HP 39g Master Manual

Graphing calculator.

hp 39g+ graphing calculator
Mastering the hp 39g+
A guide for teachers, students and other
users of the hp 39g+, hp 39g & hp 40g
Edition 1.1
HP part number F2224-90010
Printed Date: 2005/10/11 Summary of Contents for HP 39g

• Page 1 39g+ graphing calculator Mastering the hp 39g+ A guide for teachers, students and other users of the hp 39g+, hp 39g & hp 40g Edition 1.1 HP part number F2224-90010 Printed Date: 2005/10/11...

The MEMORY MANAGER view... 37 Downloaded aplets & memory ... 38 The GRAPHICS MANAGER ... 39 The LIBRARY MANAGER... 39 Fractions on the hp 39g+... 40 Pitfalls to watch for ... 42 The HOME History ... 43 COPYing calculations... 43 Clearing the History...
• Page 3 The NUM view revisited ... 77 ZOOM...78 Integration: The definite integral using the Integration: The algebraic indefinite integral ... 81 The hp 40g Computer Algebra System... 82 Integration: The definite integral using PLOT variables ... 83 Piecewise defined functions ... 85 ‘Nice’ scales... 86 Use of brackets in functions ...
• Page 4 Problems when evaluating limits ... 88 Gradient at a point... 90 Finding and accessing polynomial roots ... 91 The VIEWS menu ... 92 Plot-Detail ... 93 Plot-Table ...94 Overlay Plot ... 95 Auto Scale ... 96 Decimal, Integer & Trig... 97 Downloaded Aplets from the Internet ...
• Page 5 The Stats Aplet - Univariate Data ... 122 Uni vs. Bi-variate data ... 122 Clearing data ... 122 Sorting data ... 123 The STATS key ... 123 Functions of columns ... 124 Registering columns as ‘in use’... 124 Working with frequency tables ... 125 Auto scale...
• Page 6 Independent Notes and the Notepad Catalog... 179 Transferring notes using IR ... 180 Editing software... 180 Software ... 181 For the hp 38g, hp 39g & hp 40g... 181 For the hp 39g+ ... 181 Creating a Note ... 182 Locking ALPHA mode ... 182 The CHARS view ...
• Page 7 Some examples of saved aplets ... 192 The Triangles aplet... 192 The Prob. Distributions aplet ... 192 The Transformer aplet... 194 Copying from hp 39g+ to hp 39g+ via the infra-red link... 197 The infra-red port... 197 Time out... 199 Attached programs ... 199 Downloading aplets from the Internet...
• Page 8 The Graphics commands ... 237 The Loop commands ... 237 FOR <var> = <start> TO <end> [STEP] <statements> END ... 237 DO UNTIL... 237 WHILE REPEAT... 237 BREAK ... 238 The Matrix commands... 238 EDITMAT... 238 REDIM ... 238 The Print commands ... 239 PRDISPLAY ...
• Page 9 The ‘Tests’ group of functions... 259 The ‘Trigonometric’ & ‘Hyperbolic’ groups of functions... 259 COT, SEC etc... 259 EXP ...260 ALOG... 260 EXPM1 ... 260 LNP1...261 The ‘Calculus’ group of functions ... 261 The ‘Complex’ group of functions ... 262 ABS ...263 SIGN...263 ARG...264...
• Page 10 Analyzing vector motion and collisions... 296 Circular Motion and the Dot Product... 297 Inference testing using the Chi Appendix B: Teaching Calculus with an hp 39g+ ... 301 Investigating for n an integer ... 301 Domains and Composite Functions ... 302 Gradient at a Point...
• Page 11 Appendix C: The hp 40g & its CAS ... 310 Introduction... 310 What is a CAS? ... 310 What is the difference between the hp 39g, hp 40g & hp 39g+? ... 312 Using the CAS... 313 Entering and editing an expression... 313 In-line editing mode ...
• Page 12: Introduction

This booklet is intended to help you to master your hp 39g+ calculator but is also aimed at users of the hp 39g and hp 40g. These are very sophisticated calculators, having more capabilities than a mainframe computer of the ’70s, so don’t expect to come to grips with its abilities in one or two sessions.
• Page 13: How To Use This Manual

It has been attempted to design this manual to cover the full use of the hp 39g+ calculator. This means explanations which will be useful to anyone from a student who is just beginning to use algebra seriously, to one who is coming to grips with advanced calculus, and also to a teacher who is already familiar with some other brand of graphic calculator.
• Page 14: Pre-calculus

means and to display histograms. In the MATH menu, read about the functions ROUND, POLYFORM and POLYROOT. Make sure you know how to save and transfer aplets. Learn about the Sketch view and the Notes catalog for a bit of fun. Pre-Calculus Typical topics covered include…...
• Page 15: Where's The On Button

The sketch below shows most of the important keys. These are the ones which control the operation of the calculator - others are used to do calculations once the important keys have set up the environment to do it in.
• Page 16: Some Keyboard Examples

Probability section. − − The PLOT key - used to graph the function. The APLET key is used to choose which aplet is active. There are 10 aplets provided with the calculator and more can be downloaded from the internet.
• Page 17: Keys & Notation Conventions

& & There are a number of types of keys/buttons that are used on the hp 39g+. 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.
• Page 18: The Alpha Key

The Screen keys A special type of key unique to the hp 39g+ 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.
• Page 19 More information on memories and detailed information on the HOME view in general is given on pages 45. The calculator also comes with a large number of mathematical functions that are very useful. They can all be obtained via menus through the MATH key.
• Page 20 You should now be back HOME, with the function entered in the display as shown right. You ROUND( can also achieve the same effect by using ALPHA to type in the word letter by letter. Some people prefer to do it that way. Now type in: 4+D/18,3) and press ENTER As you can see, the effect was to round off the answer...
• Page 21: Everything Revolves Around Aplets

A set of “aplets” is provided in the APLET view on the hp 39g+. This effectively mean that it is not just one calculator but nine (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.
• Page 22: Some Typical Aplet Views

The Quadratic Explorer aplet (see page 164) This is a teaching aplet, allowing the student to investigate the properties of quadratic graphs. The Sequence aplet (see page 107) Handles sequences such as Allows you to explore recursive and non-recursive sequences. The Solve aplet (see page 113) Solves equations for you.
• Page 23 38g, hp 39g or hp 40g then you need to buy the cable separately. If you are using an hp 39g+ then the cable connects to the USB port on your computer. If you are using an hp 39g or an hp 40g then you will need to purchase the cable and download the software from Hewlett-Packard’s...
• Page 24 (follow the links to graphical calculators and then to the library of aplets) In addition to this you should check the site called The HP HOME view which can be found at… http://www.hphomeview.com (contains not only aplets and games, but also a huge amount of detailed information on the calculator.)
• Page 25: The Home View

We will explore the HOME view in the following order: Exploring the Keyboard Angle and numeric settings Memory management Fractions on the hp 39g+ The HOME History Storing and retrieving memories Referring to other aplets from the HOME view An introduction to the MATH menu...
• Page 26: Exploring The Keyboard

To see another view where all the keys are in use, change to the APLET view. Calculator Tip Develop the habit of checking the screen to see if any of those keys have been given meanings. In many views, the screen keys have been set up with useful shortcuts and functions.
• Page 27: The Symb, Plot And Num Keys

The hp 39g+ comes with ten standard aplets - Finance, Function, Inference, Parametric, Polar, Quadratic Explorer, Sequence, Solve, Statistics and Trig Explorer. Which one you want to work with is chosen via the APLET key. Calculator Tip The name of the active aplet is shown at the top of the screen, as above.
• Page 28: Intro To The Views Menu

In addition to this, the VIEWS key also has a critical role when using aplets which have been downloaded from the Internet. When a programmed aplet is created for the hp 39g+, a menu is provided by the programmer to let you control and use it. This menu is tied to the VIEWS key, replacing the menu normally found on the key.
• Page 29 Menu” on page 243. Most of the keys have another function in light blue above the key. The hp 39g+ gets twice the action from each key by having this second function. The second function is accessed via the SHIFT key on the left side of the calculator.
• Page 30: The Setup Views

The default angle setting is radians. Calculator Tip If you don’t want to use the menu then, rather than pressing key repeatedly. This will cycle through the choices without popping up a menu.
• Page 31: Numeric Formats

A setting of Scientific notation ensures that any results are displayed in scientific notation. Of course, the 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 3.203E4.
• Page 32: The Ans Key

Moving back to our tour of the keyboard, the next key is the ENTER key. This is used as an all purpose “I’ve finished - do your thing!” signal to the calculator. In situations where you would normally press the ‘=’ key on most calculators, press the ENTER key instead.
• Page 33: The Negative Key

(-) key before the 2 and the 9 rather than the subtract key. If you press the subtract key before the 2 instead of the (-) key, then the calculator will enter instead: Ans - 2, meaning, subtract 2 from the previous answer. Similarly, entering ‘subtract, subtract 9’ instead of ‘subtract (-) 9’...
• Page 34: The Del And Clear Keys

The CLEAR key above DEL can be thought of as a kind of ‘super delete’ key. For example, if pressing DEL would erase one function only in the SYMB view then CLEAR will erase the whole set. Calculator Tip Another use for the For example, if you move back into the change to Degree mode, then pressing the restore the default of Radians.
• Page 35: Angle And Numeric Settings

