

  • Page 281: Alternatives To Hp Basic Programming

    HP Basic might take 50 lines or even more in sRPL. However it is quite likely that those 50 lines will execute fifty to sixty times as fast as the five lines of HP Basic. The drawback is that they will also have a much greater risk of containing a bug –…

  • Page 282
    The HPG-CC Programming language The hp 39g+ was the first of this family of calculators which didn’t use the Saturn 5 as its ROM chip. Up to that point the HP38G, HP39G & HP40G had all shared the same chip along with others in the HP48 family.
  • Page 283
    At the time of writing this information in early 2006, HPG-CC had reached Version 2.0 but subsequent to this version the support for the hp 39g+, hp 39gs & hp 40gs had been discontinued. This is not to say that it won’t work on those calculators, just that the developers are no longer fixing bugs discovered by…

  • Page 284: Flash Rom

    In normal ROM the contents of the chip are burned in at the factory and can’t be altered. The difference with the hp 39gs & hp 40gs is that the ROM used is a ‘flash’ ROM. This is a special chip where, although the contents are preserved when the batteries are removed or a reset is performed, the contents are not frozen permanently.

  • Page 285
    40gs. The operating system of an hp 40gs is quite a bit larger than that of the hp 39gs due to the inclusion of the CAS. It will not fit onto the ROM chip of an hp 39gs and any attempt to try will result in an expensive paperweight.

  • Page 286: Programming Commands

    As was explained in a previous chapter, the hp 39gs and hp 40gs are supplied with a simple and easy to use programming language called HP Basic. All programming commands can by typed in by hand but, as with the commands, can also be obtained from a menu.

  • Page 287: The Branch Commands

    IF <test> THEN <true clause> [ELSE <false clause>] END Note the need for a double sign when comparing equalities. Any number of statements can be placed in the true and false sections. Enclosing brackets are not required, as they are in some other languages.

  • Page 288
    RUN <program name> This command runs the program named, with execution resuming in the calling program afterwards. If a particular piece of code is used repeatedly then this can be used to reduce memory use by placing the code in a separate program and calling it from different locations. See command for information on how to link a program to SETVIEWS an aplet when it does not appear on the primary menu.

  • Page 289: The Drawing Commands

    ARC <x-center>;<y-center>;<radius>;<start angle>;<end angle> This command draws an arc on the screen. It uses the current values in the PLOT SETUP coordinates and the settings in the the angle format. This command is unfortunately quite slow. BOX <x >;<y >;<x >;<y >…

  • Page 290
    This means that it can be used to erase previously drawn lines. If you would like to see this command in action, download the aplet called “Sine Define” from the author’s website The HP HOME view (at http://www.hphomeview.com). This aplet contains extensive use of this command.

  • Page 291: The Graphics Commands

    See the chapter “Programming the hp 39gs & hp 40gs” beginning on page 255 for examples illustrating some of the graphics commands that I have used regularly. Consult the manual for more. FOR <variable> = <start value> TO <end value> [STEP <increment>] <statements> END For those familiar with the Basic language in other forms, this is a standard FOR…NEXT command, except without the ‘NEXT’.

  • Page 292: The Matrix Commands

    There is no situation in which a GOTO statement cannot be replaced by one of the loops or conditional branches available in the HP Basic language. EDITMAT <matrix var> This command pops up a window in which the user can edit or input a matrix with an bottom.

  • Page 293: The Print Commands

    39g family. This printer was originally designed for the first calculator in this family, the hp 38g, released in 1995. Very few of them sold because it was far easier to simply use the connectivity software to capture screens and images and then just paste them into a document on the PC.

  • Page 294: The Prompt Commands

    BEEP <frequency>;<duration> This will use the piezo crystal in the calculator to create a sound of the specified frequency for the specified duration (in seconds). The resulting frequency is not terribly accurate, varying by up to 5% from one calculator to the next and depending also on the temperature. If you want accuracy then use a piano! The volume is also not very loud because of concerns with interruptions to tests and examinations.

  • Page 295
    DISPXY <xpos>;<ypos>;<font>;<expression> This command displays the text/object/result contained in <expression> at the screen position specified using the font specified. An extensive example can be found in the chapter “Programming the hp 39g & hp 40gs” on page 274. The xpos and ypos values refer to the top left corner of the text when displayed.
  • Page 296
    DISPTIME This command pops up a box displaying the calculator’s internal time and date. These can be set by storing values to the variables Time . Suppose the current time is 3:46:29 pm on the 1 of December, Date 1998 then you would store 15.4629 to and 12.011998 to…
  • Page 297
    WAIT <duration> This command pauses execution for the specified number of seconds. Execution resumes at the next statement after the command. WAIT…

  • Page 298: Appendix A: Some Worked Examples

    The examples which follow are intended to illustrate the ways in which the calculator can be used to help solve some typical problems. In some cases more than one method is shown. In some cases the method is chosen more to illustrate the capabilities of the calculator than because it is necessarily the most efficient method.

  • Page 299: Finding Complex Solutions To A Complex Equation

    This can make the real roots harder to isolate and use. However, it is still the best method. Method 3 — Using the CAS on the hp 40gs See page 309 for an example of finding roots of real and complex polynomials using the CAS on the hp 40gs.

  • Page 300: Finding Critical Points And Graphing A Polynomial

    ( ) = x For the function find the intercepts. (ii) find the turning points. (iii) draw a sketch graph showing this information. (iv) find the area under the curve between the two turning points. Step 1. Enter the function into the it is available for plotting.

  • Page 301
    Step4. Because I know that part (iv) of the question requires me to re­ use these extremum values in an integration (which I would like to be as accurate as possible), I am going to ‘save’ the extremum value just found. I change into the store it as shown in memory Note: You MUST store the point of interest before moving the cursor in the…

  • Page 302: Solving Simultaneous Equations

    Solve the systems of equations below: − 3 y = − 7 ⎫ y = 2 ⎭ Method 1 — Graphing the lines Because the first set of equations is a 2×2 system it can be graphed in the Function aplet. To do this it is necessary to re-arrange the functions into the form y = ………

  • Page 303
    If you are fortunate enough to own an hp 40gs rather than an hp 39gs then you can use the CAS for this. See page 346 for an example.

  • Page 304: Expanding Polynomials

    Expand the expressions below. (i) 2x + 3 (ii) 3a − 2b (i) POLYFORM((2X+3)^4,X) Use the key to examine the result. Result: 16x + 96 x + 216x (ii) POLYFORM((3A-2B)^5,B) as a function of . Then use the polynomial function again, ing the result from the first expansion and expanding this time as a function of used to view it, using the left and right arrows to scroll the…

  • Page 305: Exponential Growth

    Predict the number of bacteria colonies after 15 hours. (iii) How long does it take for the number of colonies to double? (i) Find and k using the calculator. Step 1. Start up the Statistics aplet, set it to given. Change to the SYMB SETUP Exponential line of best fit for the data.

  • Page 306
    (ii) Predict N for t = 15 hours. In the view, press up arrow to move the cursor onto the PLOT curve of best fit. Now press cursor will jump to the predicted value for x=15, which is currently off screen. Alternatively, change to the function.

  • Page 307: Solution Of Matrix Equations

    ⎟ , ⎝ − 1 5 ⎠ The algebraic calculation for this process is shown above right. Having done this, we will now see how to calculate this result on the calculator. Store the values of A and B into respectively.

  • Page 308: Finding Complex Roots

    Find the complex roots of z The best way to do this is using POLYROOT the hp 39gs and hp 40gs can be complex vectors, not just real valued matrices. (i) The coefficients can be entered into a+bi or as (a,b). In this case the roots are integers so there is no need to store it into a matrix.

  • Page 309: Complex Roots On The Hp 40Gs

    Find all roots of the complex polynomial f z Find the complex roots of z On the hp 40gs you can obtain exact roots for polynomials using the CAS function . The instructions following assume that the SOLVEVX CAS is in its default configuration. See page 324 for more details on the CAS.

  • Page 310: Analyzing Vector Motion And Collisions

    Ship A is currently at position vector 21 velocity of -4 km/hr. Ship B is at 30j and traveling at 2i + 3j km/hr. If the ships continue on their present courses, show that they will not collide and find the distance between them at the time of their closest approach.

  • Page 311: Circular Motion And The Dot Product

    I want to graph this function for the first six seconds but I am not sure what y scale to use so I will set XRng — Auto Scale. The result is shown right. view and then choose VIEWS Using Extremum, I find that the time of closest approach is at t = 3.4 hours (3:24 pm) with a separation at that time of d = 1.3416 km.

  • Page 312: Inference Testing Using The Chi 2 Test

    A teacher wishes to decide, at the 5% level of significance, whether the performance in a problem solving test is independent of the students’ year at school. The teacher selected 120 students, 40 from each of Years 8, 9 & 10, and graded their performance in a test as either A or B.

  • Page 313
    Changing into the Solve aplet we can enter a formula which will allow us to calculate values from the Chi distribution using the function. UTPC With a 3×2 contingency table the number of degrees of freedom are 2. To find the critical χ…

  • Page 314: Appendix B: Teaching Or Learning Calculus

    ‘nice’ values. This aplet can now be sent to each student’s calculator at the end of a lesson using the infra-red link. Accompanying questions should address the issues below, and students should be required to either hand in a short written response, or contribute to a verbal discussion the next day.

  • Page 315: Domains And Composite Functions

    There are a number of ways that the calculator can help with this. Examples are given below but others will no doubt occur to experienced teachers. Rational functions can be investigated using the example, enter the functions Discussion will elicit the fact that they are ‘identical’ algebraically…

  • Page 316
    ii. When discussing the concept of a domain, the very useful in developing this (see right). In the view, enter the functions shown right, un SYMB first two non-composite functions. In the used the view to set the scale to start at -1 and NUM SETUP increase in steps of 0.25.

  • Page 317: Gradient At A Point

    This is best introduced using an aplet called “Chords” downloaded from The HP HOME View web site (at http://www.hphomeview.com), but you can also use the Function aplet. If you use the aplet you will find that there is a worksheet supplied with it.

  • Page 318: Gradient Function

    The process can be done in a far more visual style using an aplet downloaded from The HP HOME View web site (http://www.hphomeview.com) called “Tangent Lines”. This aplet will add a moveable tangent line to an existing graph, as shown in the screen shot above, allowing the user to move it along the curve with the gradient displayed at the top left of the screen.

  • Page 319: The Chain Rule

    If desirable, an aplet is available from The HP HOME View web site (at http://www.hphomeview.com), called “Chain Rule”, which will encourage the student to deduce the Chain Rule for themselves. It is pre-loaded with five sets of functions, of increasing complexity, the first three of which are shown right.

  • Page 320: Area Under Curves

    One of the concepts which students find quite difficult to come to grips with is that of sketching a field of slopes from a derivative function and, from this, sketching a family of curves. An aplet from The HP HOME View web site (at http://www.hphomeview.com), called “Slope Fields”, will assist with this process.

  • Page 321: Inequalities

    The topic of inequalities is one that is often included in calculus courses, particularly during the study of domains and this is usually extended to graphing intersecting regions such as Although the hp 39gs & hp 40gs do not have the in-built ability to plot inequalities, the process is easily handled using an aplet from The HP HOME View web site (at http://www.hphomeview.com) called “Inequations”.

  • Page 322: Piecewise Defined Functions

    Through the Sequence aplet the hp 39gs & hp 40gs provide very flexible tools for the investigation of sequences. These can easily be adapted to investigate series as well. Information and worked examples of using the calculator for evaluation of sequences and series can be found in the chapter “The Expert –…

  • Page 323: Transformations Of Graphs

    “Quad Explorer” and “Trig Explorer” and are built into the calculator. Both of these aplets allow the student to explore the effect of changing parameters on the shape of the graph, one using a quadratic and the other with the sine and cosine curves.

  • Page 324: Appendix C: The Cas On The Hp 40Gs

    This appendix is intended to give a useful introduction and over view to the user who is new to an hp 40gs. It is not intended to fully cover the topic, nor is it intended to serve as a reference text for the advanced user.

  • Page 325
    Renée De Graeve, Jean-Yves Avenard and Jean Tavenas, and again adapted for inclusion in the HP49g+, HP48GII and HP 40gs calculators. The HP CAS system offers the user a vast array of functions and abilities as well as an easy user interface which displays equations as they appear on the page.
  • Page 326
    It also had two new aplets, the Triangle Solver and the Linear Solver aplets. If you own an hp 39gs and you are wondering if you can fool it into believing that it is an hp 40gs and thereby activate the CAS, then please don’t try it. If you disable the infra-red by, for example, cutting the internal wires then you won’t have an hp 40gs — you will simply have a crippled hp 39gs.

  • Page 327: Using The Cas

    For information on this and the other contents of the calculator. It is not advisable to change entries in this view without being clear on what you are doing since it can alter the behavior of the CAS. Some functions don’t work if…

  • Page 328
    Defining new variables In addition to the pre-defined variables you can also define your own using the new variables can have names that are more than one character long and can contain not only numbers but objects such as algebraic expressions. For example, STORE(X -1,FRED)
  • Page 329
    Assume that we want to show working by evaluating the binomial expression separately. Press the subtract, then press expression. The screen should appear as shown right. Press to evaluate this portion of the expression by expanding the brackets without affecting the rest of the expression. iii.
  • Page 330
    viii. Pressing this time will result in the screen shown below right which displays the two complex roots. ix. Press CLEAR in this case is the whole CAS editing screen. In the material on the following page we will explore this editing screen in more detail, looking particularly at why it is necessary to highlight expressions in some cases and not others, and how to move the highlight from one component of the expression to another and how to use special keys to manipulate the expression.
  • Page 331
    Pressing down arrow at that point moved down the tree. The default is to move to the left-most node D. This meant that the it was that expression which was cubed. At that point the tree now appears as shown right with the CAS in ‘typing/editing mode’ on node G. Pressing up arrow three times placed the highlight successively on nodes G, then D, then B.
  • Page 332
    After typing the 5, press up arrow once to highlight that node S. If you now press left arrow you will find that the highlight will jump horizontally to node A, highlighting the entire numerator. Pressing down arrow four times moves down through the tree from A to P to B to D to F. To access and change the power of 2, press up arrow twice to move up to node B, then press right arrow to move from node B to node Q.
  • Page 333
    Special characters As in the view, special characters such as inequalities are HOME available from the view, although the appearance of the CHARS view is somewhat different as can be seen right. There are no CHARS page up/down buttons, which makes it more difficult to move through. The initial two rows are invalid characters that can’t be used –…
  • Page 334
    Special editing commands – Undo, multi-select & swap Unlike most calculators the CAS editing screen has an undo function. If you have performed some operation that was incorrect then pressing SHIFT MEMORY have more memory to work with and so allow multiple levels of undo, this will only undo a single operation. However, this can be very convenient at times.
  • Page 335
    ‘in-line’ as if you were entering it in the calculator’s normal view.
  • Page 336
    Changing Font Although the default font is very easy to read, it is quite large and often makes parts of the expression or result extend off the screen. Changing to a small font can help with this, at the cost of making the characters a little more difficult to read.
  • Page 337
    If you want to delete the entire expression then the simplest method is to press re-enter it with a blank screen. Alternatively you can highlight part or all of the expression and then press . The highlighted section will be cleared. SHIFT ALPHA CLEAR Cutting and pasting of all or part of an expression can be easily done using the…
  • Page 338
    The PUSH and POP commands Occasionally it is desirable to transfer results from the normal view to the CAS screen or vice versa. This is done using the PUSH Suppose we have just expanded (2x+3) we press to exit the CAS and then type HOME then the result will be retrieved to the of the…
  • Page 339
    If you choose the Function aplet then you will be asked to nominate a destination. The current contents of each function is shown to allow you to choose whether to overwrite or not. All you need then do is exit the CAS and enter the Function aplet.
  • Page 340
    (see page 73 and the page following). A better alternative is to use the shown below, even though it still does not add the ‘+c’ (see page 73 for reasons). Calculator Tip The result of the and pressing…

  • Page 341: Examples Using The Cas

    In these examples we will begin with exercises which demonstrate the basic abilities of the CAS to simplify expressions and then move on to the use of the functions available through the various menus. In the initial examples the exact keystrokes will be supplied but in later ones this may not always be the case. Example 1: Simplifying a fraction with working Suppose you are required to simplify the expression shown right, giving your answer as a proper fraction.

  • Page 342
    ENTER ENTER iii. Finally, select the entire expression with SHIFT and press to simplify: ENTER iv. If you want the result as a decimal, press . Pressing SHIFT will cause the calculator to analyze the decimal and re-instate the surd.
  • Page 343
    Functionally there is no difference so why it was added is not clear. ENTER ENTER 2 — 0 are the same. On the old model hp 40g the only function was ” as −∞ LIMIT…
  • Page 344
    iii) Find 2
    + 5 x→∞ Limits to infinity are also permitted using the function, with infinity entered using the shortcut SHIFT 0 scroll to and press ENTER ENTER 344…
  • Page 345
    Example 4: Factorizing expressions If you highlight an expression such as (2x+3) the result extends beyond the screen we will scroll through it using the arrow keys. The results can be factorized again using the COLLECT In this example we will also illustrate the use of the CAS History to fetch a previous calculation.
  • Page 346
    Example 5: Solving equations − = Solve the equation real solutions and complex solutions. From within the CAS, press SHIFT MODES menu and ensure that you are in real mode by, if necessary, , as shown right. Complex mode Now use the function, typing: SOLVEVX function assumes that the active variable is being used.
  • Page 347
    function can also be used to solve problems with symbolic coefficients such as the one below. LINSOLVE Solve the system of equations: The command is LINSOLVE( 2.X+K.Y-1 AND (Q+3).X-Y-5, X AND Y) and it produces the results shown. Press to see the final solution in a VIEWS scrollable format.
  • Page 348
    As can be seen above, the initial integration gives an equation involving a fraction. This can be simplified by multiplying both sides by 6, highlighting the entire equation first. Notice that when the final simplification is equal to zero, the calculator does not bother to include the ‘ zero unless otherwise specified.
  • Page 349
    We can now use the LINSOLVE second linear equation is still highlighted, fetch the command from the menu. Then press highlight the linear expression again as shown right. Now, while the entire expression is highlighted, as shown above, press to obtain the ‘ ’.
  • Page 350
    Example 8: Defining a user function function allows you to define your own functions, which are then available for use. In the example below it has been used to define Fermat’s prime function . Note that the sequence of keys is: ENTER ALPHA F ( SHIFT = 2 + 1 ENTER…
  • Page 351
    We can now test to see if this is a prime number by using the function from the menu. This is found in the Integer section of the MATH CAS function list as shown right. It returns a value of (false) indicating that it is not a prime number.
  • Page 352
    1. As in the previous case, the to jump to the first function that starts with , the letter on 2. The hp 40gs will probably ask if it should turn “Complex mode” on, assuming it is in its default configuration. One of the is to tell it “Yes”.
  • Page 353
    And, having linearized it, we store it as a variable ALPHA M ENTER When the command is executed the STORE expression is echoed back to the screen. Press SHIFT ALPHA CLEAR At this point, any reference to image above is in small font purely to allow the entire expression to be seen. Your screen will not be unless you’ve selected small font earlier.
  • Page 354
    vi. Clear the current contents of the screen using SHIFT ALPHA CLEAR imaginary part of ALPHA M MATH ENTER ENTER Note: As before, the function with that letter ( ENTER ALPHA Y 1 ( ALPHA SHIFT T SHIFT SHIFT vii. In order to show that the function is symmetrical about the x axis we need to show that equivalent algebraically to evaluate each side.
  • Page 355
    When a function is sent to the Parametric aplet the real part is sent to the x and the imaginary part to the y component of the parametric equation selected. Calculator Tip Although earlier this has no relevance for the pasting into the Parametric aplet.
  • Page 356
    If you press highlight each function in turn and press This seems to make the calculator accept that it is a valid function, since it has had the chance to examine the function as if you had typed it in yourself. Pressing produce the screen shown right.
  • Page 357
    Example 10: First order linear differential equation In order to illustrate the use of the CAS help pages discussed on page 361 we will the example provided in them rather than making one up. The functions available for solving differential equations are LDEC Begin by pressing SHIFT SYNTAX…

  • Page 358: The Cas Menus

    There are a variety of different places that functions are stored, often overlapping for greater convenience. The Screen menus On the main screen of the CAS you will see six labels of discussed beginning on page 335. The others each pop up a menu of functions that are the most commonly used ones in each category but there are others that you can access via the MATH button or the menu.

  • Page 359
    The MATH menu Pressing the button in the CAS has a different effect than in the MATH screen. In the screen the result is as shown right. As was HOME HOME discussed on page 165, these commands are broken into broad groups of MTH (mathematical), CONS (constants) and CAS.
  • Page 360
    The abilities of the functions listed here and on the previous page will not be discussed in this text beyond the examples given on the previous pages. The manual supplied with your calculator is generally quite clear on their use and abilities.

  • Page 361: On-Line Help

    One of the most helpful features of the hp 40gs CAS is the on-line help provided by the button ( SYNTAX display the menu shown to the right. You can use the up or down arrow keys to scroll through this list but it is very extensive and it is far quicker to press the button corresponding to the first letter of the function on which you require information.

  • Page 362: Configuring The Cas

    One method is via the configuration line ) at the top of each menu. The line shown right of means that the calculator is set to variable, and you are working in If you select this option of the menu then you will see the further menu shown to the right.

  • Page 363
    Below the title bar you can see the first section of a series of alternatives which let you manipulate the configuration. Most alternatives are toggles having only two values. For example, choosing pressing will cause the menu to momentarily disappear and then re-display with the new setting of ENTER .
  • Page 364
    + bi or in the form of an ordered pair (a,b). If Complex mode is not selected and an operation results in a complex number, you will be asked to switch to Complex mode. If you decline, the calculator will report an error or, in the case of factorizing, simply return the original expression. [Default: unselected.] When in Complex mode, the CAS is able to perform a wider range of operations than in non- complex (or real) mode, but it will also be considerably slower.
  • Page 365
    When selected, it simplifies to ¼. I suggest that this is generally more desirable! Calculator Tip Changing the configuration can have a profound effect on the behavior of the CAS. is suggested that you read carefully the relevant information in the manual and/or the information in Renée de Graeve’s book mentioned…

  • Page 366: Tips & Tricks — Cas

    & & • In CAS, angles are always expressed in radians and no other setting is possible. When you are the calculator screen, you can use the HOME the CAS. • mode might appear to be quite useful for students but is quite limited in what it actually Step by step displays.

This manual is also suitable for:

40gs

Источник
  • Страница 1

    HP 3 9gs gr aphing calc ulato r user’s guide Ed i t io n 3 P a rt Number F2 2 2 3AA-9 0001 HP 39gs English. book Page i Wed nesday, December 7, 2 005 11:24 PM[…]

  • Страница 2

    Notice REG ISTER Y OUR PRODU CT A T: w ww .register .hp.com TH IS MANUAL AND ANY EXAMPLE S CONT AI NED HEREIN ARE PRO VIDED “ AS IS” AND ARE SUBJECT T O CHANG E WITHOUT NO TICE. HEWLETT-P A CKARD COMP ANY MAKES N O W AR- R ANTY O F ANY KIND WITH REGARD T O TH IS MANU AL , INC L UDING , B UT NO T L IMI TE D T O , TH E IM P LIE D W AR RAN T IES O[…]

  • Страница 3

    i Contents Preface Manual conventions …………. ……………. ……………. …………….. P-1 Notice .. …………….. ……………. ……………. …………….. …………. P-2 1 Getting started On/off, cancel o perations …….. ……………. …………….. …………. 1-1 The display …………… ………[…]

  • Страница 4

    ii 3 Function aplet About the Function aple t …………….. …………. ……………. ………. 3-1 Getting started w ith the Function aplet ……………. ……………. 3-1 Function aplet intera ctive analysis ……. ……………….. ……………. 3-9 Plotting a pie cewise-defined function ….. ……………. ……….. […]

  • Страница 5

    iii Exploring the graph …… ……………. ……………. ……………. 10-19 Calculating pre dicted values ……. ……………. ……………. … 10-20 11 Inference aplet About the Inference a plet ………… …………….. ……………. …….. 11-1 Getting started with the Inference aplet ………………… …….. […]

  • Страница 6

    iv Two-variab le statistic s …………. …………. ……………. ……… 13-17 Symbolic functions …. ………………. …………….. …………… 13-17 Test functions ……… ……………. …………. ……………. ……… 13-18 Trigonom etry functions ……… ……………. ……………. ……… 13-19 Sym[…]

  • Страница 7

    v Using programs ………………. ……………. ……………. …………… 18-7 Customiz ing an aplet ………… ……………. …………. ……………. .. 18-9 Aplet naming convention ……………… ……………. …………. 1 8-10 Example ……… ……………. ……………. ……………. …………. 18-[…]

  • Страница 8

    vi Polar aplet variable s ………….. ……………. ……………. ………. R-9 Sequence aplet variables ……….. ……………. …………….. …. R-10 Solve aplet variab les ………….. ……………. ……………. …….. R-11 Statistic s aplet variables ……………. …………….. …………. …. R-12 MATH […]

  • Страница 9

    P-1 Pr eface The HP 39gs is a feature-rich graphing calculator. It i s also a powerful mathematics learning tool. The HP 39gs is designed so that you can use it to explore mathematical functions and their prop erties. You can get more information on the HP 39gs from Hewlett-Packard’s Calcula tors web site. You can download customized aplets from […]

  • Страница 10

    P-2 Notice This manual and any examples contained herein are provided as-is and are subject to change without notice. Except to the extent prohibit ed by law, Hewlett-Packard Company makes no express or implied warranty of any kind with regard to this manu al and specific ally disclaims the implied warranties and conditions of merchantability and f[…]

  • Страница 11

    Getting started 1-1 1 Get ting star ted On/off, cancel operations To turn on Press to turn on the calculator. To cancel When the calculator is on, the key cancels the current operation. To turn off Press OFF to turn the calculator off. To save power, the calculator turns itself off after sev eral minutes of inactivity. All stored and displayed info[…]

  • Страница 12

    1-2 Getting started The display To adjust the contrast Simultaneously press and (or ) to increase (or decrease) the contrast. To clear the display • Pr ess CANCEL to c lear the edit line . • Pr ess CLEA R to c lear the edit line and the display history . Parts of the display Menu key or soft key labels. T he labels f or the menu k e ys ’ cur […]

  • Страница 13

    Getting started 1-3 Annunciators . Annunciators are sy mbols that appear above the title bar and give you important status information. The keyboard Menu keys Annunciator Description Shift in effect for next keystrok e. To cancel, press again. α Alpha in effect for next keystroke. To cancel, press again. (( • )) Low battery power. Busy. Data is […]

  • Страница 14

    1-4 Getting started • On the calc ulator k e y boar d, the top r ow of k ey s are called menu k ey s . The ir meanings depend on the conte xt—that’s w h y their to ps ar e blank . The menu k e y s ar e sometimes called “ so ft k ey s ” . • T he bottom line o f the displa y sho ws the la bels f or the menu k ey s ’ c u r r ent meanings[…]

  • Страница 15

    Getting started 1-5 Entry/Edit keys The entry and edit keys are: K e y Meaning ( CANCEL ) Cancels the current operation if the calculator is on by pressing . Pressing , then OFF turns the calculator off. Accesses the function printed in blue above a key. Returns to the HOME view, for performing calculations. Accesses the alphabetical characters pri[…]

  • Страница 16

    1-6 Getting started Shifted ke ystrokes There are two shift keys that you use to access the operations and characters printed above the keys: and . CHARS Displays a menu of all available characters. To type one, use the arrow keys to highlight it, and press . To select multiple character s, select each and press , then press . K e y Meaning (Contin[…]

  • Страница 17

    Getting started 1-7 HELPWITH The HP 39gs built-in hel p is available in HOME only. It provides syntax help for bu ilt-in math functions. Access the HELPWITH command by pressing SYNTAX and then the math key for which you require syntax help. Example Pr ess SYNTAX Note: R emo ve the left par enthesis fr om built -in func tio ns such a s sine , cosine[…]

  • Страница 18

    1-8 Getting started • Pr essing displa y s a menu of ph y sical constants f r om the f ields o f chemistry , phy sic s, and quantum mec hanic s. Y ou can u se these consta nts in calc ulati ons . (See “Ph ysi cal constants ” on page 13- 2 5 f or mor e inf or mation .) • Pr essing tak es yo u to the beginning of the MA TH men u . See “Math[…]

  • Страница 19

    Getting started 1-9 • If ther e are tw o columns , the left column sho ws gener al categori es and the righ t column sho w s spec ifi c cont ents w ithin a catego ry . Hi ghligh t a gener al category in the left column, then hi ghligh t an item in the r ight column. T he list in the ri ght column c hanges w hen a diffe r ent catego ry is highligh[…]

  • Страница 20

    1-10 Getting started Mode settings You use the Modes inpu t form to set the modes for HOME. HINT Although the numeric setting in Modes affects only HOME, the angle setting controls HOME and the current aplet. The angle setting selecte d in Modes is the angle setting used in both HOME and current aplet. To further configure an aplet, you u se the SE[…]

  • Страница 21

    Getting started 1-11 Setting a mode This example demonstrates how to change the angle measure from the default mode, radians, to degrees for the current aplet. The procedure is the s ame for changing number format and decimal mark modes. 1. Pr ess MODES t o o p e n t h e H O M E M O D ES i n p u t form. Engineering . Displays result wit h an expone[…]

  • Страница 22

    1-12 Getting started T he cur sor (hi ghlight) is in the fir st f ield , Angle Measur e . 2 . Pr ess to display a li st of choic es. 3. P re s s to select Degrees , and pr ess . The angle mea sur e changes to degrees . 4. Pr ess to r eturn to HOME . HINT Whenever an input form has a list of choices for a field, you can press to cycle through them i[…]

  • Страница 23

    Getting started 1-13 symbolic views of the aplets in the following table. See “Aplet view configuration” on page 1 -18 for further information. In addition to these aplets, wh ich can be u sed in a variety of applications, the HP 39 gs is supplied with two teaching aplets: Quad Explorer and Trig Explorer. You cannot modify configurati on settin[…]

  • Страница 24

    1-14 Getting started charge and transferred to the HP 39gs using the provided Connectivity Kit. Quad Explorer aplet The Quad Explorer aplet is used to investigate the behaviour of as the values of a , h and v change, both by manipulati ng the equation and seeing the change in the graph, and by manipulating the grap h and seein g the chang e in the […]

  • Страница 25

    Getting started 1-15 Trig Explorer aplet The Trig Explorer aplet is used to investigate the behaviour of the graph of as the values of a , b , c and d change, both by manipulating the equation and seeing the change in the graph, or by manipulating the graph and seeing the change in the equation. Press , select Trig Explorer , and then press to disp[…]