It is critical to your efficient use of the hp 39g+ that you understand how the angle and numeric settings work. For those upgrading from the hp 38g this is particularly important, since the behavior is significantly different. On the hp 39g+, when you set the angle measure or the numeric format in the MODES view, it applies both to the aplet and to the HOME view.
• Page 36 For this reason, the name of the active aplet is shown at the top of the HOME view as a reminder. On the hp 39g+ you can see that if we turn Labels on and then PLOT, the numeric mode also affects the axis labels.
• Page 37: Memory Management

This problem has been addressed on the hp 39g+ in two ways. Firstly, the hp 39g+ has over ten times the useable memory of the hp 38g. At 232 Kb (vs. only 23 Kb), there are very few users who will come close to filling the hp 39g+.
• Page 38: Downloaded Aplets & Memory

APLET view. If you don’t do this then they will continue to take up memory on the calculator. Even on the hp 39g+ this is not infinite and too many left over programs will eventually cause problems.
• Page 39: The Graphics Manager

‘helper’ programs. Calculator Tip Because of the amount of memory available on the hp 39g+, the Memory View is not one that you will normally need to worry about. It is probably of more interest to programmers.
• Page 40: Fractions On The Hp 39g

Most calculators opt for the easy option of switching to a decimal answer in any mixture of fractions and decimals. The makers of the hp 39g+ took a very different approach. Once you select Fraction mode, all numbers become fractions - including any decimals.
• Page 41 1 4 17 − = − The second point to remember involves the method the hp 39g+ uses 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.
• Page 42: Pitfalls To Watch For

4 d.p.) will give the desired result of 2/3. In other words, so long as you understand the approach taken by the hp 39g+ it is capable of producing results which are closer to what was probably intended by the user in entering 0.66666.
• Page 43: The Home History

Try this for yourself now. Type in at least four calculations, pressing the ENTER key after each one to tell the calculator to perform the calculation. You will now be looking at a screen similar to the one on the right (except probably with different calculations).
• Page 44: Clearing The History

This is worth doing regularly, since the history uses memory that may be needed for other things, even with the immense amount of user memory the hp 39g+ has. ! You can number of different lines in building your new expression.
• Page 45: Storing And Retrieving Memories

Each of the alphabetic characters shown in orange below the keys can function as a memory. Some examples of this are shown in the third and fourth examples above where the values of 1, -3 and -4 are stored into A, B and C and the value of 3 is stored into X.
• Page 46: Referring To Other Aplets From The Home View

MODES view. The reason for the QUOTE(X-2) rather than just X-2, is that using X-2 would tell the calculator to use the value currently stored in memory X, while QUOTE(X-2) tells it to use the symbol. The QUOTE function is available through the MATH menu under Symbolic (see page 257).
• Page 47: An Introduction To The Math Menu

The MATH menu holds all the functions that are not used often enough to be worth a key of their own. There is a very large supply of functions available, many of them extremely powerful, listed in their own chapter later in the book.
• Page 48: Resetting The Calculator

It is probably inevitable as the line between calculators and computers becomes blurred that calculators will inherit one of the more frustrating characteristics of computers: they crash! If you find that the calculator is beginning to behave strangely, or is locking up then there are a number of ways to deal with this.
• Page 49: Soft Reboot (hardware)

Just on the rare chance that you may find that the calculator locks up so completely that the keyboard will not respond a method of reset is provided which is independent of the keyboard. This should never happen but it is important to know how to deal with it in case it happened during a test or an exam.
• Page 50: Summary

9. You can reboot the calculator if it locks up. Make sure you know how to do this in case it happens during a test or an examination.
• Page 51: 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 find derivatives algebraically find simple integrals algebraically evaluate functions at particular values graph and evaluate algebraically expressions such as f(g(x)) or f(x+2) Choose the aplet...
• Page 52: The Symb View

This is the SYMB view. Notice the screen title so that you will know where you are (if you didn’t already). Calculator Tip Pressing Whenever there is an obvious choice pressing usually produce the desired effect.
• Page 53: The Num View

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. There are a number of ways of doing this. See page 86 for a discussion of ways of finding ‘nice’...
• Page 54: Auto Scale

Press the VIEWS key. Use the arrow keys to scroll down to Auto Scale and press ENTER. The calculator will adjust the y axis in an attempt to fit as much of the graph on to the screen as possible.
• Page 55: The Plot Setup View

If you press SHIFT then PLOT you will see something like the view on 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 input a negative. You MUST use the negative key labeled as the ENTER key.
• Page 56: Simultaneous

Let's have a look at the meaning of the CHKs (check marks) on the second page of PLOT SETUP. Although they are not used often they can be quite useful and I recommend highly that you use Simult: Simultaneous The first option Simult: controls whether each graph is drawn separately (one after the other) or whether they are all drawn at the same time, sweeping from left to right on the screen.
• Page 57: The Default Axis Settings

Calculator Tip Pressing SHIFT right arrow or SHIFT left arrow will jump the cursor directly to the right or left side of the screen.
• Page 58: 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 isn’t then press the key underneath to turn it on.
• Page 59: Goto

If the left arrow is now pressed, tracing will resume from the right edge of the screen, in this case at one pixel point back from x = 4. Calculator Tip could, for example, jump to a value such as e...
• Page 60: The Zoom Sub-menu

The Zoom Sub-menu The next menu key we’ll examine is Pressing the key under menu, shown right. The menu is longer than will show in one screen, so two screen shots have been included to show most of the menu. The list which follows covers the purpose of each of the ten options shown right.
• Page 61: Box

UnZoom. This option puts the screen back to the way it was before you did the Calculator Tip Zoom is very handy for allowing you to examine small sections of a graph in detail, but remember Un-Zoom! been...
• Page 62: X-zoom In/out X4 And Y-zoom In/out X4

X-Zoom In/Out x4 and Y-Zoom In/Out x4 These two options allow you to zoom in (or out) by a factor of 4 on either axis. The factors can be set using the Set Factors… option, which gives you access to the view shown above right. You will also see a CHK mark next to an option called Recenter.
• Page 63: The Fcn Menu

In general 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 64: Intersection

X axis, or the other function F2(X). The results of choosing F2(X) are shown right. Calculator Tip When you find an intersection or a root the value of the x coordinate is stored in the memory X. If you immediately change to the HOME view and type X and hit ENTER then you can retrieve and use this value.
• Page 65: Signed Area

Signed area… Another very useful tool provided in the menu is the Signed Area… tool. Before we begin to use it, make sure that is switched on, and that the cursor is on F1(X) - the quadratic. The Signed Area… tool is similar to the Box Zoom in that it requires you to indicate the start and end points of the area to be calculated.
• Page 66: Tracing The Integral In Plot

If you now press ENTER again to accept the end point, the hp 39g+ will calculate the signed area and display the result at the bottom of the screen. Calculator Tip It should be clearly understand that although the label at the bottom of the screen is Area it is a little misleading.
• Page 67: Areas Between And Under Curves

-3.75 rather than -3.75000000002. The small error is simply due to accumulated rounding error in the internal methods used by the calculator. For example, an answer of 0.4999999999 should be read as 0.5. This is quite common and students should be aware of the need for common sense interpretation.
• Page 68: Extremum

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 69: Tips & Tricks - Function

& & Finding a suitable set of axes This is probably the most frustrating aspect of graphical calculators for many users and there is unfortunately no simple answer. Part of the answer is to know your function. If you know, for example, that your function is hyperbolic then that immediately gives information about what to expect.
• Page 70 5. Another possible strategy for graphing which works quite well and, perhaps importantly, always gives ‘nice’ scales is to use ZOOM. ! Enter your graphs into the SYMB view. Remember that Auto Scale only works on the first ticked graph. ! Press VIEWS and choose Decimal, or press SHIFT CLEAR in the PLOT SETUP view.
• Page 71: Composite Functions

The result is shown in the upper right hand snapshot and the F4(X) function is shown right after pressing SHOW. Notice that the calculator is smart enough to realize in F3(X) that x − , although not, unfortunately, smart enough to keep track is the same as of the implications for the domain that F3(X) should be defined only for non- negative x.
• Page 72: Using Functions In The Home View

These functions can all be graphed but the speed of graphing is slowed if you don’t press is fast enough that the result can be lived with but the 39G and 40G are usually too slow when graphing un-evaluated composite functions.
• Page 73: Differentiating

Differentiating There are different approaches that can be taken to differentiating, most of which are best done in the SYMB view of the Function aplet. The syntax of the differentiation function is: ∂ X function where function is defined in terms of X. The function can either be already defined in the SYMB view of the Function aplet, or entered into the brackets as above.
• Page 74: Circular Functions

The best method is to define your function as F1 and its derivative as F2 (see below)… …but you can also perform the whole process in one line. As you can see the calculator’s algebraic abilities do not extend to f x = differentiating correct.
• Page 75 Let's look at the circle -3 to 3 on the x axis and is undefined outside this domain. In order to graph it on the hp 39g+ you have to rearrange it into two equations of F1(X)= (9-X for the top half &...
• Page 76: Trig Functions