  • Страница 26

    1-16 Getting started Aplet library Aplets are stored in the Aplet library. To open an aplet Press to display the Aplet library me nu. Select the aplet and press or . From within an aplet, you can return to HOME any time by pressing . Aplet views When you have configured an aplet to define th e relation or data that you want to explore, you c an dis[…]

  • Страница 27

    Getting started 1-17 Numeric view Press to dis play the aplet’s Numeric view. In this view, the functions that you have defined are displayed in tabular format. See “About the numeric view” on page 2 -16 for further information. Plot-Table view The VIEWS menu contains the Plot-Table view. Select Plot-Table Splits the screen into the plot and […]

  • Страница 28

    1-18 Getting started Note view Press NOTE to display the aplet’s note view. This note is transferred with the aplet if it is sent to another calculator or to a PC. A note view contains text to supplement an aplet. See “Notes and ske tches” on page 17-1 for further information. Sketch view Press SKETCH to dis play the ap let’s sk etch view .[…]

  • Страница 29

    Getting started 1-19 To change views Each view is a separate environment. To ch ange a view, select a different view by pressing , , keys or select a view from the VIEWS menu. To change to HOME, press . You do not explicitly close the current view, you just ente r another one—like passing from one room into another in a house. Data that you enter[…]

  • Страница 30

    1-20 Getting started Example Calculate : Long results If the result is too long to fit on the display line, or if you want to see an expression in textbook format, press to highlight it and then press . Negative numbers Type to start a negative number or to insert a negative sign. To raise a negative number to a power, enclose it in parentheses. Fo[…]

  • Страница 31

    Getting started 1-21 However, for clarity, it is better to include the multiplication sign where you expect multiplication in an expression. It is clearest to enter AB as A*B . HINT Implied multiplication will not always work as expecte d. For example, entering A(B+4 ) will not give A*(B+4) . Instead an error message is displayed: “I nvalid User […]

  • Страница 32

    1-22 Getting started Algebraic precedence order of evaluation Functions within an expression are evaluated in the following order of precedence. Functions with the same precedence are evaluated in order from left to right. 1. E xpressions w it hin parenthe ses. Neste d p ar ent heses ar e ev aluated fr om inner to outer . 2 . Pr efi x functio ns, s[…]

  • Страница 33

    Getting started 1-23 When you highlight a previous input or result (by pressing ), the and menu labels appear. To copy a previous line Highlight the line (press ) and press . The number (or expression) is co pied into the e dit line. To reuse the last result Press AN S (last answer) to put the last result from the HOME display into an expression. A[…]

  • Страница 34

    1-24 Getting started HINT When you retrieve a number from ANS , you obtain the result to its full precision. When you retrieve a number from the HOME’s display history, you obtain exactly what was displaye d. Pressing evaluates (or re-evaluates) the last input, whereas pressing ANS copies the last result (as ANS ) into the edit line. Storing a va[…]

  • Страница 35

    Getting started 1-25 Accessing the display history Pressing enables the highlight bar in the display history. While the highlight bar is active, the following menu and keyboard keys are very useful: Clearing the display history It’s a good habit to cl ear the display his tory ( CLEAR ) whenever you have finish e d working in HOME. It saves calcul[…]

  • Страница 36

    1-26 Getting started 2 . Select Number Format , pr ess to display the optio ns, and hi ghlight Fract ion or Mixed Fraction . 3 . Pr ess to sele ct the Number F ormat option , then mo ve to the prec ision value field . 4. Enter the prec ision v alue that yo u want to us e , and pr ess to set the pr ecisi on . Pres s to retur n to HOME . See “Setti[…]

  • Страница 37

    Getting started 1-27 • Pr ec ision set to 1: • Pr ec ision set to 2 : • Pr ec ision set to 3: • Pr ec ision set to 4 Fraction calculations When entering fractions: • Y ou use the ke y to separate the numerator part and the denominator par t of the fr action. • T o ent er a mi xed f r acti on , f or e x ample , 1 1 / 2 , you enter it in […]

  • Страница 38

    1-28 Getting started 2. E n t e r t h e c a l c u l a t i o n . 32 3 45 7 8 Note: Ensur e y ou ar e in the HOME v ie w . 3 . E valuat e the calc ulation . Note that if you had selected Mixed Fraction instead of Fraction as the Number format, the answer would have been expressed as 25+7/8. Converting decimals to fractions To convert a decimal value […]

  • Страница 39

    Getting started 1-29 In this e x ample , the fr action pr ec ision is s et to 6. Complex numbers Complex results The HP 39gs can return a complex number as a result for some math functions. A comp lex number appears a s an ordered pair ( x, y ), where x is the real part and y is the imaginary part. For example, entering returns (0,1). To enter comp[…]

  • Страница 40

    1-30 Getting started Catalogs and editors The HP 39gs has several catalogs and editors. You use them to create and manipulate objects. They access features and stored values (numbe rs or text or other items) that are independent of aplets. • A catalog lists items, w hich y ou can delete or tr ansmit , for e xampl e an aplet . • An edito r lets […]

  • Страница 41

    Aplets and their views 2-1 2 Aplets and t heir v ie w s Aplet views This section examines the options an d functionality of the three main views for the Function, Polar, Parametric, and Sequence aplets: Symbolic, Plot, and Numeric views. About the Symbolic view The Symbolic view is the defining view for the Functi on, Parametric, Polar, and Seque n[…]

  • Страница 42

    2-2 Aplets and their views – For a F unc tion definiti on , e nt er an e xpr es sio n to def ine F(X) . The only independent variab le in th e ex pre ss i on i s X. – Fo r a P arametric definiti on , e nt er a pair of e xpr essi ons to def ine X(T) and Y(T) . The o nly independent v ari able in the e xpr es sions is T . – Fo r a P o l ar defi[…]

  • Страница 43

    Aplets and their views 2-3 Evaluating expressions In aplets In the Symbolic view, a variable is a symbol only, and does not represent one specif ic value. To evaluate a function in Symbolic view, press . If a function calls another function, then reso lves all references to other functions in terms of their independent variable. 1. Choo se the F un[…]

  • Страница 44

    2-4 Aplets and their views In HOME You can also evaluate any expression in HOME by entering it into the edit line and pressing . For example, define F4 as below. In HOME, type F4(9) and press . This evaluates the expression, substituting 9 in place of X into F4 . SYMB view keys The following table details the menu keys that you use to work with the[…]

  • Страница 45

    Aplets and their views 2-5 About the Plot view After entering and selecting (check marking) the expression in the Symbolic view, press . To adjust the appearance of the graph or the interval that is displayed, you can change the Plot view settings. You can plot up to ten expressions at the same time. Select the expressions you want to be plotted to[…]

  • Страница 46

    2-6 Aplets and their views Plot view settings The plot view settings are: Those items with space for a checkmark are settings you can turn on or off. Press to display the second page. F ield Meaning XRNG, YRNG Specifies the minimum and maximum horizontal ( X ) and vertical ( Y ) values for the plotting window. RES For function plots: Resolution; ?[…]

  • Страница 47

    Aplets and their views 2-7 Reset plot settings To reset the default values for all plot settings, press CLEAR in the Plot Setup view. To reset the default value for a field, highlight the field, and pres s . Exploring the graph Pl o t v i ew g iv e s y ou a se l ec t io n of k ey s a n d m e nu k ey s to explore a graph further. The options vary fr[…]

  • Страница 48

    2-8 Aplets and their views Trace a graph You can trace along a function using the or key which moves the cur sor along the graph. The display also shows the current coordinate position ( x, y ) of the cursor. Trace mode and the coordinate di splay are automatically set when a plot is drawn. Note: Tracing might not appe ar to exactly follow your plo[…]

  • Страница 49

    Aplets and their views 2-9 To jump directly to a value To jump straight to a value rather than using the Trace function, use the menu key. Press , then enter a value. Press to jump to the value. To turn trace on/off If the menu labels are no t displayed, press first. • T urn o ff tr ace mode by pr essing . • T urn on tr ac e mode by pre ssing .[…]

  • Страница 50

    2-10 Aplets and their views Y-Zoom In Divides vertical scale only, using Y-factor. Y-Zoom Out Multipli es vertical scale only, using Y-factor. Square Changes the vertical scale to match the horizontal scale. (Use this after doing a Box Zoo m, X-Zoom, or Y-Zoom.) Set Factors… Sets the X-Zoom and Y-Zoom factors for zooming in or zooming out. Includ[…]

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    Aplets and their views 2-11 ZOOM examples The following screens show the effects of zooming options on a plot of . Plot of Zoom In : In Un-zoom : Un-zoom Note: Press to move to the bottom of the Zoom list. Zoom Out : Out Now un -zoom . X-Zoom In : X-Zoom In Now un -zoom . X-Zoom Out : X-Zoom Out Now un -zoom . Un-zoom Returns the display to the pre[…]

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    2-12 Aplets and their views Y-Zoom In: Y-Zoom In Now un-zoom. Y-Zoom Out: Y-Zoom Out Zoom Square: Square To box zoom The Box Zoom option lets you dr aw a box aroun d the area you want to zoom in on by selecting the endpoints of one diagonal of the zoom rectangle. 1. If necessary , pr ess to turn o n the menu -k e y labels . 2. P r e s s a n d s e l[…]

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    Aplets and their views 2-13 To set zoom factors 1. In the P lot v ie w , pr ess . 2. P r e s s . 3. S e l e c t Set Factors… and pr es s . 4. Enter the z oom fac tors . Ther e is one z oom fac tor f or the hor i z ontal sc ale ( XZOOM ) and one f or the vertical sca le ( YZOOM ). Z ooming out multipli es the s cale by the fac tor , so that a gr e[…]

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    2-14 Aplets and their views Split the screen The Plot-Detail view can give you two simultaneous views of the plot. 1. Pr ess . Se lect Plot-Detai l and pr ess . The gr aph i s plotted twi ce. Y ou can no w z oom in on the r ight si de. 2. P r e s s , selec t the z oom method and pres s or . This z ooms the r ight si de. Her e is an e x ample of s p[…]

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    Aplets and their views 2-15 – mo ves the leftmost c ursor to the scr een’s left edge an d mo ves the ri ghtmost c ursor to the s cr een ’s ri ght edge . – T he menu k e y copies the r ight plot t o the left plot . 3 . T o un -split the sc reen , pre ss . The left si de tak es o ver the wh ole scr e en . The Plot-Table view gives you two sim[…]

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    2-16 Aplets and their views About the numeric view After entering and selecting (check marking) the expression or expressions that you want to explore in the Symbolic view, press to view a table of data values for the independent variable ( X , T, θ , or N ) and dependent variables. Setting up the table (Numeric view setup) Press NUM to define any[…]

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    Aplets and their views 2-17 Numeric view settings The following table details the fields on the Numeric Setup input form. Reset numeric settings To reset the default values for all table settings, press CLEAR . Exploring the table of numbers NUM view menu keys The following table details the menu keys that you use to work with the table of numbers.[…]

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    2-18 Aplets and their views ZOOM options The following table lists the zoom options: The display on the right is a Zoom In of the display on the left. The ZOOM factor is 4. HINT To jump to an independent va riable value in the table, use the arrow keys to place the cursor in the independent variable column, then enter the value to jump to. Automati[…]

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    Aplets and their views 2-19 Building your own table of numbers The default NUMTYPE is “Automatic”, which fills the table with data for regular intervals of the independent ( X , T , θ , or N ) variable. With the NUMTYPE option set to “Build Your Own”, you fill the table yourself by typing in the independent-variable values yo u want. The d[…]

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    2-20 Aplets and their views “Build Your Own” menu keys Example: plotting a circle Plot the circle, x 2 + y 2 = 9 . Fi rst rearrange it to read . To plot both the positive and negative y values, you need to define two equations as follows: and K e y Meaning Puts the highlighted independent value ( X , T , θ , or N ) into the edit line. Pressing[…]

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    Aplets and their views 2-21 1. In the F unction aplet , spec ify the functi ons . Select Function 9 9 2 . Rese t the gr aph se tup to the de fa ult setting s. SETUP — PLOT CLEAR 3 . P lot the two func tions and hide the men u so that y ou can see all the ci rc l e. 4. R eset the n umer ic s etup to the def ault se ttings. SETUP — NUM CLEAR 5 . Disp[…]

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    HP 39gs English. book Page 22 We dnesday, December 7, 2005 11:24 PM[…]

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    Function aplet 3-1 3 F unc tion aplet About the Function aplet The Function aplet enables you to explore up to 10 real-valued, rectangu lar functions y in terms of x . For example . Once you have defined a function you can: • cr eate gr aphs to fi nd r oots, int er cepts, slope , signed ar ea, and e x tr ema • cr eate tables to evaluate f uncti[…]

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    3-2 Function aplet Define the expressions 2 . T her e are 10 f uncti on def inition f ields on the F uncti on aplet’s S y mbolic v ie w sc r een . Th ey ar e labeled F1(X) to F0(X). Highligh t the func tion de f inition f ield y ou w ant to use , and en ter a n e xpr es si on . (Y o u can pr ess to delete an e xis ting line , or CLEAR to clear al[…]

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    Function aplet 3-3 Change the scale 6 . Y ou can chan ge the scale to see mo r e or le ss of your gr aphs . In this e xam ple , ch oose Auto Scale . (See “VIEW S menu options ” on page 2 -13 f or a de scr ip t ion of Aut o Sc al e) . Select Auto Scale Trace a graph 7 . T race the linear f uncti on . 6 times Note: B y default , the tr acer is ac[…]

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    3-4 Function aplet Analyse graph with FCN functions 9. Display the Plot view menu. From the Plot view menu, you can use the functions on the FCN menu to find roots, intersections, slopes, and areas for a function defined in the Function aplet (and any Function-based ap lets). The FCN fun ctions act on the currently selecte d graph. See “FCN func […]

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    Function aplet 3-5 12 . Cho ose the linear f unction w hose int ers ecti on w ith the quadr atic functi on you w ish to f ind. T he coor dinates o f the inters ecti on poin t ar e display ed at the bottom of the scr een. Note: If ther e is more than one inter secti on (as in our e xam ple) , the coor dinates of the inter sec tion po int c lose st t[…]

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    3-6 Function aplet 15 . Mo v e the c urso r to x = –2 by pr essing the or key . 16 . Pr es s to acce pt using F2(x) = (x + 3) 2 – 2 as the other boundar y for the integr al. 17 . Choo se the end v alue for x . 1 Th e cu rs or ju mps t o x = – 1 on the linear func tion . 18. Displa y the numerical value of the integral. Note: See “Shading ar[…]

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    Function aplet 3-7 HINT The Root and Extremum functions return one value only even if the function has more than one r oot or extremum. The function finds the value closest to the position of the cursor. You need to re- locate the cursor to find oth er roots or extrema that may exist. Display the numeric view 20. Display the numer ic v ie w . Set u[…]

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    3-8 Function aplet To navigate around a table 2 4. Mo v e to X = –5 .9 . 6 times To go directly to a value 2 5. Mov e direc tly to X = 10. 1 0 To access the zoom options 2 6 . Z oom in on X = 10 by a fact or of 4. Note: NUMZOOM has a setting of 4 . In To change font size 2 7 . Displa y table numbe rs in lar ge f ont . To display the symbolic defi[…]

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    Function aplet 3-9 Function aplet interactive analysis From the Plot view ( ), you can use the functions on the FCN menu to find r oots, intersections, slopes, and areas for a function defined in the Function aplet (and any Function-based aplets). See “FCN functions” on page 3- 10. The FCN operations act on the currently sele cted graph. The re[…]

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    3-10 Function aplet FCN functions The FCN functions are: Function Description Root Select Root to find the root of the current function nearest the cursor. If no root is found, but only an extremum, then the result is labeled EXTR: instead of ROOT: . (The root-finder is also used in the Solve aplet. See also “Interpreting results” on page 7-6.)[…]

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    Function aplet 3-11 Shading area You can shade a selected area between functio ns. This process also gi ves you an appro ximate measurement of the area shaded. 1. Open the F unction aplet. T he Func tion aplet opens in the S ymbolic v ie w . 2 . Select the e xpr essi ons wh ose c ur v es y ou w ant to stu dy . 3 . Pres s to plot the functi ons . 4.[…]

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    3-12 Function aplet Plotting a piecewise-defined function Suppose you wanted to plot the following piecewise- defined function. 1. Open the F unction apl et . Sele ct Function 2 . Highlight the line you wan t to us e , and ente r the e xpre ssion . (Y ou can pre ss to delete an e xisting line , or CLEAR to c lear all lines .) 2 CHARS ≤ 1 CHARS &g[…]

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    Parametric aplet 4-1 4 Pa r a m e t r i c a p l e t About the Parametric aplet The Parametric aplet allows you to explore parametric equations. These are equ ations in which both x and y are defined as functions of t . They take the forms and . Getting started with the Parametric aplet The following example uses the parametric equations Note: This […]

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    4-2 Parametric aplet Set angle measure 3 . Set the angle measu r e to degrees. MODES Select Degrees Set up the plot 4. Display the graphing options. PLOT T he P lot Setu p inpu t for m has t w o f ields n ot inc luded in the Func tion aplet , TRNG and TSTEP . TRNG spec if ies the r ange of t val ue s. TSTEP spec if ies the step value between t valu[…]

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    Parametric aplet 4-3 Overlay plot 8. Plot a triangle graph over the existing ci rcle graph. PLOT 120 Sele ct Overlay Plot A tri angle is displa yed r ather than a c irc le ( with out c hanging the equati on) becaus e the c hanged value o f TSTEP ensur es that points be ing plot ted ar e 120 ° apart instea d of near l y continuou s. Y ou ar e able […]

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    HP 39gs English. book Page 4 Wed nesday, December 7, 2 005 11:24 PM[…]

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    Polar aplet 5-1 5 Po l a r a p l e t Getting started with the Polar aplet Open the Polar aplet 1. Open the P olar aplet . Sele ct Polar L ik e the F unction aple t , the P o lar aplet opens in the S ymboli c v ie w . Define the expression 2 . Define the po lar equati on . 2 π 2 Specify plot settings 3 . S pec ify the plot settings . In this ex amp[…]

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    5-2 Polar aplet Explore the graph 5 . Displa y the Plot v ie w menu k ey labels . Th e Pl ot vi ew op t i on s av ailable ar e the same as those f ound in the F u ncti on aplet . See “Explor ing the gra ph ” on page 2 — 7 fo r further informati on . Display the numbers 6 . Displa y the table of v alue s for θ and R1. Th e N u m eric view optio[…]

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    Sequence aplet 6-1 6 Sequence aplet About the Sequence aplet The Sequence aplet allows you to explore sequences. You can define a sequence named, for example, U1: • in terms of n • in terms of U1 ( n –1) •i n ter ms of U1 ( n –2) • in ter ms of another sequence , for e xample , U2 ( n ) • in an y combination of the a bov e. The Sequen[…]

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    6-2 Sequence aplet Open the Sequence ap let 1. Open the Sequ ence aplet . Sele ct Sequence The Sequence ap let starts in the S ymboli c view . Define the expression 2 . Def ine the F ibonacc i sequence, in w hich eac h term (after the f irst tw o) is the sum of the pr eceding tw o terms: , , for . In the S ymboli c v ie w of the Seq uence aplet , h[…]

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    Sequence aplet 6-3 Plot the sequence 4. P lot the Fibonacc i sequ ence. 5. In Plot Setup, set the SEQPLOT option to Co bweb . SETUP — PLOT Select Cobweb Display the table 6 . Displa y the table of values for this e xample . HP 39gs English. book Page 3 Wed nesday, December 7, 2 005 11:24 PM[…]

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    HP 39gs English. book Page 4 Wed nesday, December 7, 2 005 11:24 PM[…]

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    Solve aple t 7-1 7 Solve aplet About the Solve aplet The Solve aplet solves an equation or an expression for its unknown variable . You define an equation or expression in the symbolic view, then supply values for all the variables exce pt one in the numeric view. Solve works only with real numbers. Note the differences between an equation and an e[…]

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    7-2 Solve a plet Getting started with the Solve aplet Suppose you want to find th e acceleration needed to increase the speed of a car from 16.67 m/sec (60 kph) to 27.78 m/sec (100 kph) in a distance of 1 00 m. The equation to solve is: Open the Solve aplet 1. Open the Solv e aplet. Sele ct Solve T he Sol v e aplet st arts in the s y mbolic v iew .[…]

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    Solve aple t 7-3 4. Enter the values f or the kno wn va ri ables . 2 7 7 8 1 6 6 7 1 0 0 HINT If the Decimal Mark setting in the Modes input form ( MODES ) is set to Comma, use instead of . Solve the unknown variable 5. Sol v e f or the unkno wn var iable ( A ). T her ef or e , the accelerati on needed to inc r ease the speed of a car fr om 16.6 7 […]

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    7-4 Solve a plet 6. P lot the equati on f or v ari able A . Sele ct Auto Scale 7 . T race along the gr aph r epr esen ting the left side of the equati on until the c ursor nears the inter sec tion . 20 times Note the v alue o f A display ed near the bottom left corner of the scr een. T he Plo t vi e w pr o v ides a con v enien t wa y to f ind an ap[…]

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    Solve aple t 7-5 Use an initial guess You can usually obtain a fa ster and more accurate solution if you supply an estimated valu e for the unknown variable before pressing . Solve starts looking for a solution at the initial guess. Bef or e plottin g , make sur e the unkno wn v ariable is highli ghted in the nume ri c v ie w . P lot the equati on […]

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    7-6 Solve a plet Interpreting results After Solve has returned a solution, press in the Numeric view for more information. You will see one of the following three messages. Press to clear the message. Messa ge Condi tion Zero The Solve aplet found a point where both sides of the equation were equal , or wher e the expression was zero (a root), with[…]

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    Solve aple t 7-7 If Solve could not find a solution, you will see one of the following two messages. HINT It is important to check the information relating to the solve process. For example, the solution that the Solve aplet finds is not a solution, but the closest that the function gets to zero. Only by checking the information will you know that […]

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    7-8 Solve a plet where X is distance, V 0 is initial velocity, T is time, and A is acceleration. This is actually two equations, Y = X and Y = V 0 T + (AT 2 ) / 2 . Since this equation is quadratic for T , there can be both a positive and a negative solution. However, we are concerned only with posi tive so lutions, since only positive distance mak[…]

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    Solve aple t 7-9 5. Move the cursor near the positive (right-side) intersection. This cursor value will be an initial guess for T . Pr ess until the c urs or is at the inters ecti on. Th e t wo p oi nt s of inter sec tion sho w that ther e ar e tw o soluti ons f or this equati on . Ho w e ve r , on ly po si t ive va l ue s fo r X mak e sense , so w[…]

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    7-10 Solve a plet Using variables in equations You can use any of the real variable names, A to Z and θ . Do not use variable nam es defined for other type s, such as M 1 (a matrix variable). Home variables All home variables (other than t hose for aplet settings, like Xmin and Ytick ) are globa l , which means they are shared throughout the diffe[…]

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    Linear Solve r aplet 8-1 8 Li n e a r S o lve r a p l e t About the Linear Solver aplet The Linear Solver aplet allows you to solve a set of Linear Equations. The set can contain two or three linear equations. In a two-equation set, each equation must be in the form . In a three-equation set, e ach equation must be in the form . You provide values […]

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    8-2 Linear Solver aplet Choose the equation set 2 . If the last time y ou us ed the L inear Sol v er aplet yo u so l ve d fo r t wo equati ons, the tw o — equati on input f orm is display ed (as in the e x ample in the pr ev ious step) . T o solv e a th r e e -equation set , pre ss . No w the input f or m displa y s thr ee equati ons . If the three[…]

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    Linear Solve r aplet 8-3 soon as the f irst co -eff ic ient o f the last eq uation was enter ed. As you enter each of the r emaining kno wn v alues , the soluti on c hanges . T he ex ample at the ri ght sho ws the fi nal soluti on once all th e c o — efficient s a nd constants are e nter ed for the set o f equati ons w e set out to solve . HP 39gs […]

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    HP 39gs English. book Page 4 Wed nesday, December 7, 2 005 11:24 PM[…]

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    Triangle Solve apl et 9-1 9 T riangle Solv e aplet About the Triangle Solver aplet The Triangle Solver aplet a llows you to determine the length of a side of a triangle, or the ang le at the vertex of a triangle, from information you supply about the other lengths and/or other angles. You need to specify at leas t three of the six possible values?[…]

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    9-2 Triangle Solv e aplet Open the Triangle Solver aplet 1. Open the T riangle S olv er aplet . Sele ct Triangle Solver The T r iangle Solv er aplet open s . Note : if y ou h a v e alr eady u sed the T ri angle Sol v er , the entries and re sul ts fr om the pre v ious use w i ll still be display ed. T o start the T r iangle Solv er a fr esh, c lear[…]

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    Triangle Solve apl et 9-3 lengths as B and C, w e would ne ed to spec if y the angle as α . T he illustr a ti on on the displa y w ill help y ou determine wher e to enter t he know n values. Note: if y ou need to change the angle measur e mode , pres s MO DES , change the mode , and then pr ess to r eturn to the aplet . 4. Pr ess . T he solv er ca[…]

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    9-4 Triangle Solv e aplet Not enough data If you are using the general input form, you need to specify at least three values for the Triangle Solver to be able to calculate the remaining attributes of the triangle. If you specify less than three , Not enough data appears on the screen. If you are using the simplified input form (for a right- angled[…]

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    Statistics aplet 10-1 10 Statis tic s a ple t About the Statistics aplet The Statistics aplet can store up to ten data sets at one time. It can perform one- variab le or two-variable statistical analysis of one or more sets of data. The Statistics aplet starts with the Numeric view which is used to enter data. The Symbol ic view is used to specify […]

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    10-2 Statistics aplet Open the Statistics aplet 1. Open the Statis tics a plet and c lear e x isting data b y pr essing . Select Statistics Th e S ta t is ti cs ap l et starts in the Numer ical view . At an y time the Statisti cs aplet is conf igur ed for o nly one of t wo types of sta tistical explorations: one — var iable ( ) or tw o-v ariable ( […]

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    Statistics aplet 10-3 Choose fit and data columns 4. Select a fi t in the S y mbolic setu p vi e w . SETUP — SYMB Sele ct Linear Y ou c a n cre at e u p t o five ex p lo ra t io n s of t wo — va ri ab l e data , named S1 to S5 . I n t hi s exa m pl e, we wil l cre a te jus t o n e: S1 . 5 . Spec ify the columns that hold the data yo u w ant to anal[…]

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    10-4 Statistics aplet Setup plot 8. Change the plotting range t o ensur e all the data points ar e plot ted (and select a diff er ent point mar k, if yo u wi s h ) . SETUP — PLOT 7 100 400 0 Plot the graph 9 . Plo t the gr aph . Draw the regression curve 10. Dra w the reg r essi on c urve (a c ur ve to fi t the data points). T his dra w s the r egr[…]

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    Statistics aplet 10-5 Predict values 13 . T o find the pr edic ted sale s f igur e if adv er tising w er e to go up to 6 minute s: S ( to highlight Stat-Two ) (to highligh t PREDY ) 6 14. Retu rn to the P lot vi e w . 15 . Jum p to the indicat ed point on the r egr essi on line . 6 Observ e the pr edict ed y -v alue in the left bottom corner of the[…]

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    10-6 Statistics aplet Entering and editing statistical data The Numeric view ( ) is used to enter data into the Statistics aplet. Each column represents a variable named C0 to C9 . After entering the data, you must define the data set in the Symbolic view ( ). HINT A data column must have at least four data points to provide vali d two-variable sta[…]

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    Statistics aplet 10-7 Example You are measurin g the height of students in a classroom to find the mean height. The first five students have the following measurements 160cm, 165cm, 1 70cm, 175cm, 180cm. 1. Open the Stati stics aplet . Sele ct Statistics 2 . Enter the measurement data. 160 16 5 17 0 17 5 180 3 . F ind the mean of the sampl e. Ensur[…]

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    10-8 Statistics aplet Note that the title o f the colu mn o f st atis ti cs i s H1 . Ther e a r e 5 data set de f initions a vailable for one -v ari able sta tis tics : H1–H5 . If data is entered in C1 , H1 is automatically set to use C1 fo r data , and the fr equency of eac h data point is set to 1. Y ou can select other columns o f data fr om t[…]

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    Statistics aplet 10-9 To continue our example, supp ose that the heights of the rest of the students in the class are measured, but each one is rounded to the nearest of the five values first recorded. Instead of entering all the new data in C1 , we shall simply add another column, C2 , that holds the frequencies of our five data points in C1 . 5 .[…]

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    10-10 Statistics aplet 6 . R eturn t o the numer ic vi ew . 7 . Ente r the fr equency data sho wn in the a bo ve t able . 5 3 8 2 1 8. Display the comp uted sta tis tics. The mean height is approxim ately 167.63cm. 9 . Setu p a histogr am plot for the data . SETUP — PLOT Enter s et up inf or matio n appropriate to your data. 10. P lot a histogr am […]

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    Statistics aplet 10-11 Delete data • T o delete a single data item, highli ght it and pr ess . T he value s belo w the delet ed cell w ill scr oll up one ro w . • T o delete a column of data , highli ght an entry in that column and press CLEAR . Select the co lumn name . • T o delete all columns of data , pres s CLEAR . Sele ct All columns . […]

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    10-12 Statistics aplet Defining a regression model The Symbolic view includes an expression (Fit1 through Fit5) that defines the regression model, or “fit”, to use for the regression analysis of each two-variable data set. There are three ways to select a regression model: • Accept the d efa ult opt ion to f it th e data to a straight line . […]

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    Statistics aplet 10-13 To define your own fit 1. In Numeric v iew , make sur e is set. 2 . Display the S y mbolic v iew . 3 . Highligh t the F it expr es sion ( Fit1 , et c.) f or the desir ed data set. 4. T y pe in an e xpr essi on and pr ess . The independent variable must be X , and the e xpr essi on mu st not cont ain any unkn o wn v aria bles.[…]

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    10-14 Statistics aplet Computed statistics One-variable When the data set contains an odd number of values, the data set’s median value is no t us ed when calculating Q1 and Q3 in the table above. For example, for the following data set: { 3,5,7,8,15,16,17 } only the first three items, 3, 5, and 7 are used to calculate Q1, and only the last three[…]

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    Statistics aplet 10-15 Two-variable Plotting You can p lot: • histogr ams ( ) • bo x -and-whisk er plots ( ) • scat ter plots ( ) . Once you have ente red your data ( ), defined your data set ( ), and defined your Fit model for two- variable statistics ( SETUP — SYMB ), you can plot your data. You can plot up to five scatter or box-an d-whisk[…]

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    10-16 Statistics aplet To plot statistical data 1. In Sy mbolic v i ew ( ) , se lect ( ) the data sets y ou w ant to plot . 2 . Fo r one -var iable dat a ( ) , selec t the plot type in P lot Setup ( SETUP — PLOT ) . Highli ght ST A TPLOT , pr ess , select e ither Histogram or BoxWhisker , and pr es s . 3 . F or any plot , but espec iall y fo r a hi[…]

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    Statistics aplet 10-17 Scatter Plot Tw o-variable statistics . The numbers below the plot indicate that the cursor is at the first data point for S2, at (1, 6). Press to move to the next data point and display information about it. To connect the data points as they are plotted, checkmark CONNECT in the second page of the Plot Setup. This is not a […]

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    10-18 Statistics aplet Relati ve Error The relative error is a measure of the error between predicted values and actual va lues based on the specified Fit. A smaller number means a better fit. The relative error is stored in a variable named RELERR . The relative error provides a measur e of fit accuracy for all fits, and it does depend on the Fit […]

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    Statistics aplet 10-19 For instance, the data set (1,1 ), (3,9), (4,16), (2,4) would be plotted and traced in the order (1,1), (2,4), (3,9), (4,16). Trouble-shooting a plot If you have problems plotting, check that you have the following: • T he cor r ect or menu label o n (Numer ic vi ew ) . • T he corr ect fit (r egres sion model), if the dat[…]

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    10-20 Statistics aplet Calculating predicted values The functions PREDX and PREDY estimate (predict) values for X or Y given a hypothetical value for the other. The estimation is made based on the curve that has been calculated to fit the data a ccording to the specified fit. Find predicted values 1. In Plot v ie w , dra w the r egr ess ion c ur ve[…]

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    Statistics aplet 10-21 • Enter P RED Y( x-value ) to f ind the pr edicted v alue of the dependent var iable gi ven a h ypothetical independent va riab l e. You can type PREDX and PREDY into the edit line, or you can copy these function names from the MATH menu under the Stat-Two category. HINT In cases where more than one fit curve is displayed, […]

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    HP 39gs English. book Page 22 We dnesday, December 7, 2005 11:24 PM[…]

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    Inference aplet 11-1 11 Inference aplet About the Inference aplet The Inference capabilities include calculation of confidence intervals and hy pothesis tests based on the Normal Z-distribution or Student’s t-distribution. Based on the statistics from one or two samples, you can test hypotheses and find confidence intervals for the following quan[…]

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    11-2 Inferenc e aplet Inference aplet’s SYMB view keys The table below summarizes the options available in Symbolic view. If you choose one of the hypoth esis tes ts, you can choose the alternative hypothesis to test against the null hypothesis. For each test, th ere are three possible choices for an alternative hypothesis based on a quantitative[…]

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    Inference aplet 11-3 Select the inferential method 2. Select the Hypothesis Test infer ential method. Select HYPOTH TEST 3. Define the type of test. Z–Test: 1 μ 4. Select an alternative hypothesis. μ< μ0 Enter data 5. Enter the sample statistics and population parameters. setup-NUM The table below lists the fields in this view for our curre[…]

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    11-4 Inferenc e aplet By default, each field already contains a value. These values constitu te the example database and are expla ined in the feature of this aplet. Display on-line help 6. To display the on-line help, press 7. To close the on-line help, press . Display test results in numeric format 8. Display the test results in numeric format. T[…]

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    Inference aplet 11-5 A calculator produces the following 6 random number s: 0.529, 0.295, 0.95 2, 0.259, 0.925, and 0. 592 Open the Statistics aplet 1. Open the Statistics aplet and reset the current settings. Select Statistics The Statistics aplet opens in the Numeric view. Enter data 2. In the C1 column, enter the random numbers produced by the c[…]

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    11-6 Inferenc e aplet Open Inference aplet 6. Open the Inference aplet and clear current s ettings. Select Inference Select inference method and type 7. Select an inference method. Select CONF INTERVAL 8. Select a distribution statistic type. Select T-Int: 1 μ Set up the interval calculation 9. Set up the interval calculation. Note: The default va[…]

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    Inference aplet 11-7 Import the data 10. Import the data from the Statistics aple t. Note: The data from C1 is disp layed by default. Note: Press to see the statistics before importing them into the Numeric Setup view. Also, if there is more than one ap let based on the Statistics aplet, you are prompted to choose one. 11. Specify a 90% confidence […]

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    11-8 Inferenc e aplet Hypothesis tests You use hypothesis tests to test the validity of hypotheses that relate to the statistical parameters of one or two populations. The tests are base d on statistics of samples of the populations. The HP 39gs hypothesis tests use the Normal Z-distribution or Student’ s t-distribution to calcula te probabilitie[…]

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    Inference aplet 11-9 Results The results are: Two-Sample Z-Test Menu name Z-Test: μ 1– μ 2 On the basis of two samples, each from a separate population, this test measu res the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the mean of the two populations are equal (H 0 : μ 1= μ 2).[…]

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    11-10 Inferenc e aplet Results The results are: One-Proportion Z-Test Menu name Z-Test: 1π On the basis of statistics from a single sample, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the proportion of su ccesses in the two populations is equal: H 0 : π = π 0 […]

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    Inference aplet 11-11 Inputs The inputs are: Results The results are: Two-Proportion Z-Test Menu name Z-Test: π 1 – π 2 On the basis of statistics fr om two samples, each from a different population, the Two-Proportion Z-Test measures the stre ngth of the evidence for a selected hypo thesis against the null hypothesis. The null hypothesis is th[…]

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    11-12 Inferenc e aplet Inputs The inputs are: Results The results are: One-Sample T-Test Menu name T-Test: 1 μ The One-sample T-Test is used when the population standard deviation i s not know n. On the basis of statistics from a single sample, this tes t measures the strength of the evidence for a selected hypothesis against the nu ll hypothesis.[…]

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    Inference aplet 11-13 Inputs The inputs are: Results The results are: Field name Definiti on Sample mean. Sx Sample standard de viation. n Sample size. μ0 Hypothetical population mean. α Significance level. x Result Description Test T T-Test statistic. Prob Probability associated with the T-Test statistic. Critical T Boundary value of T assoc iat[…]

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    11-14 Inferenc e aplet Two-Sample T-Test Menu name T-Test: μ 1 – μ 2 The Two-sample T-Test is used when the population standard deviation i s not know n. On the basis of statistics from two samples, each sample from a different population, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The[…]

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    Inference aplet 11-15 Results The results are: Confidence intervals The confidence interval calculations that the HP 39gs can perform are based on the Normal Z-distribution or Student’s t-distribution. One-Sample Z-Interval Menu name Z-INT: μ 1 This option uses the Normal Z-distributio n to calculate a confidence interval for m, the true mean of[…]

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    11-16 Inferenc e aplet Results The results are: Two-Sample Z-Interval Menu name Z-IN T: μ1 – μ2 This option uses the Normal Z- distribution to calculate a confidence interval for the difference between the means of two populations, μ 1 – μ 2 , when the population standard deviations, σ 1 and σ 2 , are known. Inputs The inputs are: Results[…]

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    Inference aplet 11-17 One-Proportion Z-Interval Menu name Z-INT: 1 π This option uses the Normal Z-distributio n to calculate a confidence interval for the proportion of successes in a population for the case in wh ich a sample of size, n , has a number of successes, x . Inputs The inputs are: Results The results are: Two-Proportion Z-Interval Men[…]

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    11-18 Inferenc e aplet Results The results are: One-Sample T-Interval Menu name T-INT: 1 μ This option uses the Student’s t-distribution to ca lculate a confidence interval for m, the true mean of a population, for the case in which the true population standard deviation, s, is unknown. Inputs The inputs are: n1 Sample 1 si ze. n2 Sample 2 si ze[…]

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    Inference aplet 11-19 Results The results are: Two-Sample T-Interval Menu name T-INT: μ 1 – μ 2 This option uses the Student’s t-distribution to calculate a confidence interval for the difference between the means of two populations, μ 1 – μ 2, when the population standard deviations, s1 and s2, are unknown. Inputs The inputs are: Result […]

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    11-20 Inferenc e aplet Results The results are: Result Description Critical T Critical value for T. μ Min Lower bound for μ 1 – μ 2 . μ Max Upper bound for μ 1 – μ 2 . Δ Δ HP 39gs English. book Page 20 We dnesday, December 7, 2005 11:24 PM[…]

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    Using th e Finance So lver 12-1 12 Using the Finance Solver The Finance Solver, or Fin ance aplet , is available by using the APLET key in your calculator. Use the up and down arrow keys to select the Finance aplet. Your screen should look as follows: Press the key or the soft m enu key to activate the aplet. The result ing screen shows the differe[…]

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    12-2 Using t he Finance Sol ver combined amount earns interest at a certain rate. Financial calculations involvin g compound interest include savings accounts, mo rtgages, pension funds, leases, and annuities. Time Value of Money (TVM) calculations, as the name implies, make use of the notion that a dollar today will be worth more than a dollar som[…]

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    Using th e Finance So lver 12-3 flow diagram shows lease payments at the beginning of each period. The following cash flow diagram shows deposits into an account at the end of each period. As these cash-flow diagrams imply, there are five TVM variables: PV 1 23 4 5 FV Capital i zed value of lease } PM T PM T PM T PM T PM T PV 1 23 4 5 FV PM T PM T […]

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    12-4 Using t he Finance Sol ver Performing TVM calculations 1. Launch the F inanc ial Sol ver as indi cated at the beginning of this secti on . 2 . Use the arr o w k e ys to hi ghlight the diff ere nt f ields and enter the kno wn var iables in the T VM calc ulations , pr essing the soft -menu k ey after enter ing each kno wn value . Be sure that va[…]

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    Using th e Finance So lver 12-5 Example 1 — Loan calculations Suppose you finance the purcha se of a car with a 5-year loan at 5.5% annual intere st, compounded monthly. The purchase price of the car is $19,500, and the down payment is $3,000. What are the r equired monthly payments? What is the largest loan you can afford if your maximum monthly p[…]

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    12-6 Using t he Finance Sol ver Example 2 — Mortgage with balloon payment Suppose you have taken out a 30-year, $150,000 house mortgage at 6.5% annual interest. You expect to sell the house in 10 years, repaying the loan in a balloon payment. Find the size of the balloon payment, the value of the mortgage after 10 years of payment. Solution. The fo[…]

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    Using th e Finance So lver 12-7 Calculating Amortizations Amortization calculations, which also use the TVM variables, determine the amounts applied towards principal and interest in a payment or series of payments. To calculate amortizations: 1. Start the F inance Sol ver as indicated at the beginning of t hi s se ction. 2 . Se t the follo w ing T[…]

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    12-8 Using t he Finance Sol ver 3 . Pr ess the soft menu k ey to amorti z e the new batch o f pay ments . Repeat st eps 1 thr ough 3 as often as needed. Example 4 — Amortization for home mortgage For the results of Example 3, show the amortization of the next 10 years of the mortgage loan. First, press the soft menu key. Then, keeping 120 in the PA[…]

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    Using mathemati cal functions 13-1 13 Using math ematical func tions Math functions The HP 39gs contains many math func tions. The functions are grouped in categories. For example, the Matrix category contains functions for manipulating matrices. The Probability category (shown as Prob. on the MATH menu) contains functions for working with probabil[…]

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    13-2 Using math ematical functions 2 . The list o f func tions (on the r ight) applie s to the c urr ently hi ghlighted category (on the left) . U se and to sw itch bet w een the categor y list and th e func tion lis t . 3 . Hi ghlight the name of the func tion y ou wan t and pr ess . This copi es the fu nctio n name (and an initial par enthesis, i[…]

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    Using mathemati cal functions 13-3 Keyboard functions The most frequently used functions are available directly from the keyboard. Many of the keyboard functions also accept complex numbers as arguments. ,, , Ad d, Subtract, Multiply, Di vide . Also accepts c omplex numbers, lists and matrices. va lu e 1+ va lu e 2 , etc. e x Natural exponential. A[…]

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    13-4 Using math ematical functions 10 x Exponential (antilogarithm). Also accepts complex numbers. 10^ val u e Example 10^3 r etur ns 1000 Common logarithm. Also accepts co mplex numbers. LOG ( val u e ) Example LOG(100) r eturns 2 ,, Sine, cosine, tangent. Inputs and outputs depend on the current angle format (Degrees, Radi ans, or Grads). SIN ( v[…]

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    Using mathemati cal functions 13-5 ATAN A rc tangent: tan –1 x . Output range is from –90° to 90°, 2 π /2 to π /2, or –100 to 100 grad s. Inputs and outputs depend on the current an gle format. Also accept s complex numbers. ATAN ( valu e ) Example ATAN(1) ret u rn s 45 (Degrees mode). Square. Also accept s complex numbers. va lu e 2 Exam[…]

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    13-6 Using math ematical functions Takes the n th root of x . ro ot NTHROOT val ue Example 3 NTHROOT 8 r eturns 2 Calculus functions The symbols for differentiation and integration are available directly form the k eyboard— and S respectively—as well as from the MATH menu. Differentiates expr ession with respect to the vari able of differentiat[…]

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    Using mathemati cal functions 13-7 TAYLOR Calculates the n th order Taylor polynomial of expression at the point where the given variab le = 0. TAYLOR ( e xpr ession , var iable , n ) Example TAYLOR(1 + sin(s1) 2 ,s1,5) w ith Radians angle measur e and F rac tion n umber f ormat (s et in MODE S) r etur ns 1+s1^2-1/3*s1^4 . Complex number functions […]

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    13-8 Using math ematical functions Constants The constants available from the MATH FUNCTIONS menu are mathematical constants. These are described in this section. The hp 39gs has two other menus of constants: program constant s and physical constants. These are described in “Program constants and physical constants” on page 13-24. e Natural log[…]

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    Using mathemati cal functions 13-9 → IN Convert from centimeters to inches. → L Convert from US gallons to liters. → LGAL Convert from liters to US gallons. → KG Convert from pounds to kilograms. → LBS Convert from kilograms to pounds. → KM Convert from miles to kilometers. → MILE Convert from kilometers to miles. → DEG Convert from[…]

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    13-10 Using mathe matical functions EXP Natural exponential. This is more accurate than due to limitations of the power function. EXP ( val u e ) EXPM1 Exponent minus 1 : . This is more accurate than EXP when x is close to zero. EXPM1 ( val ue ) LNP1 Natural log plus 1 : ln( x+1 ). This is more accurate than the natural logarithm function when x is[…]

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    Using mathemati cal functions 13-11 Σ Summation. Finds the sum of expression with respect to variable from initialvalue to finalvalue. Σ ( v ar iable = initial v alue , fin a lval u e , e xp r essio n ) Example Σ (C=1,5,C 2 ) r eturns 5 5 . Matrix functions These functions are for matr ix data stored in matrix variables. See “Matrix func tions[…]

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    13-12 Using mathe matical functions POLYROOT Polynomial roots. Returns the roots for the n th-order polynomial with the specified n +1 coeffici ents . POLYROOT ([ coe ff ic ien ts ]) Example Fo r x 4 +2x 3 –25x 2 –26x+120 : POLYROOT([1,2,-25,-26,120]) r eturns [2,-3,4,-5] . HINT The results of POLYROOT will often not be easily seen in HOME due […]

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    Using mathemati cal functions 13-13 RANDOM Random number (between zero and 1). Produced by a pseudo-random number sequence. The algorithm used in the RANDOM function uses a seed number to begin its sequence. To ensure that two calculators must produce different results for the RANDOM function, use the RANDSEED function to seed different starting va[…]

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    13-14 Using mathe matical functions Examples CEILING(3.2) r eturns 4 CEILING(-3.2) r eturns -3 DEG → RAD Degrees to radians. Converts value from Degrees angle format to Radians angle format. DEG → RAD ( val ue ) Example DEG → RAD( 180 ) r eturns 3.14159265 359 , the va lu e of π . FLOOR Greatest integer less than or equal to value . FLOOR ( […]

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    Using mathemati cal functions 13-15 with a decimal fraction) to H.MMSSs forma t (tim e or angle up to fractions of a second). → HMS ( x.x ) Example → HMS(8.5) r eturns 8.3 INT Integer part. INT ( val ue ) Example INT(23.2) r eturns 23 MANT Mantissa (significant digits) of value . MANT ( valu e ) Example MANT(21.2E34) r eturns 2.12 MAX Maximum. […]

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    13-16 Using mathe matical functions Example % CHANGE(20,50) r eturns 150 %TOTAL Percent total : (100) y/ x . What percentage of x , is y . % TOTAL ( x , y ) Example % TOTAL(20,50) r eturns 250 RAD → DEG Radians to degrees. Converts value from radians to degrees. RAD → DEG ( va lu e ) Example RAD → DEG( π ) r eturns 180 ROUND Rounds value to […]

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    Using mathemati cal functions 13-17 XPON Exponent of value . XPON ( valu e ) Example XPON(123.4) r eturns 2 Two-variable statistics These are functions for use with two-variable statistics. See “Two-variable” on pa ge 10-15. Symbolic functions The symbolic functions are used for symbolic manipulations of expression s. The variables can be forma[…]

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    13-18 Using mathe matical functions QUAD Solves quadratic expression= 0 for variab le and returns a new expression, where variable = newexpression. The result is a general solution th at represents both positive and negative solutions by in cluding the formal variable S1 to represent any sign: + or – . QUAD( ex pre ss i on , variab l e ) Example […]

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    Using mathemati cal functions 13-19 = = Equals (logical test). Returns 1 if true, 0 if false. va lu e 1 == va l ue 2 ≠ Not equal to. Returns 1 if true, 0 if false. va lu e 1 ≠ va l ue 2 > Greater than. Returns 1 if true, 0 if false. va lu e 1 > va l ue 2 ≥ Greater than or equal to. Returns 1 if true, 0 if false. va lu e 1 ≥ va l ue 2 […]

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    13-20 Using mathe matical functions ACSC Arc cosecant. ACSC ( val u e ) ASEC Arc secant. ASEC ( val u e ) COT Cotangent: cos x /sin x . COT ( val u e ) CSC Cosecant: 1/sin x CSC ( val u e ) SEC Secant: 1/cos x . SEC ( val u e ) Symbolic calculations The HP 39gs has the ability to perform symbo lic calculations, for example, symbolic integration and[…]

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    Using mathemati cal functions 13-21 (The | symbol is in the CHARS menu: press CHARS . The = sign is listed in the MATH menu under Symbolic functions.) Symbolic calculations in the Function aplet You can perform symbolic operations i n the Function aplet’s Symbolic view. For example, to find the derivative of a function in the Function aplet’s S[…]

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    13-22 Using mathe matical functions S1 2 . E valuate the f uncti on . 3 . Show the r esult . To find derivatives in the Function aplet’s Symbolic view To find the derivative of the fu nction in the Function aplet’s Symbolic view, you define two functions and define the second function as a derivati ve of the first function. For example, to diff[…]

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    Using mathemati cal functions 13-23 4. Pr ess to display the r esult . Note: Us e the arr ow k ey s to v ie w the entir e functi on . | Y ou coul d also j us t def ine . To find the indefinite integral using formal variables F or ex ample, to f ind t he indefinite integral of use: 1. Enter the func tion . 0 S1 3 X 5 X 2 . Show the r esult f orm at […]

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    13-24 Using mathe matical functions This result is de rived from substituting X = S1 and X = 0 into the original expression found in step 1. However, substituting X = 0 will not always evaluate to zero and may result in an unwanted constant. To see this, consider: The ‘extra’ constant of 6.4 results from the substitution of into ( x –2 ) 5 /5[…]

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    Using mathemati cal functions 13-25 To access the menu of program constants: 1. Pr ess . 2. P r e s s . 3 . Use the ar r o w k e y s to na v igate thr ough the options . 4. Clic k and then to di spla y the number assigned to th e option you selected in th e pr ev ious step. The use of program constants i s illustrated in more detail in “Programmi[…]

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    13-26 Using mathe matical functions Example Suppose you want to know the potential energy of a mass of 5 units according to the equation . 1. Enter 5 2 . Pr ess and then pr ess . 3 . Select light s… f r om the Phy sic s menu . 4. Pres s . The menu c lose s and the v alue of the selec ted constant is cop ied to the edit line . 5 . Complete the equ[…]

  • Страница 179

    Variables an d memory manageme nt 14-1 14 V ariables and memory manag ement Introduction The HP 39gs has approximately 200K of user memory. The calculator uses this memory to store variables, perform computations, and store history. A v a r i a b l e i s a n o b j e c t t h a t y o u c r e a t e i n m e m o r y t o h o l d data. The hp 39gs has two[…]

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    14-2 Variables and m emory management Storing and recalling variables You can store numbers or expressi ons from a previous input or result into variables. Numeric Precision A number stored in a variable is always stored as a 12- digit mantissa with a 3-digit exponent. Numeric precision in the display, however, de pends on the display mode (Standar[…]

  • Страница 181

    Variables an d memory manageme nt 14-3 5 . Enter a name for the v ari able . A 6 . Pres s to stor e the re sult . The results of a calculation can also be stored directly to a variable. For example: 2 5 3 B To recall a value To recall a variable’s value, type the name of the variable and press . A To use variables in calculations You can use vari[…]

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    14-4 Variables and m emory management The VARS menu You use the VARS menu to access all variables in the calculator. The VARS menu is organi sed by category. For each variable category in the left column, there is a list of variables in the right colu mn. You select a variable category and then select a variable in the category. 1. Open the V ARS m[…]

  • Страница 183

    Variables an d memory manageme nt 14-5 5 . Ch oose w h ether to place the var ia ble name or the v ari able v alue on the command line . – Pr ess to indicate that y ou want the v ari able ’s contents t o appear on the command line . – Pr ess to indicat e that y ou w ant the v ari able ’s name to a ppear on the command line . 6 . Pr ess to p[…]

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    14-6 Variables and m emory management 4. Enter data for L2 . 55 48 86 90 77 5 . Pr ess to ac cess HO ME . 6 . Open the v ar iable men u and selec t L1. 7 . Cop y it to th e command line . Note: Because the option is hi ghlighted , the var iable ’s name , r ather than its contents , is copied to the command line . 8. Insert the + operato r and sel[…]

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    Variables an d memory manageme nt 14-7 Home variables It is not possible to store data of one type in a variable of another type. For example, yo u use the Matrix catalog to create matrices. You can crea te up to ten matrices, and you can store these in variables M0 to M9. You cannot store matr ices in variab les other than M0 to M9. Cate- gory A v[…]

  • Страница 186

    14-8 Variables and m emory management Aplet variables Most aplet variables stor e values t hat are uniqu e to a particular aplet. These includ e symbolic expressions and equations (see below), settings for the Plot and Numeric views, and the results of some calculations such as roots and intersections. See the Reference Information chapter for more[…]

  • Страница 187

    Variables an d memory manageme nt 14-9 6 . T o cop y the v alue of the v ar iable in to the edit line , pr es s and pr ess . Memory Manager You can use the Memory Manager to determine the amount of available memory on the calculator. You can also use Memory Manager to organize memory. For example, if the available memory is low, you can use the Mem[…]

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    HP 39gs English. book Page 10 We dnesday, December 7, 2005 11:24 PM[…]

  • Страница 189

    Matrices 15-1 15 M atr ices Introduction You can perform matrix calc ulation s in HOME and in programs. The matrix and each row of a matrix appear in brackets, and the elements and rows are separated by commas. For example, the following matrix: is displayed in the history as: [[1,2,3],[4,5,6]] (If the Decimal Mark mode is set to Comma , then separ[…]

  • Страница 190

    15-2 Matr ices Creating and storing matrices You can create, edit, delete, send, and receiv e matrices in the Matrix catalog. To open the Matrix catalog, press MATRIX . You can also create and store matrices—named or unnamed—-in HOME. For example, the command: POLYROOT([1,0,–1,0])  M1 stores the root of the c omplex vector of length 3 into[…]

  • Страница 191

    Matrices 15-3 To create a ma trix in the Matrix Catalog 1. Pr ess MATRIX to open the Matr i x Ca talog . The Matri x catalog lists the 10 av ailable matr ix v ar iable s, M0 to M9 . 2 . Hi ghlight the matr ix v a r iable name you w ant to use and pres s . 3 . Select the type o f matr i x to c r eate. – For a ve c tor (one -dimensio nal array) , s[…]

  • Страница 192

    15-4 Matr ices A matrix is listed with two dimensions, even if it is 3×1. A vector is listed with the number of elements, such as 3. To transmit a matrix You can send matrices between c alculators just as you can send aplets, programs, lists, and notes. 1. Align the HP 3 9gs calculator s ’ infr ared ports (or connect the calc ulators using an ap[…]

  • Страница 193

    Matrices 15-5 To display a matrix • In the Matri x catalog ( MATRIX ) , highlight the matri x name and pres s . • In HOME , ente r the name of the matr i x v ari able and pr ess . To display one element In HOME, enter matrixname ( row,column ). For example, if M2 is [[3,4],[5,6]] , then M2(1,2) returns 4 . To create a ma trix in HOME 1. Enter t[…]

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    15-6 Matr ices To store one element In HOME, enter, value matrixname ( row, column ). For example, to change the element in the first row and second column of M5 to 728, then display the resulting matrix: 728 M 512 M5 . An attempt to store an element to a row or column beyond the size of the matrix results in an error message. Matrix arithmetic You[…]

  • Страница 195

    Matrices 15-7 3 . Add the matr ices that yo u cre a t e d. M1 M2 To multiply and divide by a scalar For division by a scalar, enter the matrix first, then the operator, then the scalar. For multiplication, the order of the operands does not matter. The matrix and the scalar can be real or complex. For example, to divide the result of the previous e[…]

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    15-8 Matr ices M1 2 To divide by a square matrix For division of a matrix or a vector by a square matrix, the number of rows of the dividend (or th e number of elements, if it is a vector) must equal the number of rows in the divisor. This operation is not a mathematical di vision: it is a left- multiplication by the inverse of th e divisor. M1/M2 […]

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    Matrices 15-9 2 . Cr eate the vec tor of the constants in the linear sys t em . 5 7 1 3 . R etur n to the Matri x Cat al og. MATRIX In this e x ample , the ve ctor y ou cr eated is listed a s M1. 4. Create a ne w matri x . Sele ct Real matrix 5 . Enter the equati on coeff ic ients . 23 4 11 1 4 12 In this e x ample , the matri x y ou c r eated is l[…]

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    15-10 Matr ices Matrix functions and commands About functions • Fu n c t i o n s c a n b e u s e d i n a ny a p l e t o r i n H O M E. T h e y ar e listed in the MA TH menu unde r the Matr i x categor y . T h e y can be used in mathematical e xpr essi ons —pr imar ily in HOME—a s w ell as in pr ogr ams. • F unctions al wa ys pr oduce and di[…]

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    Matrices 15-11 COND Condition Number. Finds the 1-norm (column norm) of a square matrix . COND ( matr i x ) CROSS Cross Product of vector1 with vecto r2 . CROSS ( vec to r 1 , ve ct or 2 ) DET Determinant of a square matrix . DET ( matr i x ) DOT Dot Product of two arrays, matrix1 matrix2 . DOT ( matr i x1, matr i x2 ) EIGENVAL Displays the eigenva[…]

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    15-12 Matr ices LU LU Decomposition. Factors a square matrix into three matrices: {[[ lowertriangular ]],[[ uppertriangular ]],[[ permutation ]]} The uppertriangular has ones on its diagonal. LU ( matr ix ) MAKEMAT Make Matrix. Creates a matrix of dimension rows × columns , using expression to calculate each ele ment. If expression contains the va[…]

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    Matrices 15-13 SPECNORM Spect ral Norm of matrix . SPECNORM ( matri x ) SPECRAD Spectral Radius o f a square matrix . SPECRAD ( matri x ) SVD Singular Value Decomp osition. Factors an m × n matrix into two matrices and a vector: {[[ m × m square orthogonal ]],[[ n × n square orthogonal ]], [ real ]}. SVD ( matr i x ) SVL Singular Values. Returns[…]

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    15-14 Matr ices Trans posi ng a Matrix The TRN function swaps the row-column and column-row elements of a matrix. For instance, e lement 1,2 (row 1, column 2) is swapped with element 2,1; element 2,3 is swapped with element 3,2; and so on. For examp le, TRN([[1,2],[3,4]]) creates the matrix [[1,3],[2,4]] . Reduced-Row Echelon Form The following set[…]

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    Matrices 15-15 The final row of zeros in the reduced-row echelon form of the augmented matrix indicates an inconsistent system with infinite solutio ns. HP 39gs English. book Page 15 We dnesday, December 7, 2005 11:24 PM[…]

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    HP 39gs English. book Page 16 We dnesday, December 7, 2005 11:24 PM[…]

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    Lists 16-1 16 L ists You can do list operations in HOME and in programs. A list consists of comma-separated real or complex numbers, expressions, or matr ices, all enclosed in braces . A list may, for example, contain a sequence of real numbers such as {1,2,3} . (If the Decimal Mark mode is set to Comma , then the separators are periods.) Lists rep[…]

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    16-2 Lists 3 . E nter the values you want i n th e l ist, pressi ng after each one. V alue s can be r eal or comple x numbers (o r an expr ession) . If you enter a calc ulation , it is e valuated and the r esult is inserted in the list . 4. When done , pr ess LIST to see the List catalog, or pr ess to re turn to HO ME . List catalog ke ys The list […]

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    Lists 16-3 List edit keys When you press to create or change a list, the following keys are available to you: Create a list in HOME 1. Enter the list on the edit line . Start and end the list w ith br aces (the shifted and ke ys) and separ ate each element with a comma. 2 . Pr ess to ev a luate and display the list. Immediatel y after typing in the[…]

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    16-4 Lists Displaying and editing lists To display a list • In the List cata log, hi ghlight the list name and pr ess . • In HOME , ente r the name of the list and pr ess . To display one element In HOME, enter listname ( element# ). For example, if L2 is {3,4,5,6}, then L2(2) returns 4 . To edit a list 1. Open th e L ist catalog. LIST . 2 . Pr[…]

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    Lists 16-5 To insert an element in a list 1. Open the List catalog. LIST . 2. P r e s s o r t o highli ght the name of the list y ou wan t to edit (L1, etc .) and pre ss to displa y the list conten ts. New elements are inserted abov e the highlighted positi on . In this example, an element, with the value of 9, is inserted between the first and sec[…]

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    16-6 Lists Deleting lists To delete a list In the List catalog, highli ght the list name and press . You are prompted to confirm that you want to delete the contents of the highlighted list variable. Press to delete the contents. To delete all lists In the List catalog, press CLEAR . Transmitting lists You can send lists to calculators or PCs just […]