If you try to trace the circle you'll see that the pixels fall on 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.
• Page 77: Retaining Calculated Values

Retaining calculated values When you find an extremum or an intersection, the point is remembered until you move again 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 return to the menu and choose Slope, the slope calculated will be for the intersection just found rather than for the nearest pixel point.
• Page 78: Zoom

Firstly, one can change the start value and the step size for the view. NumStart & NumStep For example, values of 10 and 2 give: Automatic vs. Build Your Own Looking at the NUM SETUP view you will see an entry called NumType: with the default value of Automatic.
• Page 79 Pressing the key pops up the menu on the right. The first option of In causes the step size to decrease from 0.1 to 0.025. This is a factor of 4 and is changeable via the NUM SETUP view. I find a zoom factor setting of 2 or 5 to be more useful.
• Page 80: Function

Integration: The definite integral using the The situation for integration is very similar to that of differentiation. The difference is that both the HOME view and the Function aplet require the use of a “formal variable” S1. As with differentiation, the results are better in the ∫...
• Page 81: Integration: The Algebraic Indefinite Integral

This is shown right, together with the results of highlighting the answer and pressing . The calculator assumes that X itself may be a function of some other variable and integrates accordingly as a ‘partial integration’ which, while mathematically correct, is not what most of us want.
• Page 82: The Hp 40g Computer Algebra System

Essentially, beyond polynomials forget it. The hp 40g Computer Algebra System Owners of the hp 40g will be aware that it has a CAS which allows it to perform the most complex algebra, including complex integrations, with ease.
• Page 83: Integration: The Definite Integral Using Plot Variables

Integration: The definite integral using PLOT variables As was discussed earlier, when you find roots, intersections, extrema or signed areas in the PLOT view, the results are stored into variables for later use. For example, if we use Root to find the x intercept of then the result is stored −...
• Page 84 Suppose we want to find the area between − ( ) 0.5 the first positive intersection of the two graphs. From the 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 85: Piecewise Defined Functions

Piecewise defined functions It is possible to graph piecewise defined functions using the Function aplet, although it involves literally splitting the function into pieces.   For example: −   −  To graph this we need to enter it into the SYMB view as three separate functions: F1(X)=(X+3)/(X <...
• Page 86: Nice' Scales

‘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 along the graph.
• Page 87: Use Of Brackets In Functions

The reason for this apparent ‘error’ is that all of the built-in functions such as SIN(...) and COS(...) and ROUND(...) work with brackets. When the calculator encounters X(X+1) it interprets this as asking it to evaluate a function called X(...) at the value X+1. Since there is no such function it returns the error message that you are trying to use a function that is unknown.
• Page 88: Problems When Evaluating Limits

1 (see right). The reason for this is that the value of passes the limit of the capacity of the calculator (10 ), and so the top and bottom of the fraction become equal (both at a value of ) instead of the true situation of the bottom being roughly twice the top.
• Page 89 2 85 10 2 5087719298 10 add 1 to this, the calculator is forced to discard all but the last decimal place. Thus 1 + 1/X = 1.00000000003 (rounded off from 1.00000000002508...) 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...
• Page 90: Gradient At A Point

Gradient at a point This can be introduced via the Function aplet. In the Function aplet, enter the function being studied into F1(X). To examine the gradient at x=3, store 3 into memory A in the HOME view as shown right. Return to the SYMB view, un-CHK F1(X) and enter the expression F2(X)=(F1(A+X)-F1(A))/X in F2(X).
• Page 91: Finding And Accessing Polynomial Roots

In addition to this, you can access the roots in the HOME view as shown. Calculator Tip This trick is particularly helpful if you are working with complex roots. Not only does it make it easier to re-use them it makes it easier to tell at a glance which are real and which complex.
• Page 92: 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 93: Plot-detail

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. For example a Box zoom shows the result on the right allowing easy comparison of ‘before’...
• Page 94: Plot-table

Plot-Table The next item on the VIEWS menu is Plot- Table. This option plots the 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 95: Overlay Plot

Nice table values What makes this view even more useful is that the table keeps its ‘nice’ scale even while the usual ‘FCN’ 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 96: Auto Scale

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 PLOT SETUP view to adjust the results. It is important to understand two points about how Auto Scale works.
• Page 97: Decimal, Integer & Trig

Decimal, Integer & Trig The next option of Decimal resets the scales so that each pixel (dot on the screen) is exactly − ⋅ ≤ ≤ ⋅ 1. The result is an X scale of − ⋅ ≤ ≤ ⋅ . This may not and a Y scale of 3 1 give the best view of the function.
• Page 98 Alternatively you can move the cursor to The example below uses zoom factors of 2x2 with Recenter: Calculator Tip In the graphs above the cursor is at x = π. 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 99: Downloaded Aplets From The Internet

Two quick examples of aplets that are available are shown here. More are listed in the supplementary appendix on “Teaching Calculus using the hp 39g+”. Notice that in each case the aplet is controlled by a menu. This menu is created by the programmer and ‘attached’ to the VIEWS button so that it displays in place of the normal menu.
• Page 100: The Parametric Aplet

T range to that of the X and Y. Calculator Tip 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.
• Page 101: The Effect Of Trng

The effect of TRng The X and Y ranges control the lengths of the axes. They determine how much of the function, when drawn, that you will be able to see. For example… Notice that in both cases, ordered pair giving (X,Y). Unlike XRng & YRng, the effect of TRng is to decide how much of the graph is drawn at all, not how much is displayed of the total picture.
• Page 102 Calculator Tip ! Decreasing TStep beyond a certain point will only slow down the graphing process but not smooth the graph further. ! Since trig functions are often used in parametric equations, one should always be careful that the angle measure chosen in all aplets is radian measure.
• Page 103: Tips & Tricks - Parametric Equations

& & 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 3 2sin 4 Example 2 Try varying the values of a and b in the equations:...
• Page 104: 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 any time t (in seconds, t>0) is given by Illustrate its motion during the first 2.5 seconds.
• Page 105: Example 2

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. Ship A Ship B Enter the equations of motion as shown right. Now change to the PLOT SETUP view and set the axes to suitable values.
• Page 106: The Polar Aplet

This aplet is used to graph functions of the type where the radius r is a function of the angle θ (theta). As with 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 107: The Sequence Aplet

This aplet is used to deal with sequences, and indirectly series, in both non- recursive form (where T form (where T is a function of T Recursive or non-recursive Examples of these types of sequences are: (explicit/non-recursive) − 1 ... (implicit/recursive) −...
• Page 108: Convenient Screen Keys Provided

As they do, marks appear on all three, but any one does the same for all three. 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 - available as soon as the cursor moves onto the U(N) line (see right).
• Page 109 The NUM SETUP view offers more useful features. Change to that view now and change the NumStep value to 10. If you then swap back to the NUM view you will see (as right) that the sequence jumps in steps of 10. In case you don’t realize…...
• Page 110: Tips & Tricks - Sequences & Series

& & & & Defining a generalized GP and the sum to n terms. 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 A and R in the HOME view to change the sequence.
• Page 111 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 CLEAR (above DEL) clears out the existing expressions, and I can enter my formula.
• Page 112: Modeling Loans

Modeling loans I need to see the progress of a loan of \$10,000 at a compound interest of 5.5% p.a., starting Jan. 1 1995, with a quarterly repayment rate of \$175. Set up U1 and U2 as shown above. You can now follow the progress of the loan, with U1 containing time and U2 the amount owing at the start of each time period, showing it is repaid during the first quarter of 2023.
• Page 113: 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 114: Solving For A Missing Value

Suppose you had the problem: “What acceleration is needed to increase the speed of a car from m/s (60kph or ~38mph) to ⋅ 16 67 a distance of 100m (~110 yd)?” We’ll assume that you have already entered the equation into E2 (as above) and have made sure that it is Solving for a missing value If you press NUM to change to the NUM view,...
• Page 115: Multiple Solutions And The Initial Guess

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. The Solve aplet will then try to find a solution which is ‘near’...
• Page 116: Graphing In Solve

PLOT view. Calculator Tip The Solve aplet is not able to cope with inequalities. Although there is no error message when you use < or >, the answer it supplies is not what you would expect.
• Page 117: Referring To Functions From Other Aplets

In the NUM view, set A to an initial guess of 3, and position the highlight on A. Ignore X since it is not really involved except as a temporary variable during the integration. Press 2.4495. The delay is caused by the repeated integrations as the calculator searches for better solutions. Example 4 “Let X be a random variable, representing the heights of...
• Page 118: A Detailed Explanation Of Plot In Solve

Solve interprets your equation. When you select B by highlighting it, the calculator substitutes the supplied values into all other variables except B 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...
• Page 119 When you do so, the approximate value you chose with the cursor is transferred as your first ‘guess’. Now press and you will see the hp 39g+ find the nearest solution to your guess. Finish by pressing to verify that the solution is valid.
• Page 120: The Meaning Of Messages

27 78 16 67 ‘Zero’ - The calculator tried to find a value of A which made this zero and, in message shown above, it is reporting that it succeeded. ‘Sign reversal’ - also indicates a correct solution, since normally one expects to find an answer of zero at the point where the equation changes from positive to negative (or vice versa).
• Page 121: Tips & Tricks - Solve

& & Easy problems Have you ever thought “There has to be an easier way!” when confronted in a test with something like: − 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 SYMB view and solving it.
• Page 122: The Stats Aplet - Univariate Data

One of the major strengths of the hp 39g+ is the tools it provides 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 123: Sorting Data

As you can see in the screens above right, the hp 39g+ 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 124: Functions Of Columns

Functions of columns Let's create a second column of data, and cheat by making all its values double the values in the first column. We can use the HOME view to avoid having to retype the values as follows… * Change to the HOME view and type the command shown right, then press ENTER.
• Page 125: Working With Frequency Tables

You may be wondering why the SYMB view is organized around histograms H1, H2..H9 rather than simply around the columns C1, C2..C9. The reason is that it allows you to easily cope with a frequency table by setting up one column to represent values and another to represent the frequencies. If not using a frequency table, the frequencies are normally set, by default, to 1 as can be seen on the previous page.
• Page 126: Plot Setup Options

Plot Setup options The setting of Statplot controls what type of graph is drawn. There two choices are Hist (short for histogram) or BoxW (Box and Whisker). Pressing the + key while Statplot is highlighted will switch between these two, or you use the key to pick from the menu that pops up.
• Page 127: The Effect Of Hrng

For example, suppose we want to analyze the set of grouped data in the table on the right. The hp 39g+ provides some 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 128 However this can be fixed by using the setting HWidth. This variable controls the width of the columns, with the initial starting value and end value set by HRng. The PLOT SETUP views shown above will produce the graph shown below.
• Page 129: Tips & Tricks - Univariate Data

& & New columns as functions of old You have already seen the use of one trick when we created a new column C1 by storing 2*C1 into C2 using the HOME view. This can easily be extended to create new columns as functions of any number of others. For example, a set of data that you suspect is exponential could be ‘straightened’...
• Page 130: Simulating Random Variables

The expression INT(RANDOM*6+1) will simulate one roll of the die. This means that MAKELIST(INT(RANDOM*6+1),X,1,500,1) will 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 131 Yours will be different of course - after all, that’s the point of using random numbers! Calculator Tip The RANDOM function is not truly ‘random’ any more than it is on any computer. You can, however, make it as random as possible by using the RANDSEED command.
• Page 132: The Stats Aplet - Bivariate Data

As mentioned in the Univariate section, one of the major strengths of the hp 39g+ is the tools it provides for dealing with statistical data. Unlike the others, the Statistics aplet begins in the NUM view which offers easy input and...
• Page 133: Entering Data As Ordered Pairs

( 1 , 5 ) In fact, you can even leave off the closing bracket! The calculator will complete it for you. We could use VIEWS 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 134: Sorting Paired Columns

If you have more than one data set displayed on the screen then the up/down arrows move from one set to the other, unless the fit line is also showing in which case the behavior is slightly different. Information is given later on how to display the fit curve and to choose the type of curve.
• Page 135: Choosing From Available Fit Models

Choosing from available fit models On the hp 39g+ the Statistics aplet is the only one which has a SYMB SETUP view, and even then only in mode. This view is supplied to allow you to specify what type of fit equation is to be used.
• Page 136: Connected Data

This may seem to be a useless model but it can be quite useful. For example, suppose you had collected a set of data using a data logger and a motion detector which you suspected might represent simple harmonic motion. There is no trig model supplied in the list of models built-in but some work and experimentation may allow us to find a valid...
• Page 137: Two Variable Statistics

Calculator Tip If you have trouble seeing the small dots that the hp 39g+ uses in its scatter-graphs by default then you will be interested in the settings circled on the right. If you move the highlight onto the mark for the data set you are using and press from which you can choose a different mark.
• Page 138: Showing The Line Of Best Fit

From the NUM view, press the in the two screens shown below. Calculator Tip Make sure that your data set is defined and SYMB SETUP view before you try to obtain these results. Results are only given for data sets that are defined and...
• Page 139 As long as you press problem but if you press ENTER it changes the FitType from whatever you chose to ‘User Defined’.
• Page 140: Predicting Using Predy

We can make predictions from our line of best fit in two places - the HOME view and the PLOT view. The hp 38g was able to do this only from the HOME view. PREDY Predicting using In the HOME view we use the functions PREDY and PREDX from the Stat-Two section of the MATH menu.
• Page 141: Relerr As A Measure Of Non-linear Fit

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 below). The hp 39g+ provides an alternative measure of goodness of fit via the RelErr value in the...
• Page 142 The curve which results in the PLOT view is exactly what is required and the equation = ⋅ comes out as (0.693147 ) This “EXP(“ is the calculator’s notation for = ⋅ which then changes to 0.693147 Checking the key shows that the correlation is unchanged at 0.9058 even when the new equation clearly fits the data perfectly.
• Page 143: Tips & Tricks - Bivariate Data

‘multiply the mean by 3.5’ is not hard. The values shown on the screen can also be retrieved for use on the hp 39g+ relatively easily. For example, the set of data below contains a suspected outlier (erroneous value).
• Page 144 ENTER then the variable name will be pasted into the HOME view for use. People often find it easier to simply type them. Calculator Tip The values of the mean and standard deviation retrieved are those of the last set calculated. If you have more than...
• Page 145: Obtaining Coefficients From The Fit Model

Obtaining coefficients from the fit model Coefficients can be obtained from the chosen fit model algebraically. The function PREDY from MATH gives a predicted y value using the last line of best fit that was calculated. This means that you must use the SYMB view to ensure that your set of data is the only one SETUP is set to the correct fit model, and also use the PLOT screen and the key to ensure that your set of data was the last one graphed and that it...
• Page 146: Correct Interpretation Of The Predx Function

However, it should not be interpreted to mean “predict an x value based on this y value”. It should not be felt that the hp 39g+ is unusual in this interpretation. Most calculators’ equivalent of the PREDX function behave in the same manner.
• Page 147: Assigning Rank Orders To Sets Of Data

Assigning rank orders to sets of data It is occasionally handy to be able to assign rank orders to a set of data. You might be running a Quiz Competition Night, or recording times for the 100 meter sprint, but in either case it is handy to be able to sort the data into descending order and assign rankings.
• Page 148: Using Stats To Find Equations From Point Data

Using Stats to find equations from point data eg. 1 Find the equation of the quadratic which passes through the points (1,5), (3,15) and (-5,71). In the Statistics aplet, choose enter the data. Now change to the SYMB SETUP view and choose the Quadratic data model.
• Page 149 Either use the VIEWS Auto Scale option, or change to the PLOT SETUP view and adjust it so that it will display the data. This is not really needed, since the line of best fit is what we need and it will be calculated even if the data doesn’t show.
• Page 150: 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. Before we look at the Inference aplet in detail I am going to take a small digression to look at a simple inferential problem which can be solved using only the Statistics and Solve aplets.
• Page 151: Hypothesis Test: T-test 1-µ

The values can be seen by changing to the NUM view. In the MATH menu, Probability section, there is a function called UTPC (Upper-Tailed Probability Chi-squared) which will give the critical X probability for a supplied number of degrees of freedom and a value. See page 283.
• Page 152 Choose the test and the alternate hypothesis in the SYMB view of the Inference aplet. In this case we are working with a single sample and we do not know the standard deviation of the underlying population, so we will use the Student-t test and the alternate hypothesis that the mean of the real underlying population from which the sample was drawn is not equal to that of the proposed underlying population.
• Page 153: Confidence Interval: T-int 1-µ

The test value for the Student-t and the sample mean are listed in the middle of the screen and the rough position of these values is shown by a vertical line in both the upper and lower diagrams. The regions for rejection of the null hypotheses are shown at the very top of the screen by the ‘...
• Page 154: Hypothesis Test: T-test µ

As before, a more visual display can be seen in the PLOT view. Thus the sample data indicates in our two examples that: ! we can be confident the average number of matches is not 50 with less than a 5% chance of being wrong, and ! we can conclude, with a confidence of 95%, that the true average number of matches is between 50.16 and 52.44.
• Page 155 We are dealing with two independent samples in this case and so we need to choose from those tests which involve two samples. Since we know the standard deviations of only these samples, we must again use a Student-t test. We then change to the NUM SETUP view to import the summary statistics.
• Page 156: Hypothesis Test: Z-test 1-µ

Hypothesis test: Z-Test 1- A teacher has developed a new teaching technique for hearing-impaired students which he believes is producing significantly better results. He wishes to publish a paper on this and needs to check his results statistically. A standardized test is available for which it is known that the normal performance of hearing-impaired students at the same stage of study has a mean of 53.6% and a standard deviation of 12.2%.
• Page 157 Enter the values for the mean and standard deviation of the standardized test, and the significance level of 0.05 (5%). If we now change to the NUM view we can see that the test z score is less than the required critical z*, and the probability of obtaining a mean of the value found is 0.1080, which is larger than the required test value of 0.05.
• Page 158: Tips & Tricks - Inference