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    Lists 16-7 CONCAT(L1,L2) . An ar gument can be either a list v ari able name (su ch as L1) or the actual list . F or e xample , REVERSE({1 ,2,3}) . • If Dec i mal Mark in Modes is set to C omma, u se peri ods to separat e ar guments. F or e x ample , CONCAT(L1.L2) . Common operators like +, –, ×, and / c an take lists as arguments. I f there a[…]

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    16-8 Lists Example In HOME, store {3,5,8,12,17 ,23} in L5 and find the first differences for the list. { 3,5, 8,12 ,1 7 ,2 3 } L 5 L Select Δ LIST L5 MAKELIST Calculates a sequence of elements for a new list. Evaluates expression with variable from begin to end values, taken at increment steps. MAKELIST( expression , va ria b le , begin , end , in[…]

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    Lists 16-9 position of the first occurrence is retu rned. A value of 0 is returned if there is no occurrence of the specified element. POS( list , element ) Example POS ({3, 7, 12, 19},12) returns 3 REVERSE Creates a list by reversing the order of the elements in a list. REVERSE( list ) SIZE Calculates the number of elements in a list. SIZE( list )[…]

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    16-10 Lists 2 . In HOME , st or e L1 into C1. Y ou w ill then be able to see the list data in the Numer ic vi e w of the Statis tics aplet . L1 C1 3 . S tart the Statis tic s aplet , and select 1-v ar ia ble mode (pr ess , i f necess ary , to displa y ) . Sele ct Statistics Note: Y our list values ar e no w in column 1 (C1) . 4. In the Sy mbolic v […]

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    Notes and sketches 17-1 17 Notes and sk etc hes Introduction The HP 39gs has text and pi cture editors for entering notes and sketche s. • E ach a plet has its o wn independent Note v iew and Sk etch vi e w . Not es and sk etc hes that y ou cr eate in these vi e ws ar e assoc iated w ith t he aplet. When y ou sa v e the aplet , or send it to anot[…]

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    17-2 Notes and sketches Note edit keys Key M e a n i n g Space key for text entry. Displays next page of a multi-pa ge note. Alpha-lock for letter entry. Lower-case alpha-loc k for letter entry. Backspaces cursor and deletes character. Deletes current character. Starts a new line. CLEAR Erases the entire note. Menu for entering variable names, and […]

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    Notes and sketches 17-3 Aplet sketch view You can attach pictures to an aplet in its Sketch view ( SKETCH ). Y our wo rk is au tomaticall y sav e d w ith th e aplet . Press an y other vi e w ke y or to e x it the Sk etch v ie w Sketch keys To dr aw a li ne 1. In an aplet, pr ess SKETCH f or the Sk etch v iew . 2 . In Sk etch v iew , pr ess and mo v[…]

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    17-4 Notes and sketches To draw a box 1. In Sk etc h vi e w , pres s and mov e the c urs or to wher e you w ant any corner of the bo x to be. 2. P r e s s . 3 . Mo v e the cur sor to mar k the opposite cor ner for the bo x . Y ou can adj ust the si ze of the bo x by mo v ing the cu rs o r . 4. Pres s to f inish the bo x . To draw a circle 1. In Ske[…]

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    Notes and sketches 17-5 To label parts of a sketch 1. Pr ess and type the te xt on the edit line . T o lock the Alpha shift on , pre ss (for upper case) or (for lo w er cas e) . T o mak e the label a smalle r c har acte r si z e , turn o ff befo r e pres sing . ( i s a toggle betw een small and lar ge f ont si z e) . The smaller c har acter si z e […]

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    17-6 Notes and sketches To import a graphics variable You can copy the contents of a graphics variable into the Sketch view of an aplet. 1. Open the Sketch v iew of the aplet ( SKETCH ). T he graphi c w ill be copied her e. 2 . Pr ess , . 3 . Highlight Graphic , then pr ess and highligh t the name of the v ari able ( G1 , etc .) . 4. Pres s to r ec[…]

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    Notes and sketches 17-7 4. W r ite y our note . See “Note e dit ke ys ” on page 17 — 2 for mor e infor mation on the entry and editing of notes. 5 . When yo u are f inis hed , press or an aplet ke y to e x it Notepad . Y our wor k is automaticall y sav ed. Notepad Catalog keys Key M e a n i n g Opens the selected note for editing. Begins a new […]

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    17-8 Notes and sketches To import a note You can import a note from the Notepad into an aplet’s Note view, and vice versa. Supp ose you want to copy a note named “Assignments” fr om the Notepad into the Function Note view: 1. In the Func tion aplet , display the No te v ie w ( NOTE ). 2 . Pr ess , highlight Notepad in the left column, then hi[…]

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    Programming 18-1 18 Pr ogr amming Introduction This chapter describes how to pro gram using the hp 39gs. In this chapter you’ll learn about: • using the Pr ogram catalog to c r eate and edit pr ogr ams • pr ogr amming commands • stor ing and retr ie v ing var iables in pr ograms • pr ogr amming var iables. HINT More informatio n on progra[…]

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    18-2 Programming Example RUN GETVALUE: RUN CALCULATE: RUN » SHOW ANSWER » : This program is separated into three main tasks, each an individual program. Within each progr am, the task can be simple—or it can be di vided further into other programs that perform smaller tasks. Program catalog The Program catalog is wher e you create, edit[…]

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    Programming 18-3 Program catalog k eys The program catalog keys are: Key M e a n i n g Opens the highlighted program for editing. Prompts for a new program name, then opens an empty program. Transmits the highlighted program to another HP 39gs or to a disk drive. Receives the highlighted program from another HP 39gs or from a disk drive. Runs the h[…]

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    18-4 Programming Creating and editing programs Create a new program 1. Pr ess PROGR M to open the Pr ogr am catalog . 2. P r e s s . The HP 3 9gs pr ompts yo u fo r a n a m e. A pr ogr am name can contain spec ial char acters , such as a space . Ho we ve r , if y ou use spec ial char acters and then run the pr ogr am b y typing it in HOME , y ou mu[…]

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    Programming 18-5 2 . On the left, u se or to highligh t a command category , then pr ess to ac cess the commands in the category . Select the command that y ou w ant . 3 . Pr ess to paste the command into the pr ogram editor . Edit a program 1. Pres s PR OGRM to open the Pr ogram catalog. 2 . Use the arr o w k e y s to hi ghlight the pr ogram y ou […]

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    18-6 Programming Editing keys The editing keys are: Key M e a n i n g Inserts the character at the editing point. Inserts space into text. Display s previous page of the program. Displays next page of the program. Moves up or down one line. Moves right or left one character. Alpha-lock for letter entry. Press A…Z to lock lower case. Backspaces cu[…]

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    Programming 18-7 Using programs Run a program From HOME, type RUN program_name. or From the Program catalog, highlight the program you want to run and press Regardless of where you star t the program, all programs run in HOME. What you see will differ slightly depending on where you started the program. If you start the program from HOME, the HP 39[…]

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    18-8 Programming Copy a program You can use the following procedure if you want to make a copy of y our work before editing—or if you want to use one program as a template for another. 1. Pr ess PROGR M to open the Pr ogr am catalog . 2. P r e s s . 3 . T ype a ne w f ile name, then c hoose . T he Progr am Edito r opens with a ne w pr ogr am . 4.[…]

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    Programming 18-9 Delete a program To delete a program: 1. Pr ess PROGRM to open the Progr am catalog. 2 . Highligh t a pr ogr am to delet e , then pr ess . Delete all programs You can delete all programs at once. 1. In the Progr am catalog, pr ess CLEAR . 2. P r e s s . Delete the contents of a program You can clear t he contents of a program witho[…]

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    18-10 Programming 4. D e v elop a pr ogram that u ses the SE TVI EW S command to modify the aplet’s VIEW S menu . The menu opti ons pr o v ide links to ass oc iated pr ograms . Y ou can spec i fy an y other progr ams that you w ant tr ansfe rr ed with the aplet . See “SETVIEW S” on page 18-14 for inf ormati on on the command . 5 . Ensur e tha[…]

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    Programming 18-11 Save the aplet 1. Open the F uncti on aplet and sa ve it as “EXP ERIMENT ” . The ne w aplet appear s in the Aplet library . Select Function EXP ERIMENT 2 . Cr eate a pr ogr am called EXP .ME1 with contents as show n. T his pr ogr am conf igur es the plot r anges, then r uns a pr ogr am that allo ws y ou to s et the angle f orm[…]

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    18-12 Programming 6 . Open the Pr ogram cat alog and cr eate a progr am named “EXP .S V” . Include the f ollo w ing code in the pr ogr am. E a c h entry line after the command SE T VIEW S is a tri o that consists of a VIEW S menu te xt li ne (a space indicate s none), a progr am name , and a number that def ines the v ie w to go to afte r the p[…]

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    Programming 18-13 ’ ’ ’ ’ ;’ ’ EXP.ANG’ ’ ;0 ; The pr o gr am EXP .ANG is a small routine that is called by other pr ogr ams that the aplet us es . This e ntry spec ifi es that the pr ogr am EXP.ANG is transfer r ed w hen the aplet is tr ansfer r ed, bu t the space in the fir st quotes en sur es that no entry appears on the menu . ?[…]

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    18-14 Programming Aplet commands CHECK Checks (selects) the correspon ding function in the current aplet. For example, Check 3 would check F3 if the current aplet is Function. T hen a checkmark would appear next to F3 in Symbolic view, F3 would be plotted in Plot view, and evaluated in Numeric view. CHECK n : SELECT Selects the named aplet and ma k[…]

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    Programming 18-15 options u se , or the pr ogr am that def ines the a plet’s VIEW S menu . • Y ou can inclu de a “Start ” optio n in the VIEW S men u to spec if y a pr ogr am that y ou w ant to run auto maticall y when the aplet s tarts. This pr ogram typically sets up the aplet’ s initial confi guration . T he S T AR T option on the men […]

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    18-16 Programming ProgramName ProgramName is the name of the program that runs when the corresponding menu entry is selected. All pr ograms that are identified in the aplet’s SETV IEWS command are transferred when the aplet is transmitted. ViewNumber V iewNumber is the number of a view to start after the program finishes runn ing. For example, if[…]

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    Programming 18-17 View numbers The Function aplet views are numbered as follows: View numbers from 15 on will vary according to the parent aplet. The list shown above is for the Function aplet. Whatever the normal VIEWS menu for the parent aplet, the first entry will become number 1 5, the second number 16 and so on. UNCHECK Unchecks (unselects) th[…]

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    18-18 Programming Example 1  A : IF A==1 THEN MSGBOX » A EQUALS 1″ : END: IF… THEN… ELSE… END Executes the true-clause sequence of commands if the test- clause is true, or the false-clause se quence of commands if the test-clause is false. IF test-clause THEN true-clause ELSE fals e-clause END Example 1  A : IF A==1 THEN MSGBO[…]

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    Programming 18-19 IFERR…THEN…ELSE…END allows a program to intercept error conditions that otherwise would cause the program to abort. Its syntax is: IFERR tr ap-cla us e THEN clause _1 ELSE clause _2 END : Example IFERR 60/X  Y: THEN MSGBOX «Error: X is zero.»: ELSE MSGBOX «Value is «Y: END: RUN Runs the named program. […]

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    18-20 Programming Example ARC 0;0;2;0;2 π : FREEZE: Dr a w s a c irc le center ed at (0, 0) of r adius 2 . T he FREEZE command causes the c ir cle to r emain di spla ye d on t he sc reen until y ou pr ess a k ey . BOX Draws a box with diagonally opposite corners ( x1,y1 ) and ( x2,y2 ). BOX x1 ; y1 ; x2 ; y2 : Example BOX -1;-1;1;1: FREEZE: Dr a w[…]

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    Programming 18-21 Example TLINE 0;0;3;3: Er ase s pr e v iou sly dr a wn 4 5 degr ee line fr om (0, 0) to (3, 3) , or dr aw s that line if it doesn’t alr eady e xist . Graphic commands The graphic commands use th e graphics variables G0 through G9—or the Page variable from Sketch—as graphicname arguments. The position argument takes the form […]

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    18-22 Programming will superimpose G1 onto G0 starting a position (1,1), where the position is given in terms of the current axes settings, not as a pixel position. GROBXOR Usin g the logical XOR, superimposes graphicname2 onto graphicname1 . The upper left corner of graphicname2 is placed at position . GROBXOR gr aphi cname1 ; ( pos ition) ; gr ap[…]

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    Programming 18-23 ZEROGROB Creates a blank graphic with given width and height , and stores i t in graphicname . ZEROGROB gr aphicname ; wid t h ; heigh t : Loop commands Loop hp allow a program to execute a routine repeatedly. The HP 39gs has three loop structures. The example programs below illustrate each of these structures incrementing the var[…]

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    18-24 Programming Note that the STEP parameter is optional. If it is omitted, a step value of 1 is assumed. BREAK Terminates loop. BREAK: Matrix commands The matrix commands take variables M0–M9 as arguments. ADDCOL Add Column. Inserts values into a column before column_number in the specified matrix . You enter the values as a vector. The values[…]

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    Programming 18-25 RANDMAT Creates random matrix with a specified number of rows and columns and stores the result in name ( name must be M0…M9 ). The entries will be integers ranging from –9 to 9. RANDMAT name ; rows ; columns : REDIM Redimensions the specified matrix or v ector to size . For a matrix, size is a list of two integers {n1,n2} . F[…]

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    18-26 Programming Print commands These commands print to an HP infrared printer, for example the HP 82240B printer. PRDISPLAY Prints the contents of the display. PRDISPLAY: PRHISTORY Prints all objects in the hi story. PRHISTORY: PRVAR Prints name an d contents of variablename . PRVAR va ri ablename : You can also use the PRVAR comman d to print th[…]

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    Programming 18-27 Example 3  A:CHOOSE A; «COMIC STRIPS»; «DILBERT»; «CALVIN&HOBBES»; «BLONDIE»: CLRVAR Clears the specified va riable. The syntax is: CLR V AR v ari able : Example If you have stored {1,2,3,4} in variable L1, entering CLVAR L1 w ill clear L1. DISP Displays textitem in a row of the displ[…]

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    18-28 Programming Example DISPXY –3.5;1.5;2;»HELLO WORLD»: DISPTIME Displays the current date and time. DISPTIME To set the date and time, simply store the correct settings in the date and time variables. Use the following formats: M.DDYYYY for the date and H.MMSS for the time. Examples 5.152000  DATE( sets the date to May 15, 2000) […]

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    Programming 18-29 GETKEY Waits for a key, then st ores the k eycode rc.p in name, where r is row number, c is column number, and p is key- plane number. The key-planes numbers are: 1 for unshifted; 2 for shifted; 4 for alpha-shifted; and 5 for both alpha-shifted and shifted . GETKEY name : INPUT Creates an input form with a title bar and one field.[…]

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    18-30 Programming PROMPT Displays an input box with name as the title, and prompts for a value for name . name can be a variable such as A…Z, θ , L1…l9, C1…C9 or Z1…Z9. PROMPT nam e : WAIT Halts program execution for the specified number of seconds. WAIT sec onds : Stat-One and Stat-Two commands The following commands are used for analyzin[…]

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    Programming 18-31 Datasetname can be SI, S2,…, or S5 . Datasetname must include at least two pairs of data points. DO2VSTATS datasetname : SETDEPEND Sets datasetname dependent column . Datasetname can be S1, S2, …, or S5 and column can be C0–C9. SETDEPEND datasetname ; column : SETINDEP Sets datasetname independent column . Datasetname can be[…]

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    18-32 Programming Plot-view variables Area Function Contains the last value found by the Area function in Plot- FCN menu. Axes All Aplets Turns axes on or off. From Plot Setup, check (o r uncheck) AXES . or In a program, type: 1  Axes —to turn axes on (def ault) . 0  Axes —to turn ax es off . Connect Function Parametric Polar Solve Statis[…]

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    Programming 18-33 Grid All Aplets Turns the background grid in Plot view o n or off. From Plot setup, check (or uncheck) GRID . or In a program, type 1  Grid to tur n the gr id on . 0  Grid to tur n the gri d off (def ault). Hmin/Hmax Statistics Defines minimum and maximum values for histogram bars. From Plot Setup for one-variable statistics[…]

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    18-34 Programming Isect Function Contains the last value found by the Intersection function in the Plot-FCN menu. Labels All Aplets Draws labels in Plot view showing X and Y ranges. From Plot Setup, check (o r uncheck) Labels or In a program, type 1  Labels —to turn labels on . 0  Labels —to turn labels o ff (def ault) . Nmin / Nmax Seque[…]

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    Programming 18-35 S1mark–S5mark Statistics Sets the mark to use for scatter plots. From Plot Setup for two-variable statistics, S1mark- S5mark , then choose a mark. or In a program, type n  S1mark wh ere n is 1,2,3,…5 SeqPlot Sequence Enables you to choose types of sequence plot: Stairstep or Cobweb. From Plot Setup, select SeqPlot , then ch[…]

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    18-36 Programming Umin/Umax Polar Sets the minimum and maxi mum independent values. Appears as the URNG field in the Plot Setup input form. From the Plot Setup input form, enter values for URNG . or In a program, type  Umin  Umax wher e Ustep Polar Sets the step size for an independent v ariable. From the Plot Setup input form, enter values f[…]

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    Programming 18-37 Tstep Parametric Sets the step size for the independent variable. From the Plot Setup input form, enter values for TSTEP . or In a program, type n  Tstep wh ere Xcross All Aplets Sets the horizontal coordinate of the c rosshairs. Only works with TRACE off. In a program, type n  Xcross Ycross All Aplets Sets the vertical coor[…]

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    18-38 Programming  Xmin  Xmax whe re Ymin / Ymax All Aplets Sets the minimum and maximum vertical values of the plot screen. Appears as the YRNG fields (vertical range) in the Plot Setup input form. From Plot Setup, enter the values for YRNG . or In a program, type  Ymin  Ymax whe re Xzoom All Aplets Sets the horizontal zoom factor. Fro[…]

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    Programming 18-39 Symbolic-view variables Angle All Aplets Sets the angle mode. From Symbolic Setup, choose Degrees , Radia ns , or Grads for angle measure. or In a program, type 1  Angle —for De grees. 2  Angle —for Radian s. 3  Angle —for Grads. F1…F9, F0 Function Can contain any expression. Independent variable is X . Example &a[…]

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    18-40 Programming S1fit…S5fit Statistics Sets the type of fit to be used by the FIT operation in drawing the regression line. From Symbolic Setup view, specify the fit in the field for S1FIT, S2FIT, etc. or In a program, store one of the fo llowing constant numbers or names into a variable S1fit , S2fit , etc. 1 Linear 2 LogFit 3 ExpFit 4 Power 5[…]

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    Programming 18-41 Numeric-view variables The following aplet variabl es control the Numeric view . The value of the variable appl ies to the current aplet only. C1…C9, C0 Statistics C0 through C9 , for column s of data. Can contain lists. Enter da ta in the N umeric view or In a program, type LIST  C n wh ere n = 0, 1, 2, 3 … 9 Digits All Ap[…]

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    18-42 Programming Note that if Fraction or M ixed Fraction is chosen, the setting will be ignored when labeling axes in Plot view. A setting of Scientific will be used instead. Example Scientific  Format or 3  Format NumCol All Aplets except Statistics aplet Sets the column to be highlighted in Numeric view. In a program, type n  NumCol wh[…]

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    Programming 18-43 NumStep Function Parametric Polar Sequence Sets the step size (increment value) for an independent varia ble in N umeri c view. From Num Setup, enter a value for NU MSTEP . or In a program, type n  NumStep wh ere NumType Function Parametric Polar Sequence Sets the table format. From Num Setup, choose Automatic or Build You r Ow[…]

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    Note variables The following aplet variable is available in Note view. NoteText All Aplets Use NoteText to recall text previously entered in Note view. Sketch variables The following aplet variables are available in Sk etch view. Page All Aplets Sets a page in a sketch set. The graphics can be viewed one at a time using the and keys. The Page var i[…]

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    Extending aplets 19-1 19 Extending aplets Aplets are the application environments where you explore different cla sses of mathematical operations. You can extend the capabili ty of the HP 39gs in the following ways: • Cr eate ne w aplets , based on e x isting aplets , w ith spec ifi c conf igur ations suc h as angle measur e, gr aphical or tabula[…]

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    19-2 Ext ending aple ts 1. Open the Solv e aplet and save it under the n e w name . Solve | T R I A N G L E S 2 . E nte r t h e fo ur form ul as : θ O H θ A H θ OA AB C 3 . Dec ide whether y ou want the a plet to oper ate in Degr ees , R adians , or Gr ads. MODES Degrees 4. Vie w the Aplet L i br ar y . The “ TRIANGLE S” aplet is listed in t[…]

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    Extending aplets 19-3 Using a customized aplet To use the “T riangles” aplet, simply s elect the appropriate formula, change to the Numeric view and solve for the missing variable. Find the length of a ladder leaning against a vertical wall if it forms an angle of 35 o with the hori zontal and extends 5 metres up the wall. 1. Select the aplet .[…]

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    19-4 Ext ending aple ts Annotating an aplet with notes The Note view ( NOTE ) attaches a note to the current aplet. See Chapter 17, “Notes and sketc hes”. Annotating an aplet with sketches The Sketch view ( SKETCH ) attaches a picture to the current aplet. See chapter 17, “Notes and sketches”. HINT Notes and s k et c hes th at y ou atta c h[…]

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    Extending aplets 19-5 To transmit an aplet 1. Connect the P C or aplet disk dr iv e to the calc ulator by cable or align the tw o calc ulators ’ infr ar ed ports by matc hing up the tr iangle marks on the r ims of the calc ulators . P lace the calculato rs no mor e than 4 inches (10 cm) apar t. 2 . Sending calc ulator : Open the L ibrary , highli[…]

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    19-6 Ext ending aple ts Note : ch oose a disk dri ve option if y ou are using the hp3 9gs connecti vity kit to tr ansfer the a plet . Hi ghlight y our selec tion and pr ess . The T r ansmit annu nc iator— —i s display e d until tr ansmis sion is co mplet e . If you are using the PC Connectivity Kit to download aplets from a PC, you will see a l[…]

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    R-1 R Re fer ence inf ormation Glossary aplet A small application, limited to one topic. The built-in aplet types are Function, Parametric , Polar, Sequence, Solve, Statistics, Inference, Finance, Trig Explorer, Quad Explorer, Linear Solver and Triangle Solve. An aplet can be filled with the data and solutions for a specific problem. It is reusable[…]

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    R-2 list A set of values separated by commas (periods if the Decimal Mark mode is set to Comma ) and enclosed in braces. Lists are commonly used to enter statistical data and to evaluate a function with multiple values. Created and manipulate d by the List editor and catalog. matrix A two-dimensional ar ray of values separated by commas (periods if[…]

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    R-3 Resetting the HP 39gs If the calculator “locks up” and seems to be stuc k, you must reset it. This is much like resetting a PC. It cancels certain operations, restores ce rtain conditio ns, and clears temporary memory locations. However, it does not clear stored data (variables, ap let databases, programs) unless you use the proced ure, “[…]

  • Страница 276

    R-4 If the calculator does not turn on If the HP 39gs does not turn on follow the steps below until the calculator turns on. You may find that the calculator turns on before you have completed the procedure. If the calculator still does not turn on, please contact Customer Support for further information. 1. Pr ess and hold the ke y for 10 seconds.[…]

  • Страница 277

    R-5 To install the main batteries a. Slide up the battery compartment cove r as illustrated. b. Insert 4 new AAA (LR03) batteries into the main compartment. Make sure each battery is inserted in the indicated direction. To install the backup battery a. Press down the holder. Push the plate to the shown direction and lift it. b. Insert a new CR2032 […]

  • Страница 278

    R-6 Variables Home variables The home variables are: Categor y Available name Complex Z1 … Z9 , Z0 Graphic G1 … G9 , G0 Library Function Parametric Polar Sequence Solve Statistics User-named List L1 … L9 , L0 Matrix M1 … M9 , M0 Modes Ans Date HAngle HDigits HFormat Ierr Time Notepad User-named Program Editline User-named Real A…Z, θ HP […]

  • Страница 279

    R-7 Function aplet variables The function aplet variables a re: Category Av ailable name Plot Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Simult Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Plot-FCN Area Extremum Isect Root Slope Symbolic Angle F1 F2 F3 F4 F5 F6 F7 F8 F9 F0 Nume ric Digits Format NumCol NumFo[…]

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    R-8 Parametric aplet variables The parametric aplet variables are: Categor y Available name Plot Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Tmin Tmax Tracing Tstep Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom Symbolic Angle X1 Y1 X2 Y2 X3 Y3 X4 Y4 X5 Y5 X6 Y6 X7 Y7 X8 Y8 X9 Y9 X0 Y0 Numeric Digits Format NumCol NumFo[…]

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    R-9 Polar aplet variables The polar aplet variables are: Category Av ailable names Plot Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Umin Umax θ step Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle R1 R2 R3 R4 R5 R6 R7 R8 R9 R0 Nume ric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep […]

  • Страница 282

    R-10 Sequence aplet variables The sequence aplet variables are: Categor y Available name Plot Axes Coord Grid Indep InvCross Labels Nmin Nmax Recenter SeqPlot Simult Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom Symbolic Angle U1 U2 U3 U4 U5 U6 U7 U8 U9 U0 Numeric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep Num[…]

  • Страница 283

    R-11 Solve aplet variables The solve aplet variables are: Category Av ailable name Plot Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle E1 E2 E3 E4 E5 E6 E7 E8 E9 E0 Nume ric Digits Format NumCol NumRow Note NoteText Sketc h Page PageNum HP 39gs English.[…]

  • Страница 284

    R-12 Statistics aplet variables The statistics aplet variables are: Categor y Available name Plot Axes Connect Coord Grid Hmin Hmax Hwidth Indep InvCross Labels Recenter S1mark S2mark S3mark S4mark S5mark StatPlot Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle S1fit S2fit S3fit S4fit S5fit Numeric C0,…C9 Digits F[…]

  • Страница 285

    R-13 MATH menu categories Math functions The math functions are: Category Av ailable name Calculus TAYLOR Complex ARG CONJ IM RE Constant e i MAXREAL MINREAL π Hyper b. ACOSH ASINH ATANH COSH SINH TANH ALOG EXP EXPM1 LNP1 List CONCAT Δ LIST MAKELIST π LIST POS REVERSE SIZE Σ LIST SORT Loop ITERATE RECURSE Σ ∂ ∫ HP 39gs English. book Page 1[…]

  • Страница 286

    R-14 Matrix COLNORM COND CROSS DET DOT EIGENVAL EIGENVV IDENMAT INVERSE LQ LSQ LU MAKEMAT QR RANK ROWNORM RREF SCHUR SIZE SPECNORM SPECRAD SVD SVL TRACE TRN Polynom. POLYCOEF POLYEVAL POLYFORM POLYROOT Prob. COMB ! PERM RANDOM UTPC UTPF UTPN UTPT Real CEILING DEG → RAD FLOOR FNROOT FRAC HMS → → HMS INT MANT MAX MIN MOD % %CHANGE %TOTAL RAD ?[…]

  • Страница 287

    R-15 Program constants The program constants are: Tests < ≤ = = ≠ > ≥ AND IFTE NOT OR XOR Trig ACOT ACSC ASEC COT CSC SEC Category Av ailabl e name (Continued) Category Av ailable name Angle Degrees Grads Radians Format Standard Fixed Sci Eng Fraction SeqPlot Cobweb Stairstep S1…5fit Linear LogFit ExpFit Power Trigonometric QuadFit Cu[…]

  • Страница 288

    R-16 Physical Constants The physical constants are: Categor y Available Na me Chemist • Avogadro ( A v ogadr o ’s Number , NA) • Boltz . (Boltmann, k) • mol. vo… (molar v olume , Vm) • univ gas (uni ver sal gas , R) • std temp (standard temper a tur e , St d T ) • std pres (standar d pr essur e, St d P ) Phyics • Stef Bolt (Ste fa[…]

  • Страница 289

    R-17 Program commands The program commands are: Category Command Aplet CHECK SELECT SETVIEWS UNCHECK Branch IF THEN ELSE END CASE IFERR RUN STOP Drawing ARC BOX ERASE FREEZE LINE PIXOFF PIXON TLINE Graphic DISPLAY → → DISPLAY → GROB GROBNOT GROBOR GROBXOR MAKEGROB PLOT → → PLOT REPLACE SUB ZEROGROB Loop FOR = TO STEP END DO UNTIL END WHIL[…]

  • Страница 290

    R-18 Status messages Stat-Two DO2VSTATS SETDEPEND SETINDEP Category Command (Continued) Messag e Meaning Bad Argument Type Incorrect input for this operation. Bad Argument Value The value is out of range for this operation. Infinite Result Math exception, such as 1/0. Insufficient Memory You must recover some memory to continue operation. Delete on[…]

  • Страница 291

    R-19 Invalid Syntax The function or command you entered does not include the proper arguments or order of arguments. The delimiters (parentheses, commas, periods, and semi-colons) must also be correct. Look up the function name in the index to find its proper syntax. Name Conflict The | (wher e) function attempted to assign a value to the variable […]

  • Страница 292

    HP 39gs English. book Page 20 We dnesday, December 7, 2005 11:24 PM[…]

  • Страница 293

    W-1 L imited W arr anty HP 39gs Graphing Calculator; Warranty peri od: 12 months 1. HP war r ants to you , the end- us er cu stomer , t hat HP har dw are , acc es sor ies and su pplies w i ll be fr ee fr om def ects in mater ials and w ork manship after the date of pur chase , for the peri od spec if ied abo v e . If HP r ecei ves notice of such de[…]

  • Страница 294

    W-2 6 . HP MAKE S NO O THER E XPRE S S W ARRANTY OR CONDI T ION WHET HER WRI TTEN OR OR AL . T O THE EXTENT ALL O WED B Y L OCAL LA W , ANY IMP LIED W ARRANTY OR CONDI TION OF MERCHANT ABILITY , S A T ISF A CT OR Y QU ALITY , OR FI TNE SS F OR A P AR TICUL AR P URP OSE I S LIMITED T O THE DUR A TION OF THE EXP RE S S W A RRANTY SET F OR TH ABO VE .[…]

  • Страница 295

    W-3 Service Europe Country : Telephone numbers Au str ia +4 3-1-3 60 2 77120 3 Belgium + 3 2 — 2 — 712 6 219 D e n m a r k + 45 — 8 -2 33284 4 Ea s te r n Eu ro p e countr ies +4 20-5- 414 2 2 5 2 3 Fi n l a n d + 35 — 8964 0 0 0 9 F r ance +3 3-1 — 4 9 9 3 9006 German y +4 9-6 9-9 5 30 7103 Gr eece +4 20 -5- 414 2 2 5 2 3 Holland +31- 2 -06 54 5 3[…]