& & Importing from a frequency table The import ( ) facility of the Inference aplet has a small weakness in that it can’t import from paired columns defining a frequency table. For example, suppose we use columns C1 and C2 to define a frequency table, ensuring that it is registered in the SYMB view as shown right.
• Page 159 Now change into the Program Catalogue the program you created. Assuming that it has no errors you will see a running count as it creates the new column. This is just to give you something to watch while it works. If you then change to the NUM view you will find that column C0 contains the result.
• Page 160: 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 for those who need it, as does any high school or college textbook.
• Page 161: Straightforward Compound Interest

(withdrawals) are made during the period of the investment. Five years of monthly payments means that N is 60. The view on the right shows the problem on the calculator. The pressed to give a future value FV of \$1816.70.
• Page 162: Annuity

Annuity 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 163: Amortization

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. The initial situation is as shown in the screen on the right.
• Page 164: 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. Objectives Using the Quadratic Explorer aplet, the student will investigate the behavior of the graph of a x h done both by manipulating the equation and seeing the change in the graph, and by manipulating the graph and seeing the change in the equation.
• Page 165: Symb Mode

The key labeled changes the ‘step size’ of the movements on the screen. Possible values for the increment are 0.5, 1 and 2. Pressing SYMB on the calculator, or the screen key labeled will change the emphasis from the graph to the equation in the right hand half of the screen.
• Page 166: Self Test Mode

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 record...
• Page 167: 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. Objectives Using the Trig Explorer aplet, the student will investigate the behaviour of the graph of as the values of a, b, c and d change.
• Page 168 The operation of the two modes is summarized below. PLOT mode The underlying concept in PLOT mode is that the graph controls the 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 169 π -3 to 3 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 record their answers in writing.
• Page 170: Using Matrices On The Hp 39g

Matrices, like most other objects on the hp 39g+, can be sent to and received from a computer or another hp 39g+ using the keys.
• Page 171: Matrix Calculations In The Home View

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 172: Solving A System Of Equations

Another method is to store the result into a third matrix and then to view it through the Edit screen of the MATRIX Catalog. This is shown below. Probably the most common functions that you will use are INVERSE, DET and TRN (transpose), so some worked examples are included which use them.
• Page 173 Step 3. Enter the 3x1 matrix of into M2. Note the change to make entering numbers easier. Step 4. Change to the HOME view, evaluate three methods (all of which are acceptable to the hp 39g+), and store the result into M3. − (c) INVERSE(M1)*M2 The best of these is probably (a) because it doesn’t involve fetching the...
• Page 174: Finding An Inverse Matrix

Finding an inverse matrix Eg. 2 Find the inverse matrix The first step is to store the matrix A into M1. If you now simply store its inverse into M2 you will find, depending on the determinant, that the result is probably a collection of decimal values (see right).
• Page 175: The Dot Product

Eg. 4 Find the angle between the vectors On the calculator, the functions DOT and ABS give the dot product and magnitude respectively, when fed with vectors. The hp 39g+ writes vectors as row matrices. For example would be written as [3,4]. (3, 4) The calculations are shown in the two screen shots on the right.
• Page 176: Using Lists On The Hp 39g

A list in the hp 39g+ is the same mathematically as a 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 HOME view these lists can be stored in special list variables.
• Page 177: List Functions

CONCAT function discussed on the next page. Lists can be sent from one hp 39g+ to another using the infra-red link with the aid of the two keys labeled .
• Page 178: Using The Notepad Catalog

The hp 39g+ provides access to Notes which can be either attached to an aplet or created as independent notes for any use. The notes belonging to the standard aplets are blank unless you add to them, but copies you transfer from another calculator may have had notes added to them.
• Page 179: Independent Notes And The Notepad Catalog

Most users are far more concerned with the Notepad Catalog. Notes held in it are independent of any aplet rather than being attached to only one, and can be sent to and received from another hp 39g+ or a computer via the keys in the Notepad Catalog.
• Page 180: Transferring Notes Using Ir

Notes on a computer. See page 211. For the hp 38g and hp 39g it is necessary to purchase a special cable to connect to the serial port on a PC and the software will work only on Windows computers.
• Page 181: Software

There are two versions of the ADK, one for the hp 38g and one for the hp 39g, hp 40g & hp 39g+. All of this software will only run on a Windows computer and requires that you have a cable and a serial port on your computer.
• Page 182: Creating A Note

Note, create a one or to Notes to or from another hp 39g+ (or a computer). A Note is deleted using the DEL key, while the SHIFT CLEAR key will delete all Notes in the catalog. Press the key to begin a fresh Note.
• Page 183: The Chars View

If you find that you have unintentionally opened a file in this way then exit from the word processor without saving.
• Page 184: Using The Aplet Sketchpad

Adding text to a sketch When you first enter the Sketch page on your hp 39g+ you will see the view at the top right. There are four screen keys available. The key allows you to place strings of text on the screen.
• Page 185: The Draw Menu

There are two font sizes available via the key, with the default size being large. If you press the key then it will change to . Although there is no apparent change when you are typing in the text, the font will become smaller when it appears in the window.
• Page 186: Circle

CIRCLE The circle command is similar. You should position the cursor at the center of the proposed circle. Pressing , move 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 187: Capturing The Plot Screen

Move down through the menu until you reach Graphic and across to the particular GROB you chose. Now also press the key labeled and then press You will now find yourself back in the graphics screen with a rectangle representing the size of the GROB to be pasted in.
• Page 188 ‘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 any screen as a GROB, not just a PLOT screen.
• Page 189: Using, Copying & Creating Aplets

These aplets come via the Internet, but you may be able to obtain them from your teacher, from other hp 39g+ users, or from a PC or Mac onto which they have been copied. Once aplets have been copied from the Internet (onto a PC or Mac) the software and cable provided with your hp 39g+ can be used to download the aplets to the hp 39g+.
• Page 190: 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, with the only limit being the calculator’s memory. Let’s look at each of the two scenarios in turn.
• Page 191: Copying And Adding To The Stats Aplet

An ambitious teacher might even complete his aplet by adding a set of instructions to the Note which is associated with the aplet. This would allow an absent student to download a copy from a friend’s hp 39g+ and then read up on what they are supposed to do.
• Page 192: Some Examples Of Saved Aplets

Indeed, if the students have access to the Internet and a Connectivity Kit themselves, then there is no reason that the teacher could not post the aplet on the department’s web page for downloading by any students who need access. In both of these cases, the procedure has been to save a copy of one of the standard aplets under a different name.
• Page 193 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 hp 39g+ to perform multiple integrations. Because of this the solving process will be relatively slow.
• Page 194: The Transformer Aplet

Equation E6 gives ≤ ≤ Equations E7 to E0 concern the Normal distribution, with E7 giving E8 giving , E9 giving ≤ questions such as “what distance either side of the mean will give a probability of 0.45?”. Notes: In equations E1 and E2, N!/((N-R)!R!) is used rather than the more compact formula COMB(N,R).
• Page 195 20 to 30 minutes. So… how does this aplet work? The formulas in the SYMB view form the key to the process by allowing the calculator to fetch values from the matrices, with the values fetched being determined by the settings in the PLOT SETUP view.
• Page 196 Calculator Tip Warning: Due to a bug which existed in the hp 38g and hp 39g, this aplet cannot be sent from one hp 39g to another using the infra-red link. The formulas in the SYMB view often become corrupted during the transfer and need to be re-entered.
• Page 197: Copying From Hp 39g+ To Hp 39g+ Via The Infra-red Link

Any aplet can be copied from one hp 39g+ to another via the built in infra-red link at the top of the calculator. Indeed it is not only aplets which can be copied, but lists, notes, sketches, matrices and programs. Of the family of related models, only the hp 40g does not have this capability.
• Page 198 HP38/39/40G family called the “Drive 95”. The “Drive 95” was released at the same time as the original hp 38g but there was no demand for it and it is no longer manufactured. The overwhelming majority of users decided that if they wanted to save an aplet then they would send it to a computer using the Connectivity Kit.
• Page 199: Time Out

As an example, the screen shown right contains a number of programs which belong to an aplet called “Coin Tossing” which can be downloaded from the web site 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.

PC or Mac, which both have essentially unlimited storage in comparison with any calculator. In addition to aplets, there are many other data structures on the hp 39g+ which can be sent and received to other hp 39g+’s via the infra-red link.
• Page 201: Organizing Your Collection

The aplet itself will not be harmed by this but the effect is to render it invisible to the calculator, since the two special files contain information which is sent to the calculator in order to tell it what the directory contains.
• Page 202: Software For The Hp 38g, Hp 39g & Hp 40g

PC. See page 211. Note that there are two versions of the ADK, one for the hp 38g and one for the hp 39g, hp 40g & hp 39g+. You must make sure that you get the right version for your calculator.
• Page 203: Software For The Hp 39g

Once the aplet or note has been transferred to a PC it can be edited using the same ADK software as is used for the hp 38g, hp 39g and hp 40g. The only drawback with this is that the ADK will only run on Windows machines. It may well be that by the time you are reading this there will be new editing software specifically for the hp 39g+ and running on other platforms.
• Page 204: The Hpgcomm Connectivity Program

Many computers released since 2002 only have USB ports. This was the reason why the hp 39g+ was altered so that it uses the USB port. If you own one of the earlier models this means that you will be unable to plug in the cable since it requires a COM port.
• Page 205 At the top of the window you’ll see a message saying “Please choose a directory” and, once you’ve chosen a directory you should see “This directory contains hp 39g files” (if there are files there to be downloaded). Press the OK button to select the directory.
• Page 206 Program Catalog and delete them by hand. Left undeleted they will simply consume memory. See next page. If you are a teacher using an hp 39g+ then it is highly recommend that you investigate teaching aplets. They can enhance your...
• Page 207: Deleting Downloaded Aplets From The Calculator

To delete these left over programs you will need to switch to the Program Catalog and remove them. Even on an hp 39g+ it is advisable to do this or your memory will gradually be used up.
• Page 208: Saving Notes, Aplets And Sketches Via The Connectivity Kit

The following information applies to the HPGComm program for the hp 38g, hp 39g or hp 40g. If you have an hp 39g+ then the software will be similar in behavior although the appearance may be significantly different (page 203).
• Page 209 You can re-use this directory later to save any other objects from the calculator. Next time you use it you will not see the message asking if you want to “Initialize directory?”, as the two special files are now present. They will be automatically updated each time you save to the directory.
• Page 210: Capturing Screens Using The Connectivity Kit

The File menu will allow you to save the image as a BMP file. The software for the hp 39g+ also has options to allow you to copy the image to the clipboard, or to save it as a BMP file.
• Page 211: Editing Notes With The Aplet Development Kit

Since the aplets are the same for the hp 39g, hp 40g and hp 39g+ the can all be edited by the ADK. The only difference for the hp 39g+ is that the software used to get it onto the computer is different.
• Page 212: Programming The Hp 39g

An overview Although you can choose to simply create programs which are self sufficient the whole point of working on the hp 39g+ is to use aplets. Hence this chapter will concentrate on the process of creating aplets with enhanced powers provided by attached ‘helper’...
• Page 213: Naming Conventions

VIEWS menu will be triggers for ‘helper’ programs you will write, and when the user chooses an option and presses ENTER, the appropriate ‘helper’ program will be run by the hp 39g+. When the ‘helper’ program terminates the calculator drops into whatever view you as the designer choose.
• Page 214: Planning The Views Menu

finishes.
• Page 215 When you run this program it severs the aplet’s link to the normal VIEWS menu inherited from its parent and replaces it with the new options. Calculator Tip If an aplet is created using the ADK then it may not have this .NAME.SV program.
• Page 216: Special Entries In The Setviews Command

The linking process performed by the SETVIEWS command (or by the ADK) is also important in that it tells the calculator which programs are to be transmitted with the aplet when it is copied via cable or infra-red link. Only those programs named in the SETVIEWS command (or linked by the ADK) will be transmitted.
• Page 217: The 'start' Entry

(and totally useless) aplet, which will illustrate a few of the concepts useful in programming the hp 39g+. We’ll call it the ‘Message’ aplet and create it as a descendant of the Function aplet.
• Page 218 ERASE clears the screen, ready to DISP a message on lines 4 and 5 of the screen. The calculator then FREEZEs waiting for a key to be pressed. .MSG.FN Having created all of the programs that make up the aplet ‘Message’, we can now run the program .MSG.SV, severing the aplet’s link to its current VIEWS...
• Page 219 Swap back to the Program Catalog, position the highlight on the program .MSG.SV and the program. Apart from the screen going blank for a moment nothing will appear to happen, but in fact the link to the normal VIEWS menu which ‘Message’ inherited from its parent aplet Function has been severed and a link to the new menu you built in .MSG.SV has been substituted.
• Page 220 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 INPUT statement and their effect.
• Page 221 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)' F1(X): 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 222: Example Aplet #2

Xmin and then changes it back. In the original version the user had to press PLOT to force a re-draw. This technique fools the hp 39g+ into thinking that the PLOT view has changed and therefore forces a re- draw without the need to press a key.
• Page 223 .TRANSF.SHAPE Assuming that you have altered VIEWS menu then you can now test the aplet. Its operation should be familiar to you if you have already examined its ‘cousin’ on page 194. This program (left) uses the CHOOSE command to offer a list of options.
• Page 224: Example Aplet #3

There are two versions of the ADK - one for the hp 38g and one for the hp 39g, hp 40g and hp 39g+. Aplets created by one version are not compatible with the other version’s calculators.
• Page 225 Click on “View 1” in the View List window. Change the prompt to “Change matrix”, the Object name to “.TRANSF.MAT” and the Next View to “7: Views”. In the main window, enter the code for this program (see Example 2). Special characters such as can be obtained from the...
• Page 226: Example Aplet #4

“Add <=” button to add it to the library files. You can only add files which are legitimate calculator files. I usually add the aplet file first and then each of the programs in the order that they appear on the VIEWS menu, but this has absolutely no effect on the running of the aplet.
• Page 227 In the Note view, enter the text shown right. Our VIEWS menu will only have three entries, so use the View - Custom views… command to display the menu planner and press ‘Insert’ three times. Our VIEWS menu will be as shown below. The first entry should have a Prompt of ‘Plot axes’, an Object Name of ‘.LINEXPL.AX’...
• Page 228 Save the aplet and use the File - Aplet library facility to create the two special files for the directory which allow the calculator to download it. Finally, download it to the calculator and test it. Choose the first option on the VIEWS menu to plot the axes and then the ‘Explore’...
• Page 229 The 2 and 3 lines are there to insert a function. We need a function when the axes are plotted or the normal error message will be displayed (see right), which is undesirable as it confuses the user. On the other hand we need blank axes, so we use a function ‘Ymax+1’...
• Page 230 39g. It may have been added to the hp 39g+’s manual. It does appear in the Prompt section of the MATH menu.
• Page 231 The DISPXY command allows you to place a string of text at any position on the screen using two different fonts. Until this command was added to the language the only way to do this was to: save the current screen into a graphics variable. create a special GROB which contained the text.
• Page 232 DISPXY command. The explanation so far should help you in understanding the programming process on the hp 39g+. The aplet structure is well designed and, if you take advantage of the VIEWS menu structure, offers easy creation of complex and very powerful teaching aplets.
• Page 233: Programming Commands

All programming commands can by typed in by hand but, as with the MATH commands, can also be obtained from a menu. Press SHIFT CMDS to display this. In this section I will only be covering those commands which I have used regularly and so regard as important.
• Page 234: Setviews

SETVIEWS <prompt>;<program>;<view number> This absolutely critical command is covered in great detail on page 214. 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.
• Page 235: Run

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.
• Page 236: Erase

It can be used to erase previously drawn lines. One of the aplets on The HP HOME view (at http://www.hphomeview.com) is called “Sine Define” and contains extensive use of this command.
• Page 237: The Graphics Commands

See the chapter “Programming the hp 39g+” on page 226 for examples illustrating some of the graphics commands used regularly. FOR <variable> = <start value> TO <end value> [STEP <increment>] <statements> END This is a standard FOR…NEXT command. The STEP value is optional and is assumed to be 1 if not stated.
• Page 238: Break

BREAK This command will exit from the current loop, resuming execution after the end of it. There is no GOTO <label> command in the language. EDITMAT <matrix var> This command pops up a window in which the user can edit or input a matrix with an key at the bottom.
• Page 239: The Print Commands

These commands are supplied for use with the battery operated HP infra-red thermal printer that is designed for use with the hp 38g, hp 39g, hp 40g and hp 39g+. PRDISPLAY If you place this command in a program then the current display will be sent to the infra-red printer.
• Page 240: 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.
• Page 241: Disp

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+” on page 226. DISPTIME This command pops up a box displaying the calculator’s internal time and date.
• Page 242: Input

It is also enough that an enthusiastic amateur will be able to accomplish the more common tasks required in programming the hp 39g+.
• Page 243: The Math Menu Functions

Others will be covered to varying depths. Anyone needing those not covered will find that after reading this manual they can be relatively easily deciphered from the manual that comes with the calculator. The mechanics of accessing the MATH menu is very simple.
• Page 244 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 ‘P’ (on the ‘5’ key). It is not necessary to press the ALPHA key first. You will notice in the screen on the right that there are two groups of functions beginning with a ‘P’...
• Page 245 Some of the functions are not likely to be used at school level and so will not be covered since this book is primarily aimed at teachers and students of high school, as is the hp 39g+. If you need the higher level commands then consult the manual.
• Page 246: 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. CEILING(3.2) = 4 CEILING(32.99) = 33 CEILING((12+ 6)/7) = CEILING(2.0642…) = 3 Note: CEILING(-2.56) = -2 not -3. The CEILING function rounds up to the next integer above, which is -2.
• Page 247: Fnroot

FNROOT(express.,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 248: Hms Hms

(dd.mmss) 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 ′ ′′ " if you put it into the form 45.2317...
• Page 249: Int

INT(num) This function is related to the FLOOR and CEILING functions. Unlike those two, which consistently move down or up respectively, the INT function simply drops the fractional part of the number. INT(3.786) = 3 INT(-5.84) = -5 See also: FLOOR, CEILING, ROUND, TRUNCATE, MANT(num) This function returns the mantissa (numerical part) of the number you feed it when...
• Page 250: Min

MIN(num1,num2) As with MAX, this function is used mainly by programmers. It returns the smaller of the two numbers entered. MIN(3,5) = 3 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 251: Change