  • Страница 296

    W-4 P lease logon to http://www .hp.com f or t he lat est se r v ice and supp ort info rmati on .h L.Ame r ic a Country: T elephone nu mbers Ar gentina 0 -810 -5 5 5-5 5 20 Bra zil Sao P aulo 3 7 4 7 — 77 99; RO T C 0 -800 -15 77 51 M e xi c o M x C i t y 5 258 — 9 922; RO T C 01-800 — 4 7 2 -66 84 Ven e z u e l a 0 8 0 0 — 4 7 46 — 8368 Chi le 800[…]

  • Страница 297

    W-5 Regulatory infor mation Federal Communications Commission Noti ce This equipment has been tested and found to comply with the limits for a Class B digital dev ice, pursuant to Part 15 of the FCC Rules. These limi ts are designed to provide reasonable protection agains t harmful interference in a residential installation. This equipment generate[…]

  • Страница 298

    W-6 Houston, Texas 77269-2000 Or, call 1-800-474-6836 For questions regarding this FCC declarati on, contact: Hewlett-Packard Company P. O. Box 692000, Mai l Stop 510101 Houston, Texas 77269-2000 Or, call 1-281-514-3333 To identify this produc t, refer to the part, series, or model number found on the product. Canadian Notice This Class B digital a[…]

  • Страница 299

    W-7 Korean Notice Disposal of Waste Equipment by Users in Private Household in the European Union This symbol on the product or on its packaging indicates that this product must not be disposed of with your other household waste. Instead, it is your responsibility to dispose of your waste equipment by handing it over to a designated collection poin[…]

  • Страница 300

    HP 39gs English. book Page 8 Wed nesday, December 7, 2 005 11:24 PM[…]

  • Страница 301

    I-1 Index A absolute value 13-5 add 13-3 algebraic entry 1-19 alpha characters typing 1-6 alphabetical so rting 19-6 angle measure 1-10 in statistics 10-12 setting 1-11 animation 17-5 creating 17 -5 annunciators 1-3 Ans (last answer) 1-24 antilogarithm 13-4 , 13-9 aplet attaching notes 19-4 clearing 19-3 copying 19-4 definition of R-1 deleting 19-6[…]

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    I-2 C calculus operat ions 13-7 catalogs 1-30 chronological sorting 19-6 circle dra wing 17-4 clearing aplet 19-3 character s 1-22 display 1- 22 display history 1-2 5 edit line 1-22 lists 16-6 plot 2-7 cobweb graph 6-1 coeffi cients polynomial 13-11 columns changing position 18-25 combinations 13 -12 commands aplet 18-14 branch 18-17 definition of […]

  • Страница 303

    I-3 definite integral 13-6 deleting aplet 19-6 lists 16-6 matrices 15-5 programs 18- 9 statistical data 10-11 delimiters, programming 18-1 derivatives definition of 13-6 in Function aplet 13-22 in Home 13-21 determinant square matrix 15-11 differentiation 13-6 display 18-21 adjusting contrast 1-2 annunciator line 1-2 capture 18-21 clearing 1-2 date[…]

  • Страница 304

    I-4 font size change 3-8 , 17-5 forecasting 10-20 fraction number format 1-1 1 full-precision display 1-10 function analyze graph with FCN tools 3-4 definition 2-2 , R-1 entering 1-19 gamma 13- 12 intersection point 3-5 math menu R-13 slope 3-5 syntax 13-2 tracing 2-8 Function aplet 2-20 , 3-1 function variables area 18-32 axes 18-32 connect 18-32 […]

  • Страница 305

    I-5 EXPM1 13-10 LNP1 13-10 SINH 13-9 TANH 13-9 hypothesis alternative 11-2 inference tests 11-8 null 11-2 tests 11-2 I i 13-8 implied multiplication 1-20 importing graphics 17-6 notes 17-8 increasing display contrast 1-2 indefinite integral using symbolic variables 13-23 independent values adding to table 2-18 independent variable defined for Traci[…]

  • Страница 306

    I-6 generate a series 16-8 list function syntax 16-6 list variables 16-1 returning position of element in 16-8 revers ing orde r in 16-9 sending and receiving 16-6 sorting elements 16-9 storing elements 16-1 , 16-4 , 16-5 storing one element 16 -6 logarithm 13-4 logarithmic fit 10-13 functions 13-3 logical operators AND 13-19 equals (logical test) […]

  • Страница 307

    I-7 singular value decomposition 15-13 singular values 15-13 size 15-12 spectral norm 15-13 spectral radius 15-13 start Matrix Editor 18-2 4 storing elements 15-3 , 15-5 storing matrix elements 15-6 swap column 18-25 swap row 18-25 transposing 15-13 , 15-14 variables 15-1 matrix functions 15-10 COLNORM 15-10 COND 15-11 CROSS 15-1 1 DET 15-11 DOT 15[…]

  • Страница 308

    I-8 recalc ulating 2-18 setup 2-16 , 2-19 O off automatic 1-1 power 1-1 on/cancel 1-1 One-Proportion Z-Interval 11- 17 One-Sample T-Interval 11-18 One-Sample T-Test 11-1 2 One-Sample Z-Interval 11-15 One-Sample Z-Test 11-8 order of precedence 1-21 overlaying plots 2-15 , 4-3 P π 13-8 paired columns 10-11 parametric variables axes 18-32 connect 18-[…]

  • Страница 309

    I-9 polynomial coefficients 13- 11 evaluation 13-11 form 13-11 roots 13-12 Taylor 13-7 polynomial functions POLYCOEF 13-11 POLYEVAL 13-11 POLYF ORM 13-11 POLYROOT 13-12 ports 19-5 position argument 18 -21 power (x raised to y) 13-5 preced ence 1-22 predicted values statistical 10-20 print contents of display 18-26 name and contents of variable 18-2[…]

  • Страница 310

    I-10 regression analysis 10-17 fit models 10-13 formula 10-12 user-defined fit 10-13 relative error statistical 10-18 resetting aplet 19-3 calculator R-3 memory R-3 result copying to edit line 1-22 reusing 1-22 root interac tive 3-10 n th 13-6 variable 18-34 root-finding displaying 7-7 interac tive 3-9 operat ions 3-10 variables 3-10 S S1mark-S5mar[…]

  • Страница 311

    I-11 aplets in chronological order 19-6 elements in a list 16-9 spectral norm 15-13 spectral radius 15-13 square root 13-5 stack history printing 18-26 stairsteps graph 6-1 standard number format 1-10 statistics analysis 10 -1 analyzing plots 10-19 angle mode 10-12 calculate one-variable 18 -30 calculate two-variable 18 -30 data set variables 18-41[…]

  • Страница 312

    I-12 setting 18-28 time, converting 13-14 times sign 1-20 tmax 18-36 tmin 18-36 too few arguments R-19 tracing functions 2-8 more than one curve 2-8 not matching plot 2-8 plots 2-8 transmitting lists 16-6 matrices 15-4 programs 18-8 transposing a matrix 15-13 Triangle Solver aplet 9-1 trigono metric fit 10-13 functions 13-19 scaling 2-10 , 2-14 , 2[…]

  • Страница 313

    I-13 Z Z-Interval 11-15 zoom 2-17 axes 2-12 box 2-9 center 2-9 examples of 2-11 factors 2-13 in 2-9 options 2-9 , 3-8 options within a table 2-17 out 2-9 redrawing table of numbers op- tions 2-17 square 2-1 0 un-zoom 2-11 within Numeric view 2-17 X-zoom 2-9 Y-zoom 2-10 HP 39gs English. book Page 13 We dnesday, December 7, 2005 11:24 PM[…]

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    HP 39gs English. book Page 14 We dnesday, December 7, 2005 11:24 PM[…]

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HP 39gs English.book Page i Wednesday, December 7, 2005 11:24 PM
HP 39gs graphing calculator
user’s guide
Edition3
Part Number F2223AA-90001

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title.fm Page ii Thursday, July 13, 2006 10:29 AM Notice REGISTER YOUR PRODUCT AT: www.register.hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED “AS IS” AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WAR- RANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE. HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCI

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EnterpriseTOC.fm Page i Wednesday, May 3, 2006 5:01 PM Contents Preface Manual conventions ……………………………………………………..P-1 Notice ……………………………………………………………………… P-2 1 Getting started On/off, cancel operations………………………………………………1-1 The display ………………………………………………………………..1-2 The keyboard …………………………………….

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EnterpriseTOC.fm Page ii Wednesday, May 3, 2006 5:01 PM 3 Function aplet About the Function aplet……………………………………………….. 3-1 Getting started with the Function aplet………………………….. 3-1 Function aplet interactive analysis……………………………………. 3-9 Plotting a piecewise-defined function ………………………….. 3-12 4 Parametric aplet About the Parametric aplet ……………………………………………. 4-1 G

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EnterpriseTOC.fm Page iii Wednesday, May 3, 2006 5:01 PM Exploring the graph………………………………………………10-19 Calculating predicted values……………………………………10-20 11 Inference aplet About the Inference aplet ……………………………………………..11-1 Getting started with the Inference aplet ………………………..11-1 Importing sample statistics from the Statistics aplet …………..11-4 Hypothesis tests ……………..

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EnterpriseTOC.fm Page iv Wednesday, May 3, 2006 5:01 PM Two-variable statistics…………………………………………… 13-17 Symbolic functions ………………………………………………. 13-17 Test functions……………………………………………………… 13-18 Trigonometry functions………………………………………….. 13-19 Symbolic calculations……………………………………………….. 13-20 Finding derivatives………….

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EnterpriseTOC.fm Page v Wednesday, May 3, 2006 5:01 PM Using programs …………………………………………………………18-7 Customizing an aplet…………………………………………………..18-9 Aplet naming convention………………………………………..18-10 Example…………………………………………………………….18-10 Programming commands…………………………………………….18-13 Aplet commands ………………..

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EnterpriseTOC.fm Page vi Wednesday, May 3, 2006 5:01 PM Polar aplet variables ……………………………………………….. R-9 Sequence aplet variables………………………………………… R-10 Solve aplet variables ……………………………………………… R-11 Statistics aplet variables………………………………………….. R-12 MATH menu categories………………………………………………. R-13 Math functions…………………

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HP 39gs English.book Page 1 Wednesday, December 7, 2005 11:24 PM Preface The HP 39gs is a feature-rich graphing calculator. It is also a powerful mathematics learning tool. The HP 39gs is designed so that you can use it to explore mathematical functions and their properties. You can get more information on the HP 39gs from Hewlett-Packard’s Calculators web site. You can download customized aplets from the web site and load them onto your calculator. Customized aplets are special appli

Краткое содержание страницы № 10

Preface.fm Page 2 Thursday, July 13, 2006 10:33 AM Notice This manual and any examples contained herein are provided as-is and are subject to change without notice. Except to the extent prohibited by law, Hewlett-Packard Company makes no express or implied warranty of any kind with regard to this manual and specifically disclaims the implied warranties and conditions of merchantability and fitness for a particular purpose and Hewlett-Packard Company shall not be liable for any errors o

Краткое содержание страницы № 11

HP 39gs English.book Page 1 Wednesday, December 7, 2005 11:24 PM 1 Getting started On/off, cancel operations To turn on Press to turn on the calculator. To cancel When the calculator is on, the key cancels the current operation. To turn off Press OFF to turn the calculator off. To save power, the calculator turns itself off after several minutes of inactivity. All stored and displayed information is saved. If you see the ((•)) annunciator or the Low Bat message, then the calculator need

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HP 39gs English.book Page 2 Wednesday, December 7, 2005 11:24 PM The display To adjust the Simultaneously press and (or ) to increase (or decrease) the contrast. contrast To clear the display • Press CANCEL to clear the edit line. •Press CLEAR to clear the edit line and the display history. Parts of the display Title History Edit line Menu key labels Menu key or soft key labels. The labels for the menu keys’ current meanings. is the label for the first menu key in this picture. “Pres

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HP 39gs English.book Page 3 Wednesday, December 7, 2005 11:24 PM Annunciators. Annunciators are symbols that appear above the title bar and give you important status information. Annunciator Description Shift in effect for next keystroke. To cancel, press again. α Alpha in effect for next keystroke. To cancel, press again. ((•)) Low battery power. Busy. Data is being transferred via infrared or cable. The keyboard Menu keys HP 39gs Graphing Calculator Menu Key Labels Menu Keys Cursor

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HP 39gs English.book Page 4 Wednesday, December 7, 2005 11:24 PM • On the calculator keyboard, the top row of keys are called menu keys. Their meanings depend on the context—that’s why their tops are blank. The menu keys are sometimes called “soft keys”. • The bottom line of the display shows the labels for the menu keys’ current meanings. Aplet control keys The aplet control keys are: Key Meaning Displays the Symbolic view for the current aplet. See “Symbolic view” on page 1-16. Dis

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HP 39gs English.book Page 5 Wednesday, December 7, 2005 11:24 PM Entry/Edit keys The entry and edit keys are: Key Meaning Cancels the current operation if the (CANCEL) calculator is on by pressing . Pressing , then OFF turns the calculator off. Accesses the function printed in blue above a key. Returns to the HOME view, for performing calculations. Accesses the alphabetical characters printed in orange below a key. Hold down to enter a string of characters. Enters an input or execute

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HP 39gs English.book Page 6 Wednesday, December 7, 2005 11:24 PM Key Meaning (Continued) CHARS Displays a menu of all available characters. To type one, use the arrow keys to highlight it, and press . To select multiple characters, select each and press , then press . Shifted keystrokes There are two shift keys that you use to access the operations and characters printed above the keys: and . Key Description Press the key to access the operations printed in blue above the keys. F

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HP 39gs English.book Page 7 Wednesday, December 7, 2005 11:24 PM HELPWITH The HP 39gs built-in help is available in HOME only. It provides syntax help for built-in math functions. Access the HELPWITH command by pressing SYNTAX and then the math key for which you require syntax help. Example Press SYNTAX Note: Remove the left parenthesis from built-in functions such as sine, cosine, and tangent before invoking the HELPWITH command. Math keys HOME ( ) is the place to do calculations. Ke

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HP 39gs English.book Page 8 Wednesday, December 7, 2005 11:24 PM • Pressing displays a menu of physical constants from the fields of chemistry, physics, and quantum mechanics. You can use these constants in calculations. (See “Physical constants” on page 13-25 for more information.) • Pressing takes you to the beginning of the MATH menu. See “Math functions by category” on page 13-2 for details of the math functions. HINT When using the MATH menu, or any menu on the hp 39gs, pressing

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HP 39gs English.book Page 9 Wednesday, December 7, 2005 11:24 PM • If there are two columns, the left column shows general categories and the right column shows specific contents within a category. Highlight a general category in the left column, then highlight an item in the right column. The list in the right column changes when a different category is highlighted. Press or when you have highlighted your selection. • To speed-search a list, type the first letter of the word. For e

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HP 39gs English.book Page 10 Wednesday, December 7, 2005 11:24 PM Mode settings You use the Modes input form to set the modes for HOME. HINT Although the numeric setting in Modes affects only HOME, the angle setting controls HOME and the current aplet. The angle setting selected in Modes is the angle setting used in both HOME and current aplet. To further configure an aplet, you use the SETUP keys ( and ). Press MODES to access the HOME MODES input form. Setting Options Angle Angle

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HP 39gs graphing calculator

user’s guide

Edition3
Part Number   F2223AA-90001

HP 39gs English.book  Page i  Wednesday, December 7, 2005  11:24 PM

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  • Страница 1

    HP 3 9gs gr aphing calc ulato r user’s guide Ed i t io n 3 P a rt Number F2 2 2 3AA-9 0001 HP 39gs English. book Page i Wed nesday, December 7, 2 005 11:24 PM[…]

  • Страница 2

    Notice REG ISTER Y OUR PRODU CT A T: w ww .register .hp.com TH IS MANUAL AND ANY EXAMPLE S CONT AI NED HEREIN ARE PRO VIDED “ AS IS” AND ARE SUBJECT T O CHANG E WITHOUT NO TICE. HEWLETT-P A CKARD COMP ANY MAKES N O W AR- R ANTY O F ANY KIND WITH REGARD T O TH IS MANU AL , INC L UDING , B UT NO T L IMI TE D T O , TH E IM P LIE D W AR RAN T IES O[…]

  • Страница 3

    i Contents Preface Manual conventions …………. ……………. ……………. …………….. P-1 Notice .. …………….. ……………. ……………. …………….. …………. P-2 1 Getting started On/off, cancel o perations …….. ……………. …………….. …………. 1-1 The display …………… ………[…]

  • Страница 4

    ii 3 Function aplet About the Function aple t …………….. …………. ……………. ………. 3-1 Getting started w ith the Function aplet ……………. ……………. 3-1 Function aplet intera ctive analysis ……. ……………….. ……………. 3-9 Plotting a pie cewise-defined function ….. ……………. ……….. […]

  • Страница 5

    iii Exploring the graph …… ……………. ……………. ……………. 10-19 Calculating pre dicted values ……. ……………. ……………. … 10-20 11 Inference aplet About the Inference a plet ………… …………….. ……………. …….. 11-1 Getting started with the Inference aplet ………………… …….. […]

  • Страница 6

    iv Two-variab le statistic s …………. …………. ……………. ……… 13-17 Symbolic functions …. ………………. …………….. …………… 13-17 Test functions ……… ……………. …………. ……………. ……… 13-18 Trigonom etry functions ……… ……………. ……………. ……… 13-19 Sym[…]

  • Страница 7

    v Using programs ………………. ……………. ……………. …………… 18-7 Customiz ing an aplet ………… ……………. …………. ……………. .. 18-9 Aplet naming convention ……………… ……………. …………. 1 8-10 Example ……… ……………. ……………. ……………. …………. 18-[…]

  • Страница 8

    vi Polar aplet variable s ………….. ……………. ……………. ………. R-9 Sequence aplet variables ……….. ……………. …………….. …. R-10 Solve aplet variab les ………….. ……………. ……………. …….. R-11 Statistic s aplet variables ……………. …………….. …………. …. R-12 MATH […]

  • Страница 9

    P-1 Pr eface The HP 39gs is a feature-rich graphing calculator. It i s also a powerful mathematics learning tool. The HP 39gs is designed so that you can use it to explore mathematical functions and their prop erties. You can get more information on the HP 39gs from Hewlett-Packard’s Calcula tors web site. You can download customized aplets from […]

  • Страница 10

    P-2 Notice This manual and any examples contained herein are provided as-is and are subject to change without notice. Except to the extent prohibit ed by law, Hewlett-Packard Company makes no express or implied warranty of any kind with regard to this manu al and specific ally disclaims the implied warranties and conditions of merchantability and f[…]

  • Страница 11

    Getting started 1-1 1 Get ting star ted On/off, cancel operations To turn on Press to turn on the calculator. To cancel When the calculator is on, the key cancels the current operation. To turn off Press OFF to turn the calculator off. To save power, the calculator turns itself off after sev eral minutes of inactivity. All stored and displayed info[…]

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    1-2 Getting started The display To adjust the contrast Simultaneously press and (or ) to increase (or decrease) the contrast. To clear the display • Pr ess CANCEL to c lear the edit line . • Pr ess CLEA R to c lear the edit line and the display history . Parts of the display Menu key or soft key labels. T he labels f or the menu k e ys ’ cur […]

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    Getting started 1-3 Annunciators . Annunciators are sy mbols that appear above the title bar and give you important status information. The keyboard Menu keys Annunciator Description Shift in effect for next keystrok e. To cancel, press again. α Alpha in effect for next keystroke. To cancel, press again. (( • )) Low battery power. Busy. Data is […]

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    1-4 Getting started • On the calc ulator k e y boar d, the top r ow of k ey s are called menu k ey s . The ir meanings depend on the conte xt—that’s w h y their to ps ar e blank . The menu k e y s ar e sometimes called “ so ft k ey s ” . • T he bottom line o f the displa y sho ws the la bels f or the menu k ey s ’ c u r r ent meanings[…]

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    Getting started 1-5 Entry/Edit keys The entry and edit keys are: K e y Meaning ( CANCEL ) Cancels the current operation if the calculator is on by pressing . Pressing , then OFF turns the calculator off. Accesses the function printed in blue above a key. Returns to the HOME view, for performing calculations. Accesses the alphabetical characters pri[…]

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    1-6 Getting started Shifted ke ystrokes There are two shift keys that you use to access the operations and characters printed above the keys: and . CHARS Displays a menu of all available characters. To type one, use the arrow keys to highlight it, and press . To select multiple character s, select each and press , then press . K e y Meaning (Contin[…]

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    Getting started 1-7 HELPWITH The HP 39gs built-in hel p is available in HOME only. It provides syntax help for bu ilt-in math functions. Access the HELPWITH command by pressing SYNTAX and then the math key for which you require syntax help. Example Pr ess SYNTAX Note: R emo ve the left par enthesis fr om built -in func tio ns such a s sine , cosine[…]

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    1-8 Getting started • Pr essing displa y s a menu of ph y sical constants f r om the f ields o f chemistry , phy sic s, and quantum mec hanic s. Y ou can u se these consta nts in calc ulati ons . (See “Ph ysi cal constants ” on page 13- 2 5 f or mor e inf or mation .) • Pr essing tak es yo u to the beginning of the MA TH men u . See “Math[…]

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    Getting started 1-9 • If ther e are tw o columns , the left column sho ws gener al categori es and the righ t column sho w s spec ifi c cont ents w ithin a catego ry . Hi ghligh t a gener al category in the left column, then hi ghligh t an item in the r ight column. T he list in the ri ght column c hanges w hen a diffe r ent catego ry is highligh[…]

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    1-10 Getting started Mode settings You use the Modes inpu t form to set the modes for HOME. HINT Although the numeric setting in Modes affects only HOME, the angle setting controls HOME and the current aplet. The angle setting selecte d in Modes is the angle setting used in both HOME and current aplet. To further configure an aplet, you u se the SE[…]

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    Getting started 1-11 Setting a mode This example demonstrates how to change the angle measure from the default mode, radians, to degrees for the current aplet. The procedure is the s ame for changing number format and decimal mark modes. 1. Pr ess MODES t o o p e n t h e H O M E M O D ES i n p u t form. Engineering . Displays result wit h an expone[…]

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    1-12 Getting started T he cur sor (hi ghlight) is in the fir st f ield , Angle Measur e . 2 . Pr ess to display a li st of choic es. 3. P re s s to select Degrees , and pr ess . The angle mea sur e changes to degrees . 4. Pr ess to r eturn to HOME . HINT Whenever an input form has a list of choices for a field, you can press to cycle through them i[…]

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    Getting started 1-13 symbolic views of the aplets in the following table. See “Aplet view configuration” on page 1 -18 for further information. In addition to these aplets, wh ich can be u sed in a variety of applications, the HP 39 gs is supplied with two teaching aplets: Quad Explorer and Trig Explorer. You cannot modify configurati on settin[…]

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    1-14 Getting started charge and transferred to the HP 39gs using the provided Connectivity Kit. Quad Explorer aplet The Quad Explorer aplet is used to investigate the behaviour of as the values of a , h and v change, both by manipulati ng the equation and seeing the change in the graph, and by manipulating the grap h and seein g the chang e in the […]

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    Getting started 1-15 Trig Explorer aplet The Trig Explorer aplet is used to investigate the behaviour of the graph of as the values of a , b , c and d change, both by manipulating the equation and seeing the change in the graph, or by manipulating the graph and seeing the change in the equation. Press , select Trig Explorer , and then press to disp[…]

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    1-16 Getting started Aplet library Aplets are stored in the Aplet library. To open an aplet Press to display the Aplet library me nu. Select the aplet and press or . From within an aplet, you can return to HOME any time by pressing . Aplet views When you have configured an aplet to define th e relation or data that you want to explore, you c an dis[…]

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    Getting started 1-17 Numeric view Press to dis play the aplet’s Numeric view. In this view, the functions that you have defined are displayed in tabular format. See “About the numeric view” on page 2 -16 for further information. Plot-Table view The VIEWS menu contains the Plot-Table view. Select Plot-Table Splits the screen into the plot and […]

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    1-18 Getting started Note view Press NOTE to display the aplet’s note view. This note is transferred with the aplet if it is sent to another calculator or to a PC. A note view contains text to supplement an aplet. See “Notes and ske tches” on page 17-1 for further information. Sketch view Press SKETCH to dis play the ap let’s sk etch view .[…]

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    Getting started 1-19 To change views Each view is a separate environment. To ch ange a view, select a different view by pressing , , keys or select a view from the VIEWS menu. To change to HOME, press . You do not explicitly close the current view, you just ente r another one—like passing from one room into another in a house. Data that you enter[…]

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    1-20 Getting started Example Calculate : Long results If the result is too long to fit on the display line, or if you want to see an expression in textbook format, press to highlight it and then press . Negative numbers Type to start a negative number or to insert a negative sign. To raise a negative number to a power, enclose it in parentheses. Fo[…]

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    Getting started 1-21 However, for clarity, it is better to include the multiplication sign where you expect multiplication in an expression. It is clearest to enter AB as A*B . HINT Implied multiplication will not always work as expecte d. For example, entering A(B+4 ) will not give A*(B+4) . Instead an error message is displayed: “I nvalid User […]

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    1-22 Getting started Algebraic precedence order of evaluation Functions within an expression are evaluated in the following order of precedence. Functions with the same precedence are evaluated in order from left to right. 1. E xpressions w it hin parenthe ses. Neste d p ar ent heses ar e ev aluated fr om inner to outer . 2 . Pr efi x functio ns, s[…]

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    Getting started 1-23 When you highlight a previous input or result (by pressing ), the and menu labels appear. To copy a previous line Highlight the line (press ) and press . The number (or expression) is co pied into the e dit line. To reuse the last result Press AN S (last answer) to put the last result from the HOME display into an expression. A[…]

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    1-24 Getting started HINT When you retrieve a number from ANS , you obtain the result to its full precision. When you retrieve a number from the HOME’s display history, you obtain exactly what was displaye d. Pressing evaluates (or re-evaluates) the last input, whereas pressing ANS copies the last result (as ANS ) into the edit line. Storing a va[…]

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    Getting started 1-25 Accessing the display history Pressing enables the highlight bar in the display history. While the highlight bar is active, the following menu and keyboard keys are very useful: Clearing the display history It’s a good habit to cl ear the display his tory ( CLEAR ) whenever you have finish e d working in HOME. It saves calcul[…]

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    1-26 Getting started 2 . Select Number Format , pr ess to display the optio ns, and hi ghlight Fract ion or Mixed Fraction . 3 . Pr ess to sele ct the Number F ormat option , then mo ve to the prec ision value field . 4. Enter the prec ision v alue that yo u want to us e , and pr ess to set the pr ecisi on . Pres s to retur n to HOME . See “Setti[…]

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    Getting started 1-27 • Pr ec ision set to 1: • Pr ec ision set to 2 : • Pr ec ision set to 3: • Pr ec ision set to 4 Fraction calculations When entering fractions: • Y ou use the ke y to separate the numerator part and the denominator par t of the fr action. • T o ent er a mi xed f r acti on , f or e x ample , 1 1 / 2 , you enter it in […]

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    1-28 Getting started 2. E n t e r t h e c a l c u l a t i o n . 32 3 45 7 8 Note: Ensur e y ou ar e in the HOME v ie w . 3 . E valuat e the calc ulation . Note that if you had selected Mixed Fraction instead of Fraction as the Number format, the answer would have been expressed as 25+7/8. Converting decimals to fractions To convert a decimal value […]

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    Getting started 1-29 In this e x ample , the fr action pr ec ision is s et to 6. Complex numbers Complex results The HP 39gs can return a complex number as a result for some math functions. A comp lex number appears a s an ordered pair ( x, y ), where x is the real part and y is the imaginary part. For example, entering returns (0,1). To enter comp[…]

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    1-30 Getting started Catalogs and editors The HP 39gs has several catalogs and editors. You use them to create and manipulate objects. They access features and stored values (numbe rs or text or other items) that are independent of aplets. • A catalog lists items, w hich y ou can delete or tr ansmit , for e xampl e an aplet . • An edito r lets […]

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    Aplets and their views 2-1 2 Aplets and t heir v ie w s Aplet views This section examines the options an d functionality of the three main views for the Function, Polar, Parametric, and Sequence aplets: Symbolic, Plot, and Numeric views. About the Symbolic view The Symbolic view is the defining view for the Functi on, Parametric, Polar, and Seque n[…]

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    2-2 Aplets and their views – For a F unc tion definiti on , e nt er an e xpr es sio n to def ine F(X) . The only independent variab le in th e ex pre ss i on i s X. – Fo r a P arametric definiti on , e nt er a pair of e xpr essi ons to def ine X(T) and Y(T) . The o nly independent v ari able in the e xpr es sions is T . – Fo r a P o l ar defi[…]

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    Aplets and their views 2-3 Evaluating expressions In aplets In the Symbolic view, a variable is a symbol only, and does not represent one specif ic value. To evaluate a function in Symbolic view, press . If a function calls another function, then reso lves all references to other functions in terms of their independent variable. 1. Choo se the F un[…]

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    2-4 Aplets and their views In HOME You can also evaluate any expression in HOME by entering it into the edit line and pressing . For example, define F4 as below. In HOME, type F4(9) and press . This evaluates the expression, substituting 9 in place of X into F4 . SYMB view keys The following table details the menu keys that you use to work with the[…]

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    Aplets and their views 2-5 About the Plot view After entering and selecting (check marking) the expression in the Symbolic view, press . To adjust the appearance of the graph or the interval that is displayed, you can change the Plot view settings. You can plot up to ten expressions at the same time. Select the expressions you want to be plotted to[…]

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    2-6 Aplets and their views Plot view settings The plot view settings are: Those items with space for a checkmark are settings you can turn on or off. Press to display the second page. F ield Meaning XRNG, YRNG Specifies the minimum and maximum horizontal ( X ) and vertical ( Y ) values for the plotting window. RES For function plots: Resolution; ?[…]

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    Aplets and their views 2-7 Reset plot settings To reset the default values for all plot settings, press CLEAR in the Plot Setup view. To reset the default value for a field, highlight the field, and pres s . Exploring the graph Pl o t v i ew g iv e s y ou a se l ec t io n of k ey s a n d m e nu k ey s to explore a graph further. The options vary fr[…]

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    2-8 Aplets and their views Trace a graph You can trace along a function using the or key which moves the cur sor along the graph. The display also shows the current coordinate position ( x, y ) of the cursor. Trace mode and the coordinate di splay are automatically set when a plot is drawn. Note: Tracing might not appe ar to exactly follow your plo[…]

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    Aplets and their views 2-9 To jump directly to a value To jump straight to a value rather than using the Trace function, use the menu key. Press , then enter a value. Press to jump to the value. To turn trace on/off If the menu labels are no t displayed, press first. • T urn o ff tr ace mode by pr essing . • T urn on tr ac e mode by pre ssing .[…]