%CHANGE This function calculates the percentage change moving from X to Y using the formula 100(Y-X)/X. It can be used to calculate (for example) percentage profit and loss. 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 What is the discount as a percentage?
• Page 252: Round

ROUND(num,dec.pts) This function rounds off a supplied number to the specified number of decimal places (d.p.). Round 66.65 to 1 d.p. Use: ROUND(66.65,1)=66.7 Round 34.56784 to 2 d.p. Use: ROUND(34.56784,2)=34.57 This function is also capable of rounding off to a specified number of significant figures (s.f.). To do this, simply put a negative sign on the second argument.
• Page 253: Truncate

TRUNCATE(num) This function operates similarly to the ROUND function, but simply drops the extra digits instead of rounding up or down. It is somewhat similar in effect to the FLOOR function but the TRUNCATE function will work to any number of decimal places or significant figures instead of always dropping to the nearest lower integer value.
• Page 254: The 'stat-two' Group Of Functions

(dependent) value for the x (indep.) value of 3 5 ⋅ . Calculator Tip The line of best fit used in the function PREDY is whichever one was last plotted. It is up to you to ensure that this is in...
• Page 255: The 'symbolic' Group Of Functions

‘ ’ ‘ ’ The = ‘function’ Although this is listed in the MATH menu as if it were a function, it is not really. Except in programming, the = sign is simply used in exactly the way that you would expect it to be, mainly in the Solve aplet.
• Page 256: Linear

LINEAR?(expression,var.name) This is another of those functions which is probably aimed more at the programmer than at the normal user. It is designed to test whether a supplied expression is linear or non-linear in the variable you specify, returning zero for non-linear and 1 for linear. Suppose we use the expression If X is the variable and A and B are both constants (say A=4, B=5) then the...
• Page 257: Quote

Complex numbers are expressed on the hp 39g+ in the form (a, b) representing a + bi. Thus the answer to the second quadratic shown above would represent written as a complex number.
• Page 258: The | Function

The | function written as: expression | (var1=value,var2=value,…) This is called the ‘where’ function. The reason for this is that it is used to evaluate formulas, of the type when one would say “Evaluate ….., where a = 5, b = 4 etc”. The formula must be in the form of an expression rather than an equation.
• Page 259: The 'tests' Group Of Functions

These are all functions which are of interest only to programmers, and consequently we will not cover them here. An introduction to programming on the hp 39g+ is covered in an earlier chapter (see page 212) but those wanting more detail than is given there must consult the manual.
• Page 260: Exp

EXP(num) This function gives a more accurate answer than the key labeled e^ which appears above the LN key on the calculator. As you can see on the right, the difference is normally not detectable even to 12 significant figures.
• Page 261: Lnp1

= − sin( ) = − The screen shot on the right shows the calculator deriving the Taylor polynomial for sin(x) up to the 7 power. The first is calculated with MODES set to Standard, the second with MODES set to Fraction 4.
• Page 262: The 'complex' Group Of Functions

‘ ’ ‘ ’ Complex numbers on the hp 39g+ 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 263: Abs

In addition to the trig functions, there are other functions that take complex arguments. ABS(real or complex) The absolute function, which is found on the keyboard above the -X key, returns the absolute value of a real number. ABS(-3) returns a value of 3. When you use the absolute function on a complex number a + bi it returns the magnitude of the complex number SIGN(real or complex)
• Page 264: Arg

The same information can, of course, be obtained using trig. The reason for the double brackets is that every function used by the calculator uses brackets (hence the outer pair) but so too do complex numbers (hence the inner pair).
• Page 265: The 'list' Group Of Functions

The other three, π , i , and e, are far more easily obtained via the keyboard. The first, π , is available via a key on the face of the calculator above the 3 key. The other two , i & e, are easily obtained as lowercase letters via the ALPHA key, pressing SHIFT first to get lowercase.
• Page 266: List

∆ LIST({list}) This function produces a list which contains the differences between successive values in the supplied list. The resulting list has a length one less than the original. L1={1,4,7,10,13} ∆ LIST(L1)={3,3,3,3} MAKELIST This function produces a list of the length specified using a rule of your choice.
• Page 267: πlist

The MAKELIST function can also be used to simulate observations on random variables. For example, suppose we wish to simulate 10 Bernoulli trials with p = 0.75. We can use the fact that a test like (X<4) or (Y>0.2) returns a value of either 1 (if the test is true) or 0 (if the test is false).
• Page 268: Size

SIZE({list}) and 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 269: The 'loop' Group Of Functions

‘ ’ ‘ ’ This is an interesting group of functions that may be of use for students studying discrete functions and sequences. ITERATE(expression,var.name,strt,num.iter.) This function evaluates an expression a specified number of times, starting with a supplied initial value an using the answer to the previous evaluation as the value for the variable in the next evaluation.
• Page 270: Recurse

RECURSE This functions is provided for programmers to let them define functions in the Sequence aplet. For example, typing RECURSE(U,U(N-1)*N,1,2) U1(N) seemingly produces no useful result in the HOME view, but would produce the result shown right in the SYMB view of the Sequence aplet. The resulting sequence is the factorial numbers.
• Page 271: The 'matrix' Group Of Functions

Consequently many of the functions will be covered only by the comment “See User’s manual”. A detailed set of examples for the more commonly used functions is given in the chapter titled “Using Matrices on the hp 39g+”. See page 170. COLNORM See User’s manual COND See User’s manual...
• Page 272: Det

DET(matrix) This function finds the determinant of a square matrix. See page 174 for an example of its use in finding an inverse matrix.   =  then find det(A).  −   Ans: det (A) = 2x5-3x(-1) = 13 See also: INVERSE, RREF...
• Page 273: Inverse

3 by 3 system of equations is given in the chapter on using matrices on the hp 39g+ on page 172 and 288. An error message is given (see right) when the matrix is singular (det. zero).
• Page 274: Lsq

See User’s manual See User’s manual MAKEMAT See User’s manual See User’s manual RANK See User’s manual ROWNORM See User’s manual RREF(matrix) This function takes an augmented matrix of size n by n+1 and transforms it into reduced row echelon form, with the final column containing the solution. The system of equations is written as the augmented matrix which is then stored as a 3x4 real matrix M1.
• Page 275: Schur

This gives the final result shown in the matrix M2 on the right, giving a solution of (1, -2, 3). The huge advantage of this function is that it allows for inconsistent matrices which can’t be solved by an inverse matrix. 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.
• Page 276: Trace

TRACE See User’s manual TRN(matrix) This function returns the transpose of an n x m matrix.   For example, if      − then TRN(M1) would return        −  ...
• Page 277: The 'polynomial' Group Of Functions

‘ ’ ‘ ’ This group of functions is provided to manipulate polynomials. We will use the following function to illustrate some of the tools in the Polynomial group. − ( ) ( POLYCOEF([root1,root2,…]) This function returns the coefficients of a polynomial with roots The roots must be supplied in vector form means in square brackets.
• Page 278: Polyform

POLYFORM(expression,var.name) This is a very powerful 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. If the expression contains more than one variable then any others are treated as constants.
• Page 279: Polyroot

POLYROOT([coeff1,coeff2,…]) This function returns the roots of the polynomial whose coefficients are specified. The coefficients must be input as a vector in square brackets. Using our earlier function of can enter the coefficients as [1,0,-7,6]. As you can see in the screen shot, the roots of 2, -3 and 1 have been correctly found.
• Page 280: 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 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 281: Perm

(an algorithm) which uses a ‘seed’ number to produce them. Unfortunately, taken straight out of the box, two hp 39g+’s will produce exactly the same sequence of “random” numbers! This can be a problem in that, for example, a class set of calculators doing a simulation of dice would all produce the same numbers.
• Page 282: Utpn

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...
• Page 283: Utpc

Calculator Tip The normal order for the arguments in the UTPN function is UTPN(mean,variance,value), giving the upper-tailed probability. However, many textbooks work with the lower- tailed probability instead. Fortunately the function can easily be adapted for this. If you instead enter the function’s parameters as...
• Page 284: Appendix A: 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. Sometimes these problems are quoted elsewhere in the book and repeated here for convenience.
• Page 285: Method 3 - Using The Polyroot Function

POLYROOT Method 3 - Using the The advantage of this is that it can be done in the HOME view and is quick and easy. See page 91 for a method of copying the results to a matrix so as to gain easier access to them. Find the roots of the complex equation Method 1 - Using the QUAD function Since this is a quadratic it can be done with the...
• Page 286: Finding Critical Points And Graphing A Polynomial

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 SYMB view of the Function aplet, so it is available for plotting.
• Page 287 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 HOME view and store it as shown in memory A.
• Page 288: Solving Simultaneous Equations

Solve the systems of equations below: − Method 1 - Graphing the lines Because the first set of equations is a 2x2 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 289: Third Method - Using The 3x3 Solver Aplet

Step 3. Change into the HOME view and enter the calculation M1 the (x,y) coordinate of the solution. A similar method can be used to solve the second 3x3 system of equations. Third method - using the 3x3 Solver aplet This method uses an aplet which is available from the internet called the “Simult 3x3”.
• Page 290: Expanding Polynomials