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    2-10 Aplets and their views Y-Zoom In Divides vertical scale only, using Y-factor. Y-Zoom Out Multipli es vertical scale only, using Y-factor. Square Changes the vertical scale to match the horizontal scale. (Use this after doing a Box Zoo m, X-Zoom, or Y-Zoom.) Set Factors… Sets the X-Zoom and Y-Zoom factors for zooming in or zooming out. Includ[…]

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    Aplets and their views 2-11 ZOOM examples The following screens show the effects of zooming options on a plot of . Plot of Zoom In : In Un-zoom : Un-zoom Note: Press to move to the bottom of the Zoom list. Zoom Out : Out Now un -zoom . X-Zoom In : X-Zoom In Now un -zoom . X-Zoom Out : X-Zoom Out Now un -zoom . Un-zoom Returns the display to the pre[…]

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    2-12 Aplets and their views Y-Zoom In: Y-Zoom In Now un-zoom. Y-Zoom Out: Y-Zoom Out Zoom Square: Square To box zoom The Box Zoom option lets you dr aw a box aroun d the area you want to zoom in on by selecting the endpoints of one diagonal of the zoom rectangle. 1. If necessary , pr ess to turn o n the menu -k e y labels . 2. P r e s s a n d s e l[…]

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    Aplets and their views 2-13 To set zoom factors 1. In the P lot v ie w , pr ess . 2. P r e s s . 3. S e l e c t Set Factors… and pr es s . 4. Enter the z oom fac tors . Ther e is one z oom fac tor f or the hor i z ontal sc ale ( XZOOM ) and one f or the vertical sca le ( YZOOM ). Z ooming out multipli es the s cale by the fac tor , so that a gr e[…]

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    2-14 Aplets and their views Split the screen The Plot-Detail view can give you two simultaneous views of the plot. 1. Pr ess . Se lect Plot-Detai l and pr ess . The gr aph i s plotted twi ce. Y ou can no w z oom in on the r ight si de. 2. P r e s s , selec t the z oom method and pres s or . This z ooms the r ight si de. Her e is an e x ample of s p[…]

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    Aplets and their views 2-15 – mo ves the leftmost c ursor to the scr een’s left edge an d mo ves the ri ghtmost c ursor to the s cr een ’s ri ght edge . – T he menu k e y copies the r ight plot t o the left plot . 3 . T o un -split the sc reen , pre ss . The left si de tak es o ver the wh ole scr e en . The Plot-Table view gives you two sim[…]

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    2-16 Aplets and their views About the numeric view After entering and selecting (check marking) the expression or expressions that you want to explore in the Symbolic view, press to view a table of data values for the independent variable ( X , T, θ , or N ) and dependent variables. Setting up the table (Numeric view setup) Press NUM to define any[…]

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    Aplets and their views 2-17 Numeric view settings The following table details the fields on the Numeric Setup input form. Reset numeric settings To reset the default values for all table settings, press CLEAR . Exploring the table of numbers NUM view menu keys The following table details the menu keys that you use to work with the table of numbers.[…]

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    2-18 Aplets and their views ZOOM options The following table lists the zoom options: The display on the right is a Zoom In of the display on the left. The ZOOM factor is 4. HINT To jump to an independent va riable value in the table, use the arrow keys to place the cursor in the independent variable column, then enter the value to jump to. Automati[…]

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    Aplets and their views 2-19 Building your own table of numbers The default NUMTYPE is “Automatic”, which fills the table with data for regular intervals of the independent ( X , T , θ , or N ) variable. With the NUMTYPE option set to “Build Your Own”, you fill the table yourself by typing in the independent-variable values yo u want. The d[…]

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    2-20 Aplets and their views “Build Your Own” menu keys Example: plotting a circle Plot the circle, x 2 + y 2 = 9 . Fi rst rearrange it to read . To plot both the positive and negative y values, you need to define two equations as follows: and K e y Meaning Puts the highlighted independent value ( X , T , θ , or N ) into the edit line. Pressing[…]

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    Aplets and their views 2-21 1. In the F unction aplet , spec ify the functi ons . Select Function 9 9 2 . Rese t the gr aph se tup to the de fa ult setting s. SETUP — PLOT CLEAR 3 . P lot the two func tions and hide the men u so that y ou can see all the ci rc l e. 4. R eset the n umer ic s etup to the def ault se ttings. SETUP — NUM CLEAR 5 . Disp[…]

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    HP 39gs English. book Page 22 We dnesday, December 7, 2005 11:24 PM[…]

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    Function aplet 3-1 3 F unc tion aplet About the Function aplet The Function aplet enables you to explore up to 10 real-valued, rectangu lar functions y in terms of x . For example . Once you have defined a function you can: • cr eate gr aphs to fi nd r oots, int er cepts, slope , signed ar ea, and e x tr ema • cr eate tables to evaluate f uncti[…]

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    3-2 Function aplet Define the expressions 2 . T her e are 10 f uncti on def inition f ields on the F uncti on aplet’s S y mbolic v ie w sc r een . Th ey ar e labeled F1(X) to F0(X). Highligh t the func tion de f inition f ield y ou w ant to use , and en ter a n e xpr es si on . (Y o u can pr ess to delete an e xis ting line , or CLEAR to clear al[…]

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    Function aplet 3-3 Change the scale 6 . Y ou can chan ge the scale to see mo r e or le ss of your gr aphs . In this e xam ple , ch oose Auto Scale . (See “VIEW S menu options ” on page 2 -13 f or a de scr ip t ion of Aut o Sc al e) . Select Auto Scale Trace a graph 7 . T race the linear f uncti on . 6 times Note: B y default , the tr acer is ac[…]

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    3-4 Function aplet Analyse graph with FCN functions 9. Display the Plot view menu. From the Plot view menu, you can use the functions on the FCN menu to find roots, intersections, slopes, and areas for a function defined in the Function aplet (and any Function-based ap lets). The FCN fun ctions act on the currently selecte d graph. See “FCN func […]

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    Function aplet 3-5 12 . Cho ose the linear f unction w hose int ers ecti on w ith the quadr atic functi on you w ish to f ind. T he coor dinates o f the inters ecti on poin t ar e display ed at the bottom of the scr een. Note: If ther e is more than one inter secti on (as in our e xam ple) , the coor dinates of the inter sec tion po int c lose st t[…]

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    3-6 Function aplet 15 . Mo v e the c urso r to x = –2 by pr essing the or key . 16 . Pr es s to acce pt using F2(x) = (x + 3) 2 – 2 as the other boundar y for the integr al. 17 . Choo se the end v alue for x . 1 Th e cu rs or ju mps t o x = – 1 on the linear func tion . 18. Displa y the numerical value of the integral. Note: See “Shading ar[…]

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    Function aplet 3-7 HINT The Root and Extremum functions return one value only even if the function has more than one r oot or extremum. The function finds the value closest to the position of the cursor. You need to re- locate the cursor to find oth er roots or extrema that may exist. Display the numeric view 20. Display the numer ic v ie w . Set u[…]

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    3-8 Function aplet To navigate around a table 2 4. Mo v e to X = –5 .9 . 6 times To go directly to a value 2 5. Mov e direc tly to X = 10. 1 0 To access the zoom options 2 6 . Z oom in on X = 10 by a fact or of 4. Note: NUMZOOM has a setting of 4 . In To change font size 2 7 . Displa y table numbe rs in lar ge f ont . To display the symbolic defi[…]

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    Function aplet 3-9 Function aplet interactive analysis From the Plot view ( ), you can use the functions on the FCN menu to find r oots, intersections, slopes, and areas for a function defined in the Function aplet (and any Function-based aplets). See “FCN functions” on page 3- 10. The FCN operations act on the currently sele cted graph. The re[…]

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    3-10 Function aplet FCN functions The FCN functions are: Function Description Root Select Root to find the root of the current function nearest the cursor. If no root is found, but only an extremum, then the result is labeled EXTR: instead of ROOT: . (The root-finder is also used in the Solve aplet. See also “Interpreting results” on page 7-6.)[…]

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    Function aplet 3-11 Shading area You can shade a selected area between functio ns. This process also gi ves you an appro ximate measurement of the area shaded. 1. Open the F unction aplet. T he Func tion aplet opens in the S ymbolic v ie w . 2 . Select the e xpr essi ons wh ose c ur v es y ou w ant to stu dy . 3 . Pres s to plot the functi ons . 4.[…]

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    3-12 Function aplet Plotting a piecewise-defined function Suppose you wanted to plot the following piecewise- defined function. 1. Open the F unction apl et . Sele ct Function 2 . Highlight the line you wan t to us e , and ente r the e xpre ssion . (Y ou can pre ss to delete an e xisting line , or CLEAR to c lear all lines .) 2 CHARS ≤ 1 CHARS &g[…]

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    Parametric aplet 4-1 4 Pa r a m e t r i c a p l e t About the Parametric aplet The Parametric aplet allows you to explore parametric equations. These are equ ations in which both x and y are defined as functions of t . They take the forms and . Getting started with the Parametric aplet The following example uses the parametric equations Note: This […]

  • Страница 76

    4-2 Parametric aplet Set angle measure 3 . Set the angle measu r e to degrees. MODES Select Degrees Set up the plot 4. Display the graphing options. PLOT T he P lot Setu p inpu t for m has t w o f ields n ot inc luded in the Func tion aplet , TRNG and TSTEP . TRNG spec if ies the r ange of t val ue s. TSTEP spec if ies the step value between t valu[…]

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    Parametric aplet 4-3 Overlay plot 8. Plot a triangle graph over the existing ci rcle graph. PLOT 120 Sele ct Overlay Plot A tri angle is displa yed r ather than a c irc le ( with out c hanging the equati on) becaus e the c hanged value o f TSTEP ensur es that points be ing plot ted ar e 120 ° apart instea d of near l y continuou s. Y ou ar e able […]

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    HP 39gs English. book Page 4 Wed nesday, December 7, 2 005 11:24 PM[…]

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    Polar aplet 5-1 5 Po l a r a p l e t Getting started with the Polar aplet Open the Polar aplet 1. Open the P olar aplet . Sele ct Polar L ik e the F unction aple t , the P o lar aplet opens in the S ymboli c v ie w . Define the expression 2 . Define the po lar equati on . 2 π 2 Specify plot settings 3 . S pec ify the plot settings . In this ex amp[…]

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    5-2 Polar aplet Explore the graph 5 . Displa y the Plot v ie w menu k ey labels . Th e Pl ot vi ew op t i on s av ailable ar e the same as those f ound in the F u ncti on aplet . See “Explor ing the gra ph ” on page 2 — 7 fo r further informati on . Display the numbers 6 . Displa y the table of v alue s for θ and R1. Th e N u m eric view optio[…]

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    Sequence aplet 6-1 6 Sequence aplet About the Sequence aplet The Sequence aplet allows you to explore sequences. You can define a sequence named, for example, U1: • in terms of n • in terms of U1 ( n –1) •i n ter ms of U1 ( n –2) • in ter ms of another sequence , for e xample , U2 ( n ) • in an y combination of the a bov e. The Sequen[…]

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    6-2 Sequence aplet Open the Sequence ap let 1. Open the Sequ ence aplet . Sele ct Sequence The Sequence ap let starts in the S ymboli c view . Define the expression 2 . Def ine the F ibonacc i sequence, in w hich eac h term (after the f irst tw o) is the sum of the pr eceding tw o terms: , , for . In the S ymboli c v ie w of the Seq uence aplet , h[…]

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    Sequence aplet 6-3 Plot the sequence 4. P lot the Fibonacc i sequ ence. 5. In Plot Setup, set the SEQPLOT option to Co bweb . SETUP — PLOT Select Cobweb Display the table 6 . Displa y the table of values for this e xample . HP 39gs English. book Page 3 Wed nesday, December 7, 2 005 11:24 PM[…]

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    HP 39gs English. book Page 4 Wed nesday, December 7, 2 005 11:24 PM[…]

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    Solve aple t 7-1 7 Solve aplet About the Solve aplet The Solve aplet solves an equation or an expression for its unknown variable . You define an equation or expression in the symbolic view, then supply values for all the variables exce pt one in the numeric view. Solve works only with real numbers. Note the differences between an equation and an e[…]

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    7-2 Solve a plet Getting started with the Solve aplet Suppose you want to find th e acceleration needed to increase the speed of a car from 16.67 m/sec (60 kph) to 27.78 m/sec (100 kph) in a distance of 1 00 m. The equation to solve is: Open the Solve aplet 1. Open the Solv e aplet. Sele ct Solve T he Sol v e aplet st arts in the s y mbolic v iew .[…]

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    Solve aple t 7-3 4. Enter the values f or the kno wn va ri ables . 2 7 7 8 1 6 6 7 1 0 0 HINT If the Decimal Mark setting in the Modes input form ( MODES ) is set to Comma, use instead of . Solve the unknown variable 5. Sol v e f or the unkno wn var iable ( A ). T her ef or e , the accelerati on needed to inc r ease the speed of a car fr om 16.6 7 […]

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    7-4 Solve a plet 6. P lot the equati on f or v ari able A . Sele ct Auto Scale 7 . T race along the gr aph r epr esen ting the left side of the equati on until the c ursor nears the inter sec tion . 20 times Note the v alue o f A display ed near the bottom left corner of the scr een. T he Plo t vi e w pr o v ides a con v enien t wa y to f ind an ap[…]

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    Solve aple t 7-5 Use an initial guess You can usually obtain a fa ster and more accurate solution if you supply an estimated valu e for the unknown variable before pressing . Solve starts looking for a solution at the initial guess. Bef or e plottin g , make sur e the unkno wn v ariable is highli ghted in the nume ri c v ie w . P lot the equati on […]

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    7-6 Solve a plet Interpreting results After Solve has returned a solution, press in the Numeric view for more information. You will see one of the following three messages. Press to clear the message. Messa ge Condi tion Zero The Solve aplet found a point where both sides of the equation were equal , or wher e the expression was zero (a root), with[…]

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    Solve aple t 7-7 If Solve could not find a solution, you will see one of the following two messages. HINT It is important to check the information relating to the solve process. For example, the solution that the Solve aplet finds is not a solution, but the closest that the function gets to zero. Only by checking the information will you know that […]

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    7-8 Solve a plet where X is distance, V 0 is initial velocity, T is time, and A is acceleration. This is actually two equations, Y = X and Y = V 0 T + (AT 2 ) / 2 . Since this equation is quadratic for T , there can be both a positive and a negative solution. However, we are concerned only with posi tive so lutions, since only positive distance mak[…]

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    Solve aple t 7-9 5. Move the cursor near the positive (right-side) intersection. This cursor value will be an initial guess for T . Pr ess until the c urs or is at the inters ecti on. Th e t wo p oi nt s of inter sec tion sho w that ther e ar e tw o soluti ons f or this equati on . Ho w e ve r , on ly po si t ive va l ue s fo r X mak e sense , so w[…]

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    7-10 Solve a plet Using variables in equations You can use any of the real variable names, A to Z and θ . Do not use variable nam es defined for other type s, such as M 1 (a matrix variable). Home variables All home variables (other than t hose for aplet settings, like Xmin and Ytick ) are globa l , which means they are shared throughout the diffe[…]

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    Linear Solve r aplet 8-1 8 Li n e a r S o lve r a p l e t About the Linear Solver aplet The Linear Solver aplet allows you to solve a set of Linear Equations. The set can contain two or three linear equations. In a two-equation set, each equation must be in the form . In a three-equation set, e ach equation must be in the form . You provide values […]

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    8-2 Linear Solver aplet Choose the equation set 2 . If the last time y ou us ed the L inear Sol v er aplet yo u so l ve d fo r t wo equati ons, the tw o — equati on input f orm is display ed (as in the e x ample in the pr ev ious step) . T o solv e a th r e e -equation set , pre ss . No w the input f or m displa y s thr ee equati ons . If the three[…]

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    Linear Solve r aplet 8-3 soon as the f irst co -eff ic ient o f the last eq uation was enter ed. As you enter each of the r emaining kno wn v alues , the soluti on c hanges . T he ex ample at the ri ght sho ws the fi nal soluti on once all th e c o — efficient s a nd constants are e nter ed for the set o f equati ons w e set out to solve . HP 39gs […]

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    HP 39gs English. book Page 4 Wed nesday, December 7, 2 005 11:24 PM[…]

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    Triangle Solve apl et 9-1 9 T riangle Solv e aplet About the Triangle Solver aplet The Triangle Solver aplet a llows you to determine the length of a side of a triangle, or the ang le at the vertex of a triangle, from information you supply about the other lengths and/or other angles. You need to specify at leas t three of the six possible values?[…]

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    9-2 Triangle Solv e aplet Open the Triangle Solver aplet 1. Open the T riangle S olv er aplet . Sele ct Triangle Solver The T r iangle Solv er aplet open s . Note : if y ou h a v e alr eady u sed the T ri angle Sol v er , the entries and re sul ts fr om the pre v ious use w i ll still be display ed. T o start the T r iangle Solv er a fr esh, c lear[…]

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    Triangle Solve apl et 9-3 lengths as B and C, w e would ne ed to spec if y the angle as α . T he illustr a ti on on the displa y w ill help y ou determine wher e to enter t he know n values. Note: if y ou need to change the angle measur e mode , pres s MO DES , change the mode , and then pr ess to r eturn to the aplet . 4. Pr ess . T he solv er ca[…]

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    9-4 Triangle Solv e aplet Not enough data If you are using the general input form, you need to specify at least three values for the Triangle Solver to be able to calculate the remaining attributes of the triangle. If you specify less than three , Not enough data appears on the screen. If you are using the simplified input form (for a right- angled[…]

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    Statistics aplet 10-1 10 Statis tic s a ple t About the Statistics aplet The Statistics aplet can store up to ten data sets at one time. It can perform one- variab le or two-variable statistical analysis of one or more sets of data. The Statistics aplet starts with the Numeric view which is used to enter data. The Symbol ic view is used to specify […]

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    10-2 Statistics aplet Open the Statistics aplet 1. Open the Statis tics a plet and c lear e x isting data b y pr essing . Select Statistics Th e S ta t is ti cs ap l et starts in the Numer ical view . At an y time the Statisti cs aplet is conf igur ed for o nly one of t wo types of sta tistical explorations: one — var iable ( ) or tw o-v ariable ( […]

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    Statistics aplet 10-3 Choose fit and data columns 4. Select a fi t in the S y mbolic setu p vi e w . SETUP — SYMB Sele ct Linear Y ou c a n cre at e u p t o five ex p lo ra t io n s of t wo — va ri ab l e data , named S1 to S5 . I n t hi s exa m pl e, we wil l cre a te jus t o n e: S1 . 5 . Spec ify the columns that hold the data yo u w ant to anal[…]

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    10-4 Statistics aplet Setup plot 8. Change the plotting range t o ensur e all the data points ar e plot ted (and select a diff er ent point mar k, if yo u wi s h ) . SETUP — PLOT 7 100 400 0 Plot the graph 9 . Plo t the gr aph . Draw the regression curve 10. Dra w the reg r essi on c urve (a c ur ve to fi t the data points). T his dra w s the r egr[…]

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    Statistics aplet 10-5 Predict values 13 . T o find the pr edic ted sale s f igur e if adv er tising w er e to go up to 6 minute s: S ( to highlight Stat-Two ) (to highligh t PREDY ) 6 14. Retu rn to the P lot vi e w . 15 . Jum p to the indicat ed point on the r egr essi on line . 6 Observ e the pr edict ed y -v alue in the left bottom corner of the[…]

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    10-6 Statistics aplet Entering and editing statistical data The Numeric view ( ) is used to enter data into the Statistics aplet. Each column represents a variable named C0 to C9 . After entering the data, you must define the data set in the Symbolic view ( ). HINT A data column must have at least four data points to provide vali d two-variable sta[…]

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    Statistics aplet 10-7 Example You are measurin g the height of students in a classroom to find the mean height. The first five students have the following measurements 160cm, 165cm, 1 70cm, 175cm, 180cm. 1. Open the Stati stics aplet . Sele ct Statistics 2 . Enter the measurement data. 160 16 5 17 0 17 5 180 3 . F ind the mean of the sampl e. Ensur[…]

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    10-8 Statistics aplet Note that the title o f the colu mn o f st atis ti cs i s H1 . Ther e a r e 5 data set de f initions a vailable for one -v ari able sta tis tics : H1–H5 . If data is entered in C1 , H1 is automatically set to use C1 fo r data , and the fr equency of eac h data point is set to 1. Y ou can select other columns o f data fr om t[…]

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    Statistics aplet 10-9 To continue our example, supp ose that the heights of the rest of the students in the class are measured, but each one is rounded to the nearest of the five values first recorded. Instead of entering all the new data in C1 , we shall simply add another column, C2 , that holds the frequencies of our five data points in C1 . 5 .[…]

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    10-10 Statistics aplet 6 . R eturn t o the numer ic vi ew . 7 . Ente r the fr equency data sho wn in the a bo ve t able . 5 3 8 2 1 8. Display the comp uted sta tis tics. The mean height is approxim ately 167.63cm. 9 . Setu p a histogr am plot for the data . SETUP — PLOT Enter s et up inf or matio n appropriate to your data. 10. P lot a histogr am […]

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    Statistics aplet 10-11 Delete data • T o delete a single data item, highli ght it and pr ess . T he value s belo w the delet ed cell w ill scr oll up one ro w . • T o delete a column of data , highli ght an entry in that column and press CLEAR . Select the co lumn name . • T o delete all columns of data , pres s CLEAR . Sele ct All columns . […]

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    10-12 Statistics aplet Defining a regression model The Symbolic view includes an expression (Fit1 through Fit5) that defines the regression model, or “fit”, to use for the regression analysis of each two-variable data set. There are three ways to select a regression model: • Accept the d efa ult opt ion to f it th e data to a straight line . […]

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    Statistics aplet 10-13 To define your own fit 1. In Numeric v iew , make sur e is set. 2 . Display the S y mbolic v iew . 3 . Highligh t the F it expr es sion ( Fit1 , et c.) f or the desir ed data set. 4. T y pe in an e xpr essi on and pr ess . The independent variable must be X , and the e xpr essi on mu st not cont ain any unkn o wn v aria bles.[…]

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    10-14 Statistics aplet Computed statistics One-variable When the data set contains an odd number of values, the data set’s median value is no t us ed when calculating Q1 and Q3 in the table above. For example, for the following data set: { 3,5,7,8,15,16,17 } only the first three items, 3, 5, and 7 are used to calculate Q1, and only the last three[…]

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    Statistics aplet 10-15 Two-variable Plotting You can p lot: • histogr ams ( ) • bo x -and-whisk er plots ( ) • scat ter plots ( ) . Once you have ente red your data ( ), defined your data set ( ), and defined your Fit model for two- variable statistics ( SETUP — SYMB ), you can plot your data. You can plot up to five scatter or box-an d-whisk[…]

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    10-16 Statistics aplet To plot statistical data 1. In Sy mbolic v i ew ( ) , se lect ( ) the data sets y ou w ant to plot . 2 . Fo r one -var iable dat a ( ) , selec t the plot type in P lot Setup ( SETUP — PLOT ) . Highli ght ST A TPLOT , pr ess , select e ither Histogram or BoxWhisker , and pr es s . 3 . F or any plot , but espec iall y fo r a hi[…]

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    Statistics aplet 10-17 Scatter Plot Tw o-variable statistics . The numbers below the plot indicate that the cursor is at the first data point for S2, at (1, 6). Press to move to the next data point and display information about it. To connect the data points as they are plotted, checkmark CONNECT in the second page of the Plot Setup. This is not a […]

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    10-18 Statistics aplet Relati ve Error The relative error is a measure of the error between predicted values and actual va lues based on the specified Fit. A smaller number means a better fit. The relative error is stored in a variable named RELERR . The relative error provides a measur e of fit accuracy for all fits, and it does depend on the Fit […]

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    Statistics aplet 10-19 For instance, the data set (1,1 ), (3,9), (4,16), (2,4) would be plotted and traced in the order (1,1), (2,4), (3,9), (4,16). Trouble-shooting a plot If you have problems plotting, check that you have the following: • T he cor r ect or menu label o n (Numer ic vi ew ) . • T he corr ect fit (r egres sion model), if the dat[…]

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    10-20 Statistics aplet Calculating predicted values The functions PREDX and PREDY estimate (predict) values for X or Y given a hypothetical value for the other. The estimation is made based on the curve that has been calculated to fit the data a ccording to the specified fit. Find predicted values 1. In Plot v ie w , dra w the r egr ess ion c ur ve[…]

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    Statistics aplet 10-21 • Enter P RED Y( x-value ) to f ind the pr edicted v alue of the dependent var iable gi ven a h ypothetical independent va riab l e. You can type PREDX and PREDY into the edit line, or you can copy these function names from the MATH menu under the Stat-Two category. HINT In cases where more than one fit curve is displayed, […]

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    HP 39gs English. book Page 22 We dnesday, December 7, 2005 11:24 PM[…]

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    Inference aplet 11-1 11 Inference aplet About the Inference aplet The Inference capabilities include calculation of confidence intervals and hy pothesis tests based on the Normal Z-distribution or Student’s t-distribution. Based on the statistics from one or two samples, you can test hypotheses and find confidence intervals for the following quan[…]

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    11-2 Inferenc e aplet Inference aplet’s SYMB view keys The table below summarizes the options available in Symbolic view. If you choose one of the hypoth esis tes ts, you can choose the alternative hypothesis to test against the null hypothesis. For each test, th ere are three possible choices for an alternative hypothesis based on a quantitative[…]

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    Inference aplet 11-3 Select the inferential method 2. Select the Hypothesis Test infer ential method. Select HYPOTH TEST 3. Define the type of test. Z–Test: 1 μ 4. Select an alternative hypothesis. μ< μ0 Enter data 5. Enter the sample statistics and population parameters. setup-NUM The table below lists the fields in this view for our curre[…]

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    11-4 Inferenc e aplet By default, each field already contains a value. These values constitu te the example database and are expla ined in the feature of this aplet. Display on-line help 6. To display the on-line help, press 7. To close the on-line help, press . Display test results in numeric format 8. Display the test results in numeric format. T[…]

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    Inference aplet 11-5 A calculator produces the following 6 random number s: 0.529, 0.295, 0.95 2, 0.259, 0.925, and 0. 592 Open the Statistics aplet 1. Open the Statistics aplet and reset the current settings. Select Statistics The Statistics aplet opens in the Numeric view. Enter data 2. In the C1 column, enter the random numbers produced by the c[…]

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    11-6 Inferenc e aplet Open Inference aplet 6. Open the Inference aplet and clear current s ettings. Select Inference Select inference method and type 7. Select an inference method. Select CONF INTERVAL 8. Select a distribution statistic type. Select T-Int: 1 μ Set up the interval calculation 9. Set up the interval calculation. Note: The default va[…]

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    Inference aplet 11-7 Import the data 10. Import the data from the Statistics aple t. Note: The data from C1 is disp layed by default. Note: Press to see the statistics before importing them into the Numeric Setup view. Also, if there is more than one ap let based on the Statistics aplet, you are prompted to choose one. 11. Specify a 90% confidence […]

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    11-8 Inferenc e aplet Hypothesis tests You use hypothesis tests to test the validity of hypotheses that relate to the statistical parameters of one or two populations. The tests are base d on statistics of samples of the populations. The HP 39gs hypothesis tests use the Normal Z-distribution or Student’ s t-distribution to calcula te probabilitie[…]

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    Inference aplet 11-9 Results The results are: Two-Sample Z-Test Menu name Z-Test: μ 1– μ 2 On the basis of two samples, each from a separate population, this test measu res the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the mean of the two populations are equal (H 0 : μ 1= μ 2).[…]

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    11-10 Inferenc e aplet Results The results are: One-Proportion Z-Test Menu name Z-Test: 1π On the basis of statistics from a single sample, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The null hypothesis is that the proportion of su ccesses in the two populations is equal: H 0 : π = π 0 […]

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    Inference aplet 11-11 Inputs The inputs are: Results The results are: Two-Proportion Z-Test Menu name Z-Test: π 1 – π 2 On the basis of statistics fr om two samples, each from a different population, the Two-Proportion Z-Test measures the stre ngth of the evidence for a selected hypo thesis against the null hypothesis. The null hypothesis is th[…]

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    11-12 Inferenc e aplet Inputs The inputs are: Results The results are: One-Sample T-Test Menu name T-Test: 1 μ The One-sample T-Test is used when the population standard deviation i s not know n. On the basis of statistics from a single sample, this tes t measures the strength of the evidence for a selected hypothesis against the nu ll hypothesis.[…]

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    Inference aplet 11-13 Inputs The inputs are: Results The results are: Field name Definiti on Sample mean. Sx Sample standard de viation. n Sample size. μ0 Hypothetical population mean. α Significance level. x Result Description Test T T-Test statistic. Prob Probability associated with the T-Test statistic. Critical T Boundary value of T assoc iat[…]

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    11-14 Inferenc e aplet Two-Sample T-Test Menu name T-Test: μ 1 – μ 2 The Two-sample T-Test is used when the population standard deviation i s not know n. On the basis of statistics from two samples, each sample from a different population, this test measures the strength of the evidence for a selected hypothesis against the null hypothesis. The[…]

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    Inference aplet 11-15 Results The results are: Confidence intervals The confidence interval calculations that the HP 39gs can perform are based on the Normal Z-distribution or Student’s t-distribution. One-Sample Z-Interval Menu name Z-INT: μ 1 This option uses the Normal Z-distributio n to calculate a confidence interval for m, the true mean of[…]

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    11-16 Inferenc e aplet Results The results are: Two-Sample Z-Interval Menu name Z-IN T: μ1 – μ2 This option uses the Normal Z- distribution to calculate a confidence interval for the difference between the means of two populations, μ 1 – μ 2 , when the population standard deviations, σ 1 and σ 2 , are known. Inputs The inputs are: Results[…]

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    Inference aplet 11-17 One-Proportion Z-Interval Menu name Z-INT: 1 π This option uses the Normal Z-distributio n to calculate a confidence interval for the proportion of successes in a population for the case in wh ich a sample of size, n , has a number of successes, x . Inputs The inputs are: Results The results are: Two-Proportion Z-Interval Men[…]

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    11-18 Inferenc e aplet Results The results are: One-Sample T-Interval Menu name T-INT: 1 μ This option uses the Student’s t-distribution to ca lculate a confidence interval for m, the true mean of a population, for the case in which the true population standard deviation, s, is unknown. Inputs The inputs are: n1 Sample 1 si ze. n2 Sample 2 si ze[…]

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    Inference aplet 11-19 Results The results are: Two-Sample T-Interval Menu name T-INT: μ 1 – μ 2 This option uses the Student’s t-distribution to calculate a confidence interval for the difference between the means of two populations, μ 1 – μ 2, when the population standard deviations, s1 and s2, are unknown. Inputs The inputs are: Result […]

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    11-20 Inferenc e aplet Results The results are: Result Description Critical T Critical value for T. μ Min Lower bound for μ 1 – μ 2 . μ Max Upper bound for μ 1 – μ 2 . Δ Δ HP 39gs English. book Page 20 We dnesday, December 7, 2005 11:24 PM[…]

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    Using th e Finance So lver 12-1 12 Using the Finance Solver The Finance Solver, or Fin ance aplet , is available by using the APLET key in your calculator. Use the up and down arrow keys to select the Finance aplet. Your screen should look as follows: Press the key or the soft m enu key to activate the aplet. The result ing screen shows the differe[…]

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    12-2 Using t he Finance Sol ver combined amount earns interest at a certain rate. Financial calculations involvin g compound interest include savings accounts, mo rtgages, pension funds, leases, and annuities. Time Value of Money (TVM) calculations, as the name implies, make use of the notion that a dollar today will be worth more than a dollar som[…]

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    Using th e Finance So lver 12-3 flow diagram shows lease payments at the beginning of each period. The following cash flow diagram shows deposits into an account at the end of each period. As these cash-flow diagrams imply, there are five TVM variables: PV 1 23 4 5 FV Capital i zed value of lease } PM T PM T PM T PM T PM T PV 1 23 4 5 FV PM T PM T […]

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    12-4 Using t he Finance Sol ver Performing TVM calculations 1. Launch the F inanc ial Sol ver as indi cated at the beginning of this secti on . 2 . Use the arr o w k e ys to hi ghlight the diff ere nt f ields and enter the kno wn var iables in the T VM calc ulations , pr essing the soft -menu k ey after enter ing each kno wn value . Be sure that va[…]

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    Using th e Finance So lver 12-5 Example 1 — Loan calculations Suppose you finance the purcha se of a car with a 5-year loan at 5.5% annual intere st, compounded monthly. The purchase price of the car is $19,500, and the down payment is $3,000. What are the r equired monthly payments? What is the largest loan you can afford if your maximum monthly p[…]

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    12-6 Using t he Finance Sol ver Example 2 — Mortgage with balloon payment Suppose you have taken out a 30-year, $150,000 house mortgage at 6.5% annual interest. You expect to sell the house in 10 years, repaying the loan in a balloon payment. Find the size of the balloon payment, the value of the mortgage after 10 years of payment. Solution. The fo[…]

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    Using th e Finance So lver 12-7 Calculating Amortizations Amortization calculations, which also use the TVM variables, determine the amounts applied towards principal and interest in a payment or series of payments. To calculate amortizations: 1. Start the F inance Sol ver as indicated at the beginning of t hi s se ction. 2 . Se t the follo w ing T[…]

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    12-8 Using t he Finance Sol ver 3 . Pr ess the soft menu k ey to amorti z e the new batch o f pay ments . Repeat st eps 1 thr ough 3 as often as needed. Example 4 — Amortization for home mortgage For the results of Example 3, show the amortization of the next 10 years of the mortgage loan. First, press the soft menu key. Then, keeping 120 in the PA[…]

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    Using mathemati cal functions 13-1 13 Using math ematical func tions Math functions The HP 39gs contains many math func tions. The functions are grouped in categories. For example, the Matrix category contains functions for manipulating matrices. The Probability category (shown as Prob. on the MATH menu) contains functions for working with probabil[…]

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    13-2 Using math ematical functions 2 . The list o f func tions (on the r ight) applie s to the c urr ently hi ghlighted category (on the left) . U se and to sw itch bet w een the categor y list and th e func tion lis t . 3 . Hi ghlight the name of the func tion y ou wan t and pr ess . This copi es the fu nctio n name (and an initial par enthesis, i[…]

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    Using mathemati cal functions 13-3 Keyboard functions The most frequently used functions are available directly from the keyboard. Many of the keyboard functions also accept complex numbers as arguments. ,, , Ad d, Subtract, Multiply, Di vide . Also accepts c omplex numbers, lists and matrices. va lu e 1+ va lu e 2 , etc. e x Natural exponential. A[…]

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    13-4 Using math ematical functions 10 x Exponential (antilogarithm). Also accepts complex numbers. 10^ val u e Example 10^3 r etur ns 1000 Common logarithm. Also accepts co mplex numbers. LOG ( val u e ) Example LOG(100) r eturns 2 ,, Sine, cosine, tangent. Inputs and outputs depend on the current angle format (Degrees, Radi ans, or Grads). SIN ( v[…]

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    Using mathemati cal functions 13-5 ATAN A rc tangent: tan –1 x . Output range is from –90° to 90°, 2 π /2 to π /2, or –100 to 100 grad s. Inputs and outputs depend on the current an gle format. Also accept s complex numbers. ATAN ( valu e ) Example ATAN(1) ret u rn s 45 (Degrees mode). Square. Also accept s complex numbers. va lu e 2 Exam[…]

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    13-6 Using math ematical functions Takes the n th root of x . ro ot NTHROOT val ue Example 3 NTHROOT 8 r eturns 2 Calculus functions The symbols for differentiation and integration are available directly form the k eyboard— and S respectively—as well as from the MATH menu. Differentiates expr ession with respect to the vari able of differentiat[…]

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    Using mathemati cal functions 13-7 TAYLOR Calculates the n th order Taylor polynomial of expression at the point where the given variab le = 0. TAYLOR ( e xpr ession , var iable , n ) Example TAYLOR(1 + sin(s1) 2 ,s1,5) w ith Radians angle measur e and F rac tion n umber f ormat (s et in MODE S) r etur ns 1+s1^2-1/3*s1^4 . Complex number functions […]

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    13-8 Using math ematical functions Constants The constants available from the MATH FUNCTIONS menu are mathematical constants. These are described in this section. The hp 39gs has two other menus of constants: program constant s and physical constants. These are described in “Program constants and physical constants” on page 13-24. e Natural log[…]

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    Using mathemati cal functions 13-9 → IN Convert from centimeters to inches. → L Convert from US gallons to liters. → LGAL Convert from liters to US gallons. → KG Convert from pounds to kilograms. → LBS Convert from kilograms to pounds. → KM Convert from miles to kilometers. → MILE Convert from kilometers to miles. → DEG Convert from[…]

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    13-10 Using mathe matical functions EXP Natural exponential. This is more accurate than due to limitations of the power function. EXP ( val u e ) EXPM1 Exponent minus 1 : . This is more accurate than EXP when x is close to zero. EXPM1 ( val ue ) LNP1 Natural log plus 1 : ln( x+1 ). This is more accurate than the natural logarithm function when x is[…]

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    Using mathemati cal functions 13-11 Σ Summation. Finds the sum of expression with respect to variable from initialvalue to finalvalue. Σ ( v ar iable = initial v alue , fin a lval u e , e xp r essio n ) Example Σ (C=1,5,C 2 ) r eturns 5 5 . Matrix functions These functions are for matr ix data stored in matrix variables. See “Matrix func tions[…]

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    13-12 Using mathe matical functions POLYROOT Polynomial roots. Returns the roots for the n th-order polynomial with the specified n +1 coeffici ents . POLYROOT ([ coe ff ic ien ts ]) Example Fo r x 4 +2x 3 –25x 2 –26x+120 : POLYROOT([1,2,-25,-26,120]) r eturns [2,-3,4,-5] . HINT The results of POLYROOT will often not be easily seen in HOME due […]

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    Using mathemati cal functions 13-13 RANDOM Random number (between zero and 1). Produced by a pseudo-random number sequence. The algorithm used in the RANDOM function uses a seed number to begin its sequence. To ensure that two calculators must produce different results for the RANDOM function, use the RANDSEED function to seed different starting va[…]

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    13-14 Using mathe matical functions Examples CEILING(3.2) r eturns 4 CEILING(-3.2) r eturns -3 DEG → RAD Degrees to radians. Converts value from Degrees angle format to Radians angle format. DEG → RAD ( val ue ) Example DEG → RAD( 180 ) r eturns 3.14159265 359 , the va lu e of π . FLOOR Greatest integer less than or equal to value . FLOOR ( […]

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    Using mathemati cal functions 13-15 with a decimal fraction) to H.MMSSs forma t (tim e or angle up to fractions of a second). → HMS ( x.x ) Example → HMS(8.5) r eturns 8.3 INT Integer part. INT ( val ue ) Example INT(23.2) r eturns 23 MANT Mantissa (significant digits) of value . MANT ( valu e ) Example MANT(21.2E34) r eturns 2.12 MAX Maximum. […]

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    13-16 Using mathe matical functions Example % CHANGE(20,50) r eturns 150 %TOTAL Percent total : (100) y/ x . What percentage of x , is y . % TOTAL ( x , y ) Example % TOTAL(20,50) r eturns 250 RAD → DEG Radians to degrees. Converts value from radians to degrees. RAD → DEG ( va lu e ) Example RAD → DEG( π ) r eturns 180 ROUND Rounds value to […]

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    Using mathemati cal functions 13-17 XPON Exponent of value . XPON ( valu e ) Example XPON(123.4) r eturns 2 Two-variable statistics These are functions for use with two-variable statistics. See “Two-variable” on pa ge 10-15. Symbolic functions The symbolic functions are used for symbolic manipulations of expression s. The variables can be forma[…]

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    13-18 Using mathe matical functions QUAD Solves quadratic expression= 0 for variab le and returns a new expression, where variable = newexpression. The result is a general solution th at represents both positive and negative solutions by in cluding the formal variable S1 to represent any sign: + or – . QUAD( ex pre ss i on , variab l e ) Example […]

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    Using mathemati cal functions 13-19 = = Equals (logical test). Returns 1 if true, 0 if false. va lu e 1 == va l ue 2 ≠ Not equal to. Returns 1 if true, 0 if false. va lu e 1 ≠ va l ue 2 > Greater than. Returns 1 if true, 0 if false. va lu e 1 > va l ue 2 ≥ Greater than or equal to. Returns 1 if true, 0 if false. va lu e 1 ≥ va l ue 2 […]

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    13-20 Using mathe matical functions ACSC Arc cosecant. ACSC ( val u e ) ASEC Arc secant. ASEC ( val u e ) COT Cotangent: cos x /sin x . COT ( val u e ) CSC Cosecant: 1/sin x CSC ( val u e ) SEC Secant: 1/cos x . SEC ( val u e ) Symbolic calculations The HP 39gs has the ability to perform symbo lic calculations, for example, symbolic integration and[…]

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    Using mathemati cal functions 13-21 (The | symbol is in the CHARS menu: press CHARS . The = sign is listed in the MATH menu under Symbolic functions.) Symbolic calculations in the Function aplet You can perform symbolic operations i n the Function aplet’s Symbolic view. For example, to find the derivative of a function in the Function aplet’s S[…]

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    13-22 Using mathe matical functions S1 2 . E valuate the f uncti on . 3 . Show the r esult . To find derivatives in the Function aplet’s Symbolic view To find the derivative of the fu nction in the Function aplet’s Symbolic view, you define two functions and define the second function as a derivati ve of the first function. For example, to diff[…]

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    Using mathemati cal functions 13-23 4. Pr ess to display the r esult . Note: Us e the arr ow k ey s to v ie w the entir e functi on . | Y ou coul d also j us t def ine . To find the indefinite integral using formal variables F or ex ample, to f ind t he indefinite integral of use: 1. Enter the func tion . 0 S1 3 X 5 X 2 . Show the r esult f orm at […]

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    13-24 Using mathe matical functions This result is de rived from substituting X = S1 and X = 0 into the original expression found in step 1. However, substituting X = 0 will not always evaluate to zero and may result in an unwanted constant. To see this, consider: The ‘extra’ constant of 6.4 results from the substitution of into ( x –2 ) 5 /5[…]

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    Using mathemati cal functions 13-25 To access the menu of program constants: 1. Pr ess . 2. P r e s s . 3 . Use the ar r o w k e y s to na v igate thr ough the options . 4. Clic k and then to di spla y the number assigned to th e option you selected in th e pr ev ious step. The use of program constants i s illustrated in more detail in “Programmi[…]

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    13-26 Using mathe matical functions Example Suppose you want to know the potential energy of a mass of 5 units according to the equation . 1. Enter 5 2 . Pr ess and then pr ess . 3 . Select light s… f r om the Phy sic s menu . 4. Pres s . The menu c lose s and the v alue of the selec ted constant is cop ied to the edit line . 5 . Complete the equ[…]

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    Variables an d memory manageme nt 14-1 14 V ariables and memory manag ement Introduction The HP 39gs has approximately 200K of user memory. The calculator uses this memory to store variables, perform computations, and store history. A v a r i a b l e i s a n o b j e c t t h a t y o u c r e a t e i n m e m o r y t o h o l d data. The hp 39gs has two[…]

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    14-2 Variables and m emory management Storing and recalling variables You can store numbers or expressi ons from a previous input or result into variables. Numeric Precision A number stored in a variable is always stored as a 12- digit mantissa with a 3-digit exponent. Numeric precision in the display, however, de pends on the display mode (Standar[…]

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    Variables an d memory manageme nt 14-3 5 . Enter a name for the v ari able . A 6 . Pres s to stor e the re sult . The results of a calculation can also be stored directly to a variable. For example: 2 5 3 B To recall a value To recall a variable’s value, type the name of the variable and press . A To use variables in calculations You can use vari[…]

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    14-4 Variables and m emory management The VARS menu You use the VARS menu to access all variables in the calculator. The VARS menu is organi sed by category. For each variable category in the left column, there is a list of variables in the right colu mn. You select a variable category and then select a variable in the category. 1. Open the V ARS m[…]

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    Variables an d memory manageme nt 14-5 5 . Ch oose w h ether to place the var ia ble name or the v ari able v alue on the command line . – Pr ess to indicate that y ou want the v ari able ’s contents t o appear on the command line . – Pr ess to indicat e that y ou w ant the v ari able ’s name to a ppear on the command line . 6 . Pr ess to p[…]

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    14-6 Variables and m emory management 4. Enter data for L2 . 55 48 86 90 77 5 . Pr ess to ac cess HO ME . 6 . Open the v ar iable men u and selec t L1. 7 . Cop y it to th e command line . Note: Because the option is hi ghlighted , the var iable ’s name , r ather than its contents , is copied to the command line . 8. Insert the + operato r and sel[…]

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    Variables an d memory manageme nt 14-7 Home variables It is not possible to store data of one type in a variable of another type. For example, yo u use the Matrix catalog to create matrices. You can crea te up to ten matrices, and you can store these in variables M0 to M9. You cannot store matr ices in variab les other than M0 to M9. Cate- gory A v[…]

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    14-8 Variables and m emory management Aplet variables Most aplet variables stor e values t hat are uniqu e to a particular aplet. These includ e symbolic expressions and equations (see below), settings for the Plot and Numeric views, and the results of some calculations such as roots and intersections. See the Reference Information chapter for more[…]

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    Variables an d memory manageme nt 14-9 6 . T o cop y the v alue of the v ar iable in to the edit line , pr es s and pr ess . Memory Manager You can use the Memory Manager to determine the amount of available memory on the calculator. You can also use Memory Manager to organize memory. For example, if the available memory is low, you can use the Mem[…]

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    HP 39gs English. book Page 10 We dnesday, December 7, 2005 11:24 PM[…]

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    Matrices 15-1 15 M atr ices Introduction You can perform matrix calc ulation s in HOME and in programs. The matrix and each row of a matrix appear in brackets, and the elements and rows are separated by commas. For example, the following matrix: is displayed in the history as: [[1,2,3],[4,5,6]] (If the Decimal Mark mode is set to Comma , then separ[…]

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    15-2 Matr ices Creating and storing matrices You can create, edit, delete, send, and receiv e matrices in the Matrix catalog. To open the Matrix catalog, press MATRIX . You can also create and store matrices—named or unnamed—-in HOME. For example, the command: POLYROOT([1,0,–1,0])  M1 stores the root of the c omplex vector of length 3 into[…]

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    Matrices 15-3 To create a ma trix in the Matrix Catalog 1. Pr ess MATRIX to open the Matr i x Ca talog . The Matri x catalog lists the 10 av ailable matr ix v ar iable s, M0 to M9 . 2 . Hi ghlight the matr ix v a r iable name you w ant to use and pres s . 3 . Select the type o f matr i x to c r eate. – For a ve c tor (one -dimensio nal array) , s[…]

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    15-4 Matr ices A matrix is listed with two dimensions, even if it is 3×1. A vector is listed with the number of elements, such as 3. To transmit a matrix You can send matrices between c alculators just as you can send aplets, programs, lists, and notes. 1. Align the HP 3 9gs calculator s ’ infr ared ports (or connect the calc ulators using an ap[…]

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    Matrices 15-5 To display a matrix • In the Matri x catalog ( MATRIX ) , highlight the matri x name and pres s . • In HOME , ente r the name of the matr i x v ari able and pr ess . To display one element In HOME, enter matrixname ( row,column ). For example, if M2 is [[3,4],[5,6]] , then M2(1,2) returns 4 . To create a ma trix in HOME 1. Enter t[…]

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    15-6 Matr ices To store one element In HOME, enter, value matrixname ( row, column ). For example, to change the element in the first row and second column of M5 to 728, then display the resulting matrix: 728 M 512 M5 . An attempt to store an element to a row or column beyond the size of the matrix results in an error message. Matrix arithmetic You[…]

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    Matrices 15-7 3 . Add the matr ices that yo u cre a t e d. M1 M2 To multiply and divide by a scalar For division by a scalar, enter the matrix first, then the operator, then the scalar. For multiplication, the order of the operands does not matter. The matrix and the scalar can be real or complex. For example, to divide the result of the previous e[…]

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    15-8 Matr ices M1 2 To divide by a square matrix For division of a matrix or a vector by a square matrix, the number of rows of the dividend (or th e number of elements, if it is a vector) must equal the number of rows in the divisor. This operation is not a mathematical di vision: it is a left- multiplication by the inverse of th e divisor. M1/M2 […]

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    Matrices 15-9 2 . Cr eate the vec tor of the constants in the linear sys t em . 5 7 1 3 . R etur n to the Matri x Cat al og. MATRIX In this e x ample , the ve ctor y ou cr eated is listed a s M1. 4. Create a ne w matri x . Sele ct Real matrix 5 . Enter the equati on coeff ic ients . 23 4 11 1 4 12 In this e x ample , the matri x y ou c r eated is l[…]

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    15-10 Matr ices Matrix functions and commands About functions • Fu n c t i o n s c a n b e u s e d i n a ny a p l e t o r i n H O M E. T h e y ar e listed in the MA TH menu unde r the Matr i x categor y . T h e y can be used in mathematical e xpr essi ons —pr imar ily in HOME—a s w ell as in pr ogr ams. • F unctions al wa ys pr oduce and di[…]

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    Matrices 15-11 COND Condition Number. Finds the 1-norm (column norm) of a square matrix . COND ( matr i x ) CROSS Cross Product of vector1 with vecto r2 . CROSS ( vec to r 1 , ve ct or 2 ) DET Determinant of a square matrix . DET ( matr i x ) DOT Dot Product of two arrays, matrix1 matrix2 . DOT ( matr i x1, matr i x2 ) EIGENVAL Displays the eigenva[…]

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    15-12 Matr ices LU LU Decomposition. Factors a square matrix into three matrices: {[[ lowertriangular ]],[[ uppertriangular ]],[[ permutation ]]} The uppertriangular has ones on its diagonal. LU ( matr ix ) MAKEMAT Make Matrix. Creates a matrix of dimension rows × columns , using expression to calculate each ele ment. If expression contains the va[…]

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    Matrices 15-13 SPECNORM Spect ral Norm of matrix . SPECNORM ( matri x ) SPECRAD Spectral Radius o f a square matrix . SPECRAD ( matri x ) SVD Singular Value Decomp osition. Factors an m × n matrix into two matrices and a vector: {[[ m × m square orthogonal ]],[[ n × n square orthogonal ]], [ real ]}. SVD ( matr i x ) SVL Singular Values. Returns[…]

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    15-14 Matr ices Trans posi ng a Matrix The TRN function swaps the row-column and column-row elements of a matrix. For instance, e lement 1,2 (row 1, column 2) is swapped with element 2,1; element 2,3 is swapped with element 3,2; and so on. For examp le, TRN([[1,2],[3,4]]) creates the matrix [[1,3],[2,4]] . Reduced-Row Echelon Form The following set[…]

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    Matrices 15-15 The final row of zeros in the reduced-row echelon form of the augmented matrix indicates an inconsistent system with infinite solutio ns. HP 39gs English. book Page 15 We dnesday, December 7, 2005 11:24 PM[…]

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    HP 39gs English. book Page 16 We dnesday, December 7, 2005 11:24 PM[…]

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    Lists 16-1 16 L ists You can do list operations in HOME and in programs. A list consists of comma-separated real or complex numbers, expressions, or matr ices, all enclosed in braces . A list may, for example, contain a sequence of real numbers such as {1,2,3} . (If the Decimal Mark mode is set to Comma , then the separators are periods.) Lists rep[…]

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    16-2 Lists 3 . E nter the values you want i n th e l ist, pressi ng after each one. V alue s can be r eal or comple x numbers (o r an expr ession) . If you enter a calc ulation , it is e valuated and the r esult is inserted in the list . 4. When done , pr ess LIST to see the List catalog, or pr ess to re turn to HO ME . List catalog ke ys The list […]

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    Lists 16-3 List edit keys When you press to create or change a list, the following keys are available to you: Create a list in HOME 1. Enter the list on the edit line . Start and end the list w ith br aces (the shifted and ke ys) and separ ate each element with a comma. 2 . Pr ess to ev a luate and display the list. Immediatel y after typing in the[…]

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    16-4 Lists Displaying and editing lists To display a list • In the List cata log, hi ghlight the list name and pr ess . • In HOME , ente r the name of the list and pr ess . To display one element In HOME, enter listname ( element# ). For example, if L2 is {3,4,5,6}, then L2(2) returns 4 . To edit a list 1. Open th e L ist catalog. LIST . 2 . Pr[…]

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    Lists 16-5 To insert an element in a list 1. Open the List catalog. LIST . 2. P r e s s o r t o highli ght the name of the list y ou wan t to edit (L1, etc .) and pre ss to displa y the list conten ts. New elements are inserted abov e the highlighted positi on . In this example, an element, with the value of 9, is inserted between the first and sec[…]

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    16-6 Lists Deleting lists To delete a list In the List catalog, highli ght the list name and press . You are prompted to confirm that you want to delete the contents of the highlighted list variable. Press to delete the contents. To delete all lists In the List catalog, press CLEAR . Transmitting lists You can send lists to calculators or PCs just […]

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    Lists 16-7 CONCAT(L1,L2) . An ar gument can be either a list v ari able name (su ch as L1) or the actual list . F or e xample , REVERSE({1 ,2,3}) . • If Dec i mal Mark in Modes is set to C omma, u se peri ods to separat e ar guments. F or e x ample , CONCAT(L1.L2) . Common operators like +, –, ×, and / c an take lists as arguments. I f there a[…]

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    16-8 Lists Example In HOME, store {3,5,8,12,17 ,23} in L5 and find the first differences for the list. { 3,5, 8,12 ,1 7 ,2 3 } L 5 L Select Δ LIST L5 MAKELIST Calculates a sequence of elements for a new list. Evaluates expression with variable from begin to end values, taken at increment steps. MAKELIST( expression , va ria b le , begin , end , in[…]

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    Lists 16-9 position of the first occurrence is retu rned. A value of 0 is returned if there is no occurrence of the specified element. POS( list , element ) Example POS ({3, 7, 12, 19},12) returns 3 REVERSE Creates a list by reversing the order of the elements in a list. REVERSE( list ) SIZE Calculates the number of elements in a list. SIZE( list )[…]

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    16-10 Lists 2 . In HOME , st or e L1 into C1. Y ou w ill then be able to see the list data in the Numer ic vi e w of the Statis tics aplet . L1 C1 3 . S tart the Statis tic s aplet , and select 1-v ar ia ble mode (pr ess , i f necess ary , to displa y ) . Sele ct Statistics Note: Y our list values ar e no w in column 1 (C1) . 4. In the Sy mbolic v […]

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    Notes and sketches 17-1 17 Notes and sk etc hes Introduction The HP 39gs has text and pi cture editors for entering notes and sketche s. • E ach a plet has its o wn independent Note v iew and Sk etch vi e w . Not es and sk etc hes that y ou cr eate in these vi e ws ar e assoc iated w ith t he aplet. When y ou sa v e the aplet , or send it to anot[…]

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    17-2 Notes and sketches Note edit keys Key M e a n i n g Space key for text entry. Displays next page of a multi-pa ge note. Alpha-lock for letter entry. Lower-case alpha-loc k for letter entry. Backspaces cursor and deletes character. Deletes current character. Starts a new line. CLEAR Erases the entire note. Menu for entering variable names, and […]

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    Notes and sketches 17-3 Aplet sketch view You can attach pictures to an aplet in its Sketch view ( SKETCH ). Y our wo rk is au tomaticall y sav e d w ith th e aplet . Press an y other vi e w ke y or to e x it the Sk etch v ie w Sketch keys To dr aw a li ne 1. In an aplet, pr ess SKETCH f or the Sk etch v iew . 2 . In Sk etch v iew , pr ess and mo v[…]

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    17-4 Notes and sketches To draw a box 1. In Sk etc h vi e w , pres s and mov e the c urs or to wher e you w ant any corner of the bo x to be. 2. P r e s s . 3 . Mo v e the cur sor to mar k the opposite cor ner for the bo x . Y ou can adj ust the si ze of the bo x by mo v ing the cu rs o r . 4. Pres s to f inish the bo x . To draw a circle 1. In Ske[…]

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    Notes and sketches 17-5 To label parts of a sketch 1. Pr ess and type the te xt on the edit line . T o lock the Alpha shift on , pre ss (for upper case) or (for lo w er cas e) . T o mak e the label a smalle r c har acte r si z e , turn o ff befo r e pres sing . ( i s a toggle betw een small and lar ge f ont si z e) . The smaller c har acter si z e […]

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    17-6 Notes and sketches To import a graphics variable You can copy the contents of a graphics variable into the Sketch view of an aplet. 1. Open the Sketch v iew of the aplet ( SKETCH ). T he graphi c w ill be copied her e. 2 . Pr ess , . 3 . Highlight Graphic , then pr ess and highligh t the name of the v ari able ( G1 , etc .) . 4. Pres s to r ec[…]

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    Notes and sketches 17-7 4. W r ite y our note . See “Note e dit ke ys ” on page 17 — 2 for mor e infor mation on the entry and editing of notes. 5 . When yo u are f inis hed , press or an aplet ke y to e x it Notepad . Y our wor k is automaticall y sav ed. Notepad Catalog keys Key M e a n i n g Opens the selected note for editing. Begins a new […]

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    17-8 Notes and sketches To import a note You can import a note from the Notepad into an aplet’s Note view, and vice versa. Supp ose you want to copy a note named “Assignments” fr om the Notepad into the Function Note view: 1. In the Func tion aplet , display the No te v ie w ( NOTE ). 2 . Pr ess , highlight Notepad in the left column, then hi[…]

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    Programming 18-1 18 Pr ogr amming Introduction This chapter describes how to pro gram using the hp 39gs. In this chapter you’ll learn about: • using the Pr ogram catalog to c r eate and edit pr ogr ams • pr ogr amming commands • stor ing and retr ie v ing var iables in pr ograms • pr ogr amming var iables. HINT More informatio n on progra[…]

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    18-2 Programming Example RUN GETVALUE: RUN CALCULATE: RUN » SHOW ANSWER » : This program is separated into three main tasks, each an individual program. Within each progr am, the task can be simple—or it can be di vided further into other programs that perform smaller tasks. Program catalog The Program catalog is wher e you create, edit[…]

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    Programming 18-3 Program catalog k eys The program catalog keys are: Key M e a n i n g Opens the highlighted program for editing. Prompts for a new program name, then opens an empty program. Transmits the highlighted program to another HP 39gs or to a disk drive. Receives the highlighted program from another HP 39gs or from a disk drive. Runs the h[…]

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    18-4 Programming Creating and editing programs Create a new program 1. Pr ess PROGR M to open the Pr ogr am catalog . 2. P r e s s . The HP 3 9gs pr ompts yo u fo r a n a m e. A pr ogr am name can contain spec ial char acters , such as a space . Ho we ve r , if y ou use spec ial char acters and then run the pr ogr am b y typing it in HOME , y ou mu[…]

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    Programming 18-5 2 . On the left, u se or to highligh t a command category , then pr ess to ac cess the commands in the category . Select the command that y ou w ant . 3 . Pr ess to paste the command into the pr ogram editor . Edit a program 1. Pres s PR OGRM to open the Pr ogram catalog. 2 . Use the arr o w k e y s to hi ghlight the pr ogram y ou […]

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    18-6 Programming Editing keys The editing keys are: Key M e a n i n g Inserts the character at the editing point. Inserts space into text. Display s previous page of the program. Displays next page of the program. Moves up or down one line. Moves right or left one character. Alpha-lock for letter entry. Press A…Z to lock lower case. Backspaces cu[…]

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    Programming 18-7 Using programs Run a program From HOME, type RUN program_name. or From the Program catalog, highlight the program you want to run and press Regardless of where you star t the program, all programs run in HOME. What you see will differ slightly depending on where you started the program. If you start the program from HOME, the HP 39[…]

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    18-8 Programming Copy a program You can use the following procedure if you want to make a copy of y our work before editing—or if you want to use one program as a template for another. 1. Pr ess PROGR M to open the Pr ogr am catalog . 2. P r e s s . 3 . T ype a ne w f ile name, then c hoose . T he Progr am Edito r opens with a ne w pr ogr am . 4.[…]

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    Programming 18-9 Delete a program To delete a program: 1. Pr ess PROGRM to open the Progr am catalog. 2 . Highligh t a pr ogr am to delet e , then pr ess . Delete all programs You can delete all programs at once. 1. In the Progr am catalog, pr ess CLEAR . 2. P r e s s . Delete the contents of a program You can clear t he contents of a program witho[…]

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    18-10 Programming 4. D e v elop a pr ogram that u ses the SE TVI EW S command to modify the aplet’s VIEW S menu . The menu opti ons pr o v ide links to ass oc iated pr ograms . Y ou can spec i fy an y other progr ams that you w ant tr ansfe rr ed with the aplet . See “SETVIEW S” on page 18-14 for inf ormati on on the command . 5 . Ensur e tha[…]