Expand the expressions below. − (ii) Use POLYFORM((2X+3)^4,X) to expand the polynomial. Use the key to examine the result. Result: (ii) Use POLYFORM((3A-2B)^5,B) to expand the polynomial as a function of B. Then use the polynomial function again, from the first expansion and expanding this time as a function of A.
• Page 291: Exponential Growth

A population of bacteria is known to follow a growth pattern governed by the equation there are 100 colonies of bacteria and that at t = 10 hours there are 10,000 colonies. Find the values of (ii) Predict the number of bacteria colonies after 15 hours. (iii) How long does it take for the number of colonies to double? (i) Find...
• Page 292 (ii) Predict N for t = 15 hours. Change to the HOME view and use the PREDY function. Result: 268 269 colonies. (iii) Find t so that Step 1. Find the values of into memory A and k into memory K, so that it is un-necessary to re-type them.
• Page 293: Solution Of Matrix Equations

Solve for the value of X in   where     −   Store the values of A and B into M1 and M2 respectively. Finally use the HOME view to calculate the answer, using the function IDENMAT(2) to produce a 2x2 identity matrix, and making sure to store the result into M3.
• Page 294: Inconsistent Systems Of Equations

Solve each of the systems of equations below, where possible, indicating in each case the nature of the system. − = − − = Using the RREF function In each case the most efficient method is to use the function RREF. The letters RREF stand for Reduced Row Echelon Form and the advantage of this function is that it allows the user to deal with matrices which...
• Page 295: Finding Complex Roots

Find the complex roots of The best way to do this is using POLYROOT. I usually matrix, since the matrices on the hp 39g+ can be complex vectors, not just real matrices. The coefficients can be entered into POLYROOT in the form a+bi or as (a,b).
• Page 296: Analyzing Vector Motion And Collisions

Ship A is currently at position vector 21i + 21j km and is currently travelling at a velocity of -4i + 6j km/hr. Ship B is at 30j and travelling 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 297: 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 to be 0 to 6 in the PLOT SETUP view and then choose VIEWS - Auto Scale.
• Page 298 If we now switch to the NUM view, we can see that this function is evaluating to zero for t = 0, 1, 2, 3…. Of course this is not the same as a proper algebraic proof but you wouldn’t want the calculator to do all the work would you?
• Page 299: 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 300 Changing into the Solve aplet we can enter a formula which will allow us to calculate values from the Chi distribution using the UTPC function. With a 3 x 2 contingency table the number of degrees of freedom are 2. To find the critical χ...
• Page 301: Appendix B: Teaching Calculus With An Hp 39g

There are many ways that the teaching of functions and calculus concepts can be enhanced with the aid of an hp 39g+ graphical calculator. Some of them are listed below: This can be done most economically by setting an investigation, perhaps for homework.
• Page 302: 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 NUM view. For example, enter the functions F1(X)=X+2 and F2(X)=(X will elicit the fact that they are ‘identical’...
• Page 303: 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. In the Function aplet, enter the function being studied into F1(X).
• Page 304: Gradient Function

This can be done using an aplet downloaded from The HP HOME View web site called “Tangent Lines”. This aplet will add a moveable tangent line to a graph, allowing the user to move it along the curve with the gradient displayed at the top left of the screen.
• Page 305: 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 306: 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 307: Inequalities

Try it and see. For information on evaluation of limits on the hp 39g+ and, more importantly, the pitfalls that lie in wait for the unwary, please read the information in the chapter “Tips &...
• Page 308: Piecewise Defined Functions

Inside the domain it has no effect. Note: The word ‘AND’ is available from the keyboard above the (-) sign. Through the Sequence aplet the hp 39g+ provides very flexible tools for the investigation of sequences. These can easily be adapted to investigate series as well.
• Page 309: Transformations Of Graphs

“Quad Explorer” and “Trig Explorer” and are built into the hp 39g+. 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 310: Appendix C: The Hp 40g & Its Cas

This appendix is intended to give a useful introduction and over view to the user who is new to an hp 40g. It is not intended to fully cover the topic, nor is it intended to serve as a reference text for the advanced user. For those needing a far more extensive coverage than is available here, I can highly recommend the incredibly detailed text “Computer Algebra and Mathematics...
• Page 311 The CAS on the hp 40g is based on a program called Erable, originally written by Bernard Parisse for the HP49G, which was then adapted for the hp 40g. It...
• Page 312: What Is The Difference Between The Hp 39g, Hp 40g & Hp 39g

Finance aplet. If you own an hp 39g and you are wondering if you can fool it into believing that it is an hp 40g 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 40g - you will simply have a crippled hp 39g.
• Page 313: Using The Cas

The first step is to activate the CAS. This is done from the HOME view by pressing screen key 6 (SK6), labeled When you do, you will see an empty screen with a cursor in the center and an extensive menu system at the bottom of the screen.
• Page 314 (iii) Press left arrow once then down arrow once. Press X 3, then press up arrow three times & finally press X (DO NOT use the Notice that in each case the power was applied to the currently highlighted element of the expression. Brackets are automatically added as required. Notice also the movement of the highlight.
• Page 315 (iv) Press up arrow three times and then divide by 5. This moves the highlight up to node A, high- lighting the entire expression. Dividing by 5 therefore applies to the entire expression, with the result shown right. The new tree is shown below with nodes R and S added above A.
• Page 316: In-line Editing Mode

‘in-line’ as if you were entering it in the calculator’s normal HOME view. For example, highlight part of an expression as shown right. Now press SK1 ( ) and choose ‘Edit expr.’...
• Page 317: Cursor Mode

If you want to delete the entire expression then the simplest method is to press ON and exit the CAS and then re-enter it with a blank screen. Alternatively you can highlight part or all of the expression and then press SHIFT ALPHA CLEAR.
• Page 318: The Push And Pop Commands

The PUSH and POP commands Occasionally it is desirable to transfer results from the normal HOME view to the CAS screen or vice versa. This is done using the PUSH and POP commands. Suppose we have just expanded (2x+3) in the CAS, as shown right. If we press ON to exit the CAS and then type POP in the HOME view then the result will be retrieved to the HOME screen as shown.
• Page 319: Pasting To An Aplet

Pasting to an aplet As mentioned above, one method of transferring CAS results to a normal aplet such as Function is to use the POP command. However, for graphing results, there is an even easier method - simply press PLOT. Suppose that we have a result in the CAS editor as shown right.
• Page 320: Evaluating Algebraic Expressions

‘+c’. See the page after this for information on using functions in the CAS. Calculator Tip The result of the 40! example above extends off the edge of the screen and pressing ► will not scroll it. If you press the VIEWS button, then you will find that it can now be scrolled and the entire value seen - all 48 digits of it.
• Page 321: Using Functions In The Cas

CAS. These functions will only be available on the hp 40g, not on the hp 39g+. There are two ways that functions can be used. The first is to use them as the expression is entered.
• Page 322: E.g. 2 Factorizing Expressions

E.g. 2 Factorizing expressions If you highlight an expression such as (2x+3) CAS will expand the bracket. Since the result extends beyond the screen we will scroll through it using the arrow keys. The results can be factorized again using the COLLECT function. In this example we will also illustrate the use of the CAS History to fetch a previous calculation.
• Page 323: E.g. 3 Solving Equations

E.g. 3 Solving equations x − = , giving i) real solutions and ii) complex solutions. Solve the equation From any of the screen menus, access the CFG menu (see page 329) and ensure that Real mode is selected, as shown right.
• Page 324 The LINSOLVE function can also be used to solve problems of the form below. 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.
• Page 325: E.g. 5 Solving A Simultaneous Integration

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 ‘=0’. The second probability tells us that ∫...
• Page 326 We can now use the LINSOLVE function to find A and B. While the second linear equation is still highlighted, fetch the LINSOLVE command from the menu. Then press left arrow once and up arrow twice to highlight the linear expression again as shown right. Now, while the entire expression is highlighted, as shown above, press SHIFT (-) to obtain the ‘AND’.
• Page 327: E.g. 6 Defining A User Function

E.g. 6 Defining a user function The DEF 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 f x = prime function ▼ ENTER ALPHA F ( XTθ ▲ ▲...
• Page 328: On-line Help

One of the most helpful features of the hp 40g CAS is the on-line help provided by the SYNTAX button (SHIFT 2). Pressing SYNTAX will display the menu shown to the right. You can use the up or down arrow keys to scroll...
• Page 329: Configuring The Cas

One method is via the configuration line (CFG) at the top of each menu. The line shown right of S means that the calculator is CFG R= set to exact-real mode, that X is the current variable, and you are working in Step by step mode.
• Page 330: Tips & Tricks - Cas

& 1) In CAS, angles are always expressed in radians. When you are the calculator HOME screen, you can use the MODES view to change this default but this does not affect the CAS. 2) Step by step mode is quite useful for students. Choose Step by step mode to view the details of the calculations, displayed on the screen.
• Page 331 4) Don’t use a summation variable of lower-case CAS to be the unit imaginary value - the root of x 5) Although you can use the integration symbol provided on the keyboard it has disadvantages outlined on page 82. Use the INTVX function instead. See the example on page 320.

40g39g+

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