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    Programming 18-11 Save the aplet 1. Open the F uncti on aplet and sa ve it as “EXP ERIMENT ” . The ne w aplet appear s in the Aplet library . Select Function EXP ERIMENT 2 . Cr eate a pr ogr am called EXP .ME1 with contents as show n. T his pr ogr am conf igur es the plot r anges, then r uns a pr ogr am that allo ws y ou to s et the angle f orm[…]

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    18-12 Programming 6 . Open the Pr ogram cat alog and cr eate a progr am named “EXP .S V” . Include the f ollo w ing code in the pr ogr am. E a c h entry line after the command SE T VIEW S is a tri o that consists of a VIEW S menu te xt li ne (a space indicate s none), a progr am name , and a number that def ines the v ie w to go to afte r the p[…]

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    Programming 18-13 ’ ’ ’ ’ ;’ ’ EXP.ANG’ ’ ;0 ; The pr o gr am EXP .ANG is a small routine that is called by other pr ogr ams that the aplet us es . This e ntry spec ifi es that the pr ogr am EXP.ANG is transfer r ed w hen the aplet is tr ansfer r ed, bu t the space in the fir st quotes en sur es that no entry appears on the menu . ?[…]

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    18-14 Programming Aplet commands CHECK Checks (selects) the correspon ding function in the current aplet. For example, Check 3 would check F3 if the current aplet is Function. T hen a checkmark would appear next to F3 in Symbolic view, F3 would be plotted in Plot view, and evaluated in Numeric view. CHECK n : SELECT Selects the named aplet and ma k[…]

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    Programming 18-15 options u se , or the pr ogr am that def ines the a plet’s VIEW S menu . • Y ou can inclu de a “Start ” optio n in the VIEW S men u to spec if y a pr ogr am that y ou w ant to run auto maticall y when the aplet s tarts. This pr ogram typically sets up the aplet’ s initial confi guration . T he S T AR T option on the men […]

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    18-16 Programming ProgramName ProgramName is the name of the program that runs when the corresponding menu entry is selected. All pr ograms that are identified in the aplet’s SETV IEWS command are transferred when the aplet is transmitted. ViewNumber V iewNumber is the number of a view to start after the program finishes runn ing. For example, if[…]

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    Programming 18-17 View numbers The Function aplet views are numbered as follows: View numbers from 15 on will vary according to the parent aplet. The list shown above is for the Function aplet. Whatever the normal VIEWS menu for the parent aplet, the first entry will become number 1 5, the second number 16 and so on. UNCHECK Unchecks (unselects) th[…]

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    18-18 Programming Example 1  A : IF A==1 THEN MSGBOX » A EQUALS 1″ : END: IF… THEN… ELSE… END Executes the true-clause sequence of commands if the test- clause is true, or the false-clause se quence of commands if the test-clause is false. IF test-clause THEN true-clause ELSE fals e-clause END Example 1  A : IF A==1 THEN MSGBO[…]

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    Programming 18-19 IFERR…THEN…ELSE…END allows a program to intercept error conditions that otherwise would cause the program to abort. Its syntax is: IFERR tr ap-cla us e THEN clause _1 ELSE clause _2 END : Example IFERR 60/X  Y: THEN MSGBOX «Error: X is zero.»: ELSE MSGBOX «Value is «Y: END: RUN Runs the named program. […]

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    18-20 Programming Example ARC 0;0;2;0;2 π : FREEZE: Dr a w s a c irc le center ed at (0, 0) of r adius 2 . T he FREEZE command causes the c ir cle to r emain di spla ye d on t he sc reen until y ou pr ess a k ey . BOX Draws a box with diagonally opposite corners ( x1,y1 ) and ( x2,y2 ). BOX x1 ; y1 ; x2 ; y2 : Example BOX -1;-1;1;1: FREEZE: Dr a w[…]

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    Programming 18-21 Example TLINE 0;0;3;3: Er ase s pr e v iou sly dr a wn 4 5 degr ee line fr om (0, 0) to (3, 3) , or dr aw s that line if it doesn’t alr eady e xist . Graphic commands The graphic commands use th e graphics variables G0 through G9—or the Page variable from Sketch—as graphicname arguments. The position argument takes the form […]

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    18-22 Programming will superimpose G1 onto G0 starting a position (1,1), where the position is given in terms of the current axes settings, not as a pixel position. GROBXOR Usin g the logical XOR, superimposes graphicname2 onto graphicname1 . The upper left corner of graphicname2 is placed at position . GROBXOR gr aphi cname1 ; ( pos ition) ; gr ap[…]

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    Programming 18-23 ZEROGROB Creates a blank graphic with given width and height , and stores i t in graphicname . ZEROGROB gr aphicname ; wid t h ; heigh t : Loop commands Loop hp allow a program to execute a routine repeatedly. The HP 39gs has three loop structures. The example programs below illustrate each of these structures incrementing the var[…]

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    18-24 Programming Note that the STEP parameter is optional. If it is omitted, a step value of 1 is assumed. BREAK Terminates loop. BREAK: Matrix commands The matrix commands take variables M0–M9 as arguments. ADDCOL Add Column. Inserts values into a column before column_number in the specified matrix . You enter the values as a vector. The values[…]

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    Programming 18-25 RANDMAT Creates random matrix with a specified number of rows and columns and stores the result in name ( name must be M0…M9 ). The entries will be integers ranging from –9 to 9. RANDMAT name ; rows ; columns : REDIM Redimensions the specified matrix or v ector to size . For a matrix, size is a list of two integers {n1,n2} . F[…]

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    18-26 Programming Print commands These commands print to an HP infrared printer, for example the HP 82240B printer. PRDISPLAY Prints the contents of the display. PRDISPLAY: PRHISTORY Prints all objects in the hi story. PRHISTORY: PRVAR Prints name an d contents of variablename . PRVAR va ri ablename : You can also use the PRVAR comman d to print th[…]

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    Programming 18-27 Example 3  A:CHOOSE A; «COMIC STRIPS»; «DILBERT»; «CALVIN&HOBBES»; «BLONDIE»: CLRVAR Clears the specified va riable. The syntax is: CLR V AR v ari able : Example If you have stored {1,2,3,4} in variable L1, entering CLVAR L1 w ill clear L1. DISP Displays textitem in a row of the displ[…]

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    18-28 Programming Example DISPXY –3.5;1.5;2;»HELLO WORLD»: DISPTIME Displays the current date and time. DISPTIME To set the date and time, simply store the correct settings in the date and time variables. Use the following formats: M.DDYYYY for the date and H.MMSS for the time. Examples 5.152000  DATE( sets the date to May 15, 2000) […]

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    Programming 18-29 GETKEY Waits for a key, then st ores the k eycode rc.p in name, where r is row number, c is column number, and p is key- plane number. The key-planes numbers are: 1 for unshifted; 2 for shifted; 4 for alpha-shifted; and 5 for both alpha-shifted and shifted . GETKEY name : INPUT Creates an input form with a title bar and one field.[…]

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    18-30 Programming PROMPT Displays an input box with name as the title, and prompts for a value for name . name can be a variable such as A…Z, θ , L1…l9, C1…C9 or Z1…Z9. PROMPT nam e : WAIT Halts program execution for the specified number of seconds. WAIT sec onds : Stat-One and Stat-Two commands The following commands are used for analyzin[…]

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    Programming 18-31 Datasetname can be SI, S2,…, or S5 . Datasetname must include at least two pairs of data points. DO2VSTATS datasetname : SETDEPEND Sets datasetname dependent column . Datasetname can be S1, S2, …, or S5 and column can be C0–C9. SETDEPEND datasetname ; column : SETINDEP Sets datasetname independent column . Datasetname can be[…]

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    18-32 Programming Plot-view variables Area Function Contains the last value found by the Area function in Plot- FCN menu. Axes All Aplets Turns axes on or off. From Plot Setup, check (o r uncheck) AXES . or In a program, type: 1  Axes —to turn axes on (def ault) . 0  Axes —to turn ax es off . Connect Function Parametric Polar Solve Statis[…]

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    Programming 18-33 Grid All Aplets Turns the background grid in Plot view o n or off. From Plot setup, check (or uncheck) GRID . or In a program, type 1  Grid to tur n the gr id on . 0  Grid to tur n the gri d off (def ault). Hmin/Hmax Statistics Defines minimum and maximum values for histogram bars. From Plot Setup for one-variable statistics[…]

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    18-34 Programming Isect Function Contains the last value found by the Intersection function in the Plot-FCN menu. Labels All Aplets Draws labels in Plot view showing X and Y ranges. From Plot Setup, check (o r uncheck) Labels or In a program, type 1  Labels —to turn labels on . 0  Labels —to turn labels o ff (def ault) . Nmin / Nmax Seque[…]

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    Programming 18-35 S1mark–S5mark Statistics Sets the mark to use for scatter plots. From Plot Setup for two-variable statistics, S1mark- S5mark , then choose a mark. or In a program, type n  S1mark wh ere n is 1,2,3,…5 SeqPlot Sequence Enables you to choose types of sequence plot: Stairstep or Cobweb. From Plot Setup, select SeqPlot , then ch[…]

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    18-36 Programming Umin/Umax Polar Sets the minimum and maxi mum independent values. Appears as the URNG field in the Plot Setup input form. From the Plot Setup input form, enter values for URNG . or In a program, type  Umin  Umax wher e Ustep Polar Sets the step size for an independent v ariable. From the Plot Setup input form, enter values f[…]

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    Programming 18-37 Tstep Parametric Sets the step size for the independent variable. From the Plot Setup input form, enter values for TSTEP . or In a program, type n  Tstep wh ere Xcross All Aplets Sets the horizontal coordinate of the c rosshairs. Only works with TRACE off. In a program, type n  Xcross Ycross All Aplets Sets the vertical coor[…]

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    18-38 Programming  Xmin  Xmax whe re Ymin / Ymax All Aplets Sets the minimum and maximum vertical values of the plot screen. Appears as the YRNG fields (vertical range) in the Plot Setup input form. From Plot Setup, enter the values for YRNG . or In a program, type  Ymin  Ymax whe re Xzoom All Aplets Sets the horizontal zoom factor. Fro[…]

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    Programming 18-39 Symbolic-view variables Angle All Aplets Sets the angle mode. From Symbolic Setup, choose Degrees , Radia ns , or Grads for angle measure. or In a program, type 1  Angle —for De grees. 2  Angle —for Radian s. 3  Angle —for Grads. F1…F9, F0 Function Can contain any expression. Independent variable is X . Example &a[…]

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    18-40 Programming S1fit…S5fit Statistics Sets the type of fit to be used by the FIT operation in drawing the regression line. From Symbolic Setup view, specify the fit in the field for S1FIT, S2FIT, etc. or In a program, store one of the fo llowing constant numbers or names into a variable S1fit , S2fit , etc. 1 Linear 2 LogFit 3 ExpFit 4 Power 5[…]

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    Programming 18-41 Numeric-view variables The following aplet variabl es control the Numeric view . The value of the variable appl ies to the current aplet only. C1…C9, C0 Statistics C0 through C9 , for column s of data. Can contain lists. Enter da ta in the N umeric view or In a program, type LIST  C n wh ere n = 0, 1, 2, 3 … 9 Digits All Ap[…]

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    18-42 Programming Note that if Fraction or M ixed Fraction is chosen, the setting will be ignored when labeling axes in Plot view. A setting of Scientific will be used instead. Example Scientific  Format or 3  Format NumCol All Aplets except Statistics aplet Sets the column to be highlighted in Numeric view. In a program, type n  NumCol wh[…]

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    Programming 18-43 NumStep Function Parametric Polar Sequence Sets the step size (increment value) for an independent varia ble in N umeri c view. From Num Setup, enter a value for NU MSTEP . or In a program, type n  NumStep wh ere NumType Function Parametric Polar Sequence Sets the table format. From Num Setup, choose Automatic or Build You r Ow[…]

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    Note variables The following aplet variable is available in Note view. NoteText All Aplets Use NoteText to recall text previously entered in Note view. Sketch variables The following aplet variables are available in Sk etch view. Page All Aplets Sets a page in a sketch set. The graphics can be viewed one at a time using the and keys. The Page var i[…]

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    Extending aplets 19-1 19 Extending aplets Aplets are the application environments where you explore different cla sses of mathematical operations. You can extend the capabili ty of the HP 39gs in the following ways: • Cr eate ne w aplets , based on e x isting aplets , w ith spec ifi c conf igur ations suc h as angle measur e, gr aphical or tabula[…]

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    19-2 Ext ending aple ts 1. Open the Solv e aplet and save it under the n e w name . Solve | T R I A N G L E S 2 . E nte r t h e fo ur form ul as : θ O H θ A H θ OA AB C 3 . Dec ide whether y ou want the a plet to oper ate in Degr ees , R adians , or Gr ads. MODES Degrees 4. Vie w the Aplet L i br ar y . The “ TRIANGLE S” aplet is listed in t[…]

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    Extending aplets 19-3 Using a customized aplet To use the “T riangles” aplet, simply s elect the appropriate formula, change to the Numeric view and solve for the missing variable. Find the length of a ladder leaning against a vertical wall if it forms an angle of 35 o with the hori zontal and extends 5 metres up the wall. 1. Select the aplet .[…]

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    19-4 Ext ending aple ts Annotating an aplet with notes The Note view ( NOTE ) attaches a note to the current aplet. See Chapter 17, “Notes and sketc hes”. Annotating an aplet with sketches The Sketch view ( SKETCH ) attaches a picture to the current aplet. See chapter 17, “Notes and sketches”. HINT Notes and s k et c hes th at y ou atta c h[…]

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    Extending aplets 19-5 To transmit an aplet 1. Connect the P C or aplet disk dr iv e to the calc ulator by cable or align the tw o calc ulators ’ infr ar ed ports by matc hing up the tr iangle marks on the r ims of the calc ulators . P lace the calculato rs no mor e than 4 inches (10 cm) apar t. 2 . Sending calc ulator : Open the L ibrary , highli[…]

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    19-6 Ext ending aple ts Note : ch oose a disk dri ve option if y ou are using the hp3 9gs connecti vity kit to tr ansfer the a plet . Hi ghlight y our selec tion and pr ess . The T r ansmit annu nc iator— —i s display e d until tr ansmis sion is co mplet e . If you are using the PC Connectivity Kit to download aplets from a PC, you will see a l[…]

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    R-1 R Re fer ence inf ormation Glossary aplet A small application, limited to one topic. The built-in aplet types are Function, Parametric , Polar, Sequence, Solve, Statistics, Inference, Finance, Trig Explorer, Quad Explorer, Linear Solver and Triangle Solve. An aplet can be filled with the data and solutions for a specific problem. It is reusable[…]

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    R-2 list A set of values separated by commas (periods if the Decimal Mark mode is set to Comma ) and enclosed in braces. Lists are commonly used to enter statistical data and to evaluate a function with multiple values. Created and manipulate d by the List editor and catalog. matrix A two-dimensional ar ray of values separated by commas (periods if[…]

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    R-3 Resetting the HP 39gs If the calculator “locks up” and seems to be stuc k, you must reset it. This is much like resetting a PC. It cancels certain operations, restores ce rtain conditio ns, and clears temporary memory locations. However, it does not clear stored data (variables, ap let databases, programs) unless you use the proced ure, “[…]

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    R-4 If the calculator does not turn on If the HP 39gs does not turn on follow the steps below until the calculator turns on. You may find that the calculator turns on before you have completed the procedure. If the calculator still does not turn on, please contact Customer Support for further information. 1. Pr ess and hold the ke y for 10 seconds.[…]

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    R-5 To install the main batteries a. Slide up the battery compartment cove r as illustrated. b. Insert 4 new AAA (LR03) batteries into the main compartment. Make sure each battery is inserted in the indicated direction. To install the backup battery a. Press down the holder. Push the plate to the shown direction and lift it. b. Insert a new CR2032 […]

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    R-6 Variables Home variables The home variables are: Categor y Available name Complex Z1 … Z9 , Z0 Graphic G1 … G9 , G0 Library Function Parametric Polar Sequence Solve Statistics User-named List L1 … L9 , L0 Matrix M1 … M9 , M0 Modes Ans Date HAngle HDigits HFormat Ierr Time Notepad User-named Program Editline User-named Real A…Z, θ HP […]

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    R-7 Function aplet variables The function aplet variables a re: Category Av ailable name Plot Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Simult Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Plot-FCN Area Extremum Isect Root Slope Symbolic Angle F1 F2 F3 F4 F5 F6 F7 F8 F9 F0 Nume ric Digits Format NumCol NumFo[…]

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    R-8 Parametric aplet variables The parametric aplet variables are: Categor y Available name Plot Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Tmin Tmax Tracing Tstep Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom Symbolic Angle X1 Y1 X2 Y2 X3 Y3 X4 Y4 X5 Y5 X6 Y6 X7 Y7 X8 Y8 X9 Y9 X0 Y0 Numeric Digits Format NumCol NumFo[…]

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    R-9 Polar aplet variables The polar aplet variables are: Category Av ailable names Plot Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Umin Umax θ step Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle R1 R2 R3 R4 R5 R6 R7 R8 R9 R0 Nume ric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep […]

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    R-10 Sequence aplet variables The sequence aplet variables are: Categor y Available name Plot Axes Coord Grid Indep InvCross Labels Nmin Nmax Recenter SeqPlot Simult Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom Symbolic Angle U1 U2 U3 U4 U5 U6 U7 U8 U9 U0 Numeric Digits Format NumCol NumFont NumIndep NumRow NumStart NumStep Num[…]

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    R-11 Solve aplet variables The solve aplet variables are: Category Av ailable name Plot Axes Connect Coord FastRes Grid Indep InvCross Labels Recenter Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle E1 E2 E3 E4 E5 E6 E7 E8 E9 E0 Nume ric Digits Format NumCol NumRow Note NoteText Sketc h Page PageNum HP 39gs English.[…]

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    R-12 Statistics aplet variables The statistics aplet variables are: Categor y Available name Plot Axes Connect Coord Grid Hmin Hmax Hwidth Indep InvCross Labels Recenter S1mark S2mark S3mark S4mark S5mark StatPlot Tracing Xcross Ycross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yxoom Symbolic Angle S1fit S2fit S3fit S4fit S5fit Numeric C0,…C9 Digits F[…]

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    R-13 MATH menu categories Math functions The math functions are: Category Av ailable name Calculus TAYLOR Complex ARG CONJ IM RE Constant e i MAXREAL MINREAL π Hyper b. ACOSH ASINH ATANH COSH SINH TANH ALOG EXP EXPM1 LNP1 List CONCAT Δ LIST MAKELIST π LIST POS REVERSE SIZE Σ LIST SORT Loop ITERATE RECURSE Σ ∂ ∫ HP 39gs English. book Page 1[…]

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    R-14 Matrix COLNORM COND CROSS DET DOT EIGENVAL EIGENVV IDENMAT INVERSE LQ LSQ LU MAKEMAT QR RANK ROWNORM RREF SCHUR SIZE SPECNORM SPECRAD SVD SVL TRACE TRN Polynom. POLYCOEF POLYEVAL POLYFORM POLYROOT Prob. COMB ! PERM RANDOM UTPC UTPF UTPN UTPT Real CEILING DEG → RAD FLOOR FNROOT FRAC HMS → → HMS INT MANT MAX MIN MOD % %CHANGE %TOTAL RAD ?[…]

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    R-15 Program constants The program constants are: Tests < ≤ = = ≠ > ≥ AND IFTE NOT OR XOR Trig ACOT ACSC ASEC COT CSC SEC Category Av ailabl e name (Continued) Category Av ailable name Angle Degrees Grads Radians Format Standard Fixed Sci Eng Fraction SeqPlot Cobweb Stairstep S1…5fit Linear LogFit ExpFit Power Trigonometric QuadFit Cu[…]

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    R-16 Physical Constants The physical constants are: Categor y Available Na me Chemist • Avogadro ( A v ogadr o ’s Number , NA) • Boltz . (Boltmann, k) • mol. vo… (molar v olume , Vm) • univ gas (uni ver sal gas , R) • std temp (standard temper a tur e , St d T ) • std pres (standar d pr essur e, St d P ) Phyics • Stef Bolt (Ste fa[…]

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    R-17 Program commands The program commands are: Category Command Aplet CHECK SELECT SETVIEWS UNCHECK Branch IF THEN ELSE END CASE IFERR RUN STOP Drawing ARC BOX ERASE FREEZE LINE PIXOFF PIXON TLINE Graphic DISPLAY → → DISPLAY → GROB GROBNOT GROBOR GROBXOR MAKEGROB PLOT → → PLOT REPLACE SUB ZEROGROB Loop FOR = TO STEP END DO UNTIL END WHIL[…]

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    R-18 Status messages Stat-Two DO2VSTATS SETDEPEND SETINDEP Category Command (Continued) Messag e Meaning Bad Argument Type Incorrect input for this operation. Bad Argument Value The value is out of range for this operation. Infinite Result Math exception, such as 1/0. Insufficient Memory You must recover some memory to continue operation. Delete on[…]

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    R-19 Invalid Syntax The function or command you entered does not include the proper arguments or order of arguments. The delimiters (parentheses, commas, periods, and semi-colons) must also be correct. Look up the function name in the index to find its proper syntax. Name Conflict The | (wher e) function attempted to assign a value to the variable […]

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    HP 39gs English. book Page 20 We dnesday, December 7, 2005 11:24 PM[…]

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    W-1 L imited W arr anty HP 39gs Graphing Calculator; Warranty peri od: 12 months 1. HP war r ants to you , the end- us er cu stomer , t hat HP har dw are , acc es sor ies and su pplies w i ll be fr ee fr om def ects in mater ials and w ork manship after the date of pur chase , for the peri od spec if ied abo v e . If HP r ecei ves notice of such de[…]

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    W-2 6 . HP MAKE S NO O THER E XPRE S S W ARRANTY OR CONDI T ION WHET HER WRI TTEN OR OR AL . T O THE EXTENT ALL O WED B Y L OCAL LA W , ANY IMP LIED W ARRANTY OR CONDI TION OF MERCHANT ABILITY , S A T ISF A CT OR Y QU ALITY , OR FI TNE SS F OR A P AR TICUL AR P URP OSE I S LIMITED T O THE DUR A TION OF THE EXP RE S S W A RRANTY SET F OR TH ABO VE .[…]

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    W-3 Service Europe Country : Telephone numbers Au str ia +4 3-1-3 60 2 77120 3 Belgium + 3 2 — 2 — 712 6 219 D e n m a r k + 45 — 8 -2 33284 4 Ea s te r n Eu ro p e countr ies +4 20-5- 414 2 2 5 2 3 Fi n l a n d + 35 — 8964 0 0 0 9 F r ance +3 3-1 — 4 9 9 3 9006 German y +4 9-6 9-9 5 30 7103 Gr eece +4 20 -5- 414 2 2 5 2 3 Holland +31- 2 -06 54 5 3[…]

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    W-4 P lease logon to http://www .hp.com f or t he lat est se r v ice and supp ort info rmati on .h L.Ame r ic a Country: T elephone nu mbers Ar gentina 0 -810 -5 5 5-5 5 20 Bra zil Sao P aulo 3 7 4 7 — 77 99; RO T C 0 -800 -15 77 51 M e xi c o M x C i t y 5 258 — 9 922; RO T C 01-800 — 4 7 2 -66 84 Ven e z u e l a 0 8 0 0 — 4 7 46 — 8368 Chi le 800[…]

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    W-5 Regulatory infor mation Federal Communications Commission Noti ce This equipment has been tested and found to comply with the limits for a Class B digital dev ice, pursuant to Part 15 of the FCC Rules. These limi ts are designed to provide reasonable protection agains t harmful interference in a residential installation. This equipment generate[…]

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    W-6 Houston, Texas 77269-2000 Or, call 1-800-474-6836 For questions regarding this FCC declarati on, contact: Hewlett-Packard Company P. O. Box 692000, Mai l Stop 510101 Houston, Texas 77269-2000 Or, call 1-281-514-3333 To identify this produc t, refer to the part, series, or model number found on the product. Canadian Notice This Class B digital a[…]

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    W-7 Korean Notice Disposal of Waste Equipment by Users in Private Household in the European Union This symbol on the product or on its packaging indicates that this product must not be disposed of with your other household waste. Instead, it is your responsibility to dispose of your waste equipment by handing it over to a designated collection poin[…]

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    HP 39gs English. book Page 8 Wed nesday, December 7, 2 005 11:24 PM[…]

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    I-1 Index A absolute value 13-5 add 13-3 algebraic entry 1-19 alpha characters typing 1-6 alphabetical so rting 19-6 angle measure 1-10 in statistics 10-12 setting 1-11 animation 17-5 creating 17 -5 annunciators 1-3 Ans (last answer) 1-24 antilogarithm 13-4 , 13-9 aplet attaching notes 19-4 clearing 19-3 copying 19-4 definition of R-1 deleting 19-6[…]

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    I-2 C calculus operat ions 13-7 catalogs 1-30 chronological sorting 19-6 circle dra wing 17-4 clearing aplet 19-3 character s 1-22 display 1- 22 display history 1-2 5 edit line 1-22 lists 16-6 plot 2-7 cobweb graph 6-1 coeffi cients polynomial 13-11 columns changing position 18-25 combinations 13 -12 commands aplet 18-14 branch 18-17 definition of […]

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    I-3 definite integral 13-6 deleting aplet 19-6 lists 16-6 matrices 15-5 programs 18- 9 statistical data 10-11 delimiters, programming 18-1 derivatives definition of 13-6 in Function aplet 13-22 in Home 13-21 determinant square matrix 15-11 differentiation 13-6 display 18-21 adjusting contrast 1-2 annunciator line 1-2 capture 18-21 clearing 1-2 date[…]

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    I-4 font size change 3-8 , 17-5 forecasting 10-20 fraction number format 1-1 1 full-precision display 1-10 function analyze graph with FCN tools 3-4 definition 2-2 , R-1 entering 1-19 gamma 13- 12 intersection point 3-5 math menu R-13 slope 3-5 syntax 13-2 tracing 2-8 Function aplet 2-20 , 3-1 function variables area 18-32 axes 18-32 connect 18-32 […]

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    I-5 EXPM1 13-10 LNP1 13-10 SINH 13-9 TANH 13-9 hypothesis alternative 11-2 inference tests 11-8 null 11-2 tests 11-2 I i 13-8 implied multiplication 1-20 importing graphics 17-6 notes 17-8 increasing display contrast 1-2 indefinite integral using symbolic variables 13-23 independent values adding to table 2-18 independent variable defined for Traci[…]

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    I-6 generate a series 16-8 list function syntax 16-6 list variables 16-1 returning position of element in 16-8 revers ing orde r in 16-9 sending and receiving 16-6 sorting elements 16-9 storing elements 16-1 , 16-4 , 16-5 storing one element 16 -6 logarithm 13-4 logarithmic fit 10-13 functions 13-3 logical operators AND 13-19 equals (logical test) […]

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    I-7 singular value decomposition 15-13 singular values 15-13 size 15-12 spectral norm 15-13 spectral radius 15-13 start Matrix Editor 18-2 4 storing elements 15-3 , 15-5 storing matrix elements 15-6 swap column 18-25 swap row 18-25 transposing 15-13 , 15-14 variables 15-1 matrix functions 15-10 COLNORM 15-10 COND 15-11 CROSS 15-1 1 DET 15-11 DOT 15[…]

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    I-8 recalc ulating 2-18 setup 2-16 , 2-19 O off automatic 1-1 power 1-1 on/cancel 1-1 One-Proportion Z-Interval 11- 17 One-Sample T-Interval 11-18 One-Sample T-Test 11-1 2 One-Sample Z-Interval 11-15 One-Sample Z-Test 11-8 order of precedence 1-21 overlaying plots 2-15 , 4-3 P π 13-8 paired columns 10-11 parametric variables axes 18-32 connect 18-[…]

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    HP 39gs English. book Page 14 We dnesday, December 7, 2005 11:24 PM[…]

Источник

Если вдруг вам нужен калькулятор, предлагаю обратить внимание на модель HP 39gs — это графический калькулятор начального уровня с экстремально низкой, для подобного рода устройств, ценой.

Основные характеристики:

Дисплей: Регулируемая контрастность, 7 строк x 33 символа плюс 2-строчный заголовок и 1-строчное меню, 131 x 64 пикселей
Тип дисплея: ЖК-дисплей
Регистры памяти: 70
Блок питания: AAA x 4 + CR2032

Комплектация:

Калькулятор, сдвигающаяся крышка, кабель USB.

Область применения:

Общая математика; Введение в алгебру/алгебра; Тригонометрия; Статистические вычисления; Геометрия.

Из описания производителя:

Динамически разделенный экран с регулируемой контрастностью для удобного просмотра.
Интуитивный ввод алгебраических данных позволяет решать задачи подобно тому, как они решаются на бумаге.
Символические, числовые и графические виды для расширения возможностей обучения.
Простые функции программирования для создания специальных апплетов с использованием формул и уравнений, облегчающих обучение.
Поддержка интерактивного журнала, создания заметок и набросков для просмотра и изменения данных.
Более 600 встроенных функций и различные программы и приложения HP для решения самых сложных задач.

Полезные ресурсы:

Ссылка на сайт производителя:
HP 39gs

Ссылка на сайт с расширениями для HP 39gs:
https://www.hpcalc.org/

Начало работы (76 страниц):
HP 39gs Graphing Calculator Quick Start Guide

Руководство пользователя (314 страниц):
user’s guide

Внешний вид:

Обратная сторона:

Для питания прибора требуется 4 батарейки ААА, и одна CR2032 — для питания микросхемы памяти, в которой хранятся все настройки.

Интерфейсы связи:

Для связи с ПЭВМ используется разъем USB (слева), который так же может использоваться и для питания прибора. Через USB можно загружать на калькулятор дополнительные приложения, например отсюда: https://www.hpcalc.org/. Справа разъем для подключения оборудования для сбора данных. Есть так же инфракрасный приемопередатчик, предназначенный для связи с другими HP 39gs.

Главное окно выбора приложений «APLET LIBRARY»:

Через это окно выполняется выбор встроенных и определенных пользователем приложений.

Список функций:

Можно определить до 10 собственных функций.

Примеры использования приложения «Function»:

Функция F1(x) = 1/2 + 2/π(cos(x) — 1/3cos(3x) + 1/5cos(5x)):

График функции F1(x) = 1/2 + 2/π(cos(x) — 1/3cos(3x) + 1/5cos(5x)):

Функция F(2) = x^3 — x^2 — 7x + 6:

График функции F(2) = x^3 — x^2 — 7x + 6:

Также, в сети можно найти информацию по переделке этой модели в более старшую модель, с поддержкой символьных вычислений:
Переделываем программируемый калькулятор HP 39GS в 48GII, но эта задача скорее для гиков, чем для обычных пользователей.

Источник

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