The Stat-Two group of functions...178
The Symbolic group of functions...179
The Tests group of functions...182
The Trigonometric & Hyperbolic groups of functions...182
The Calculus group of functions...184
The Complex group of functions...186
The Constant group of functions...189
The Convert group of functions...189
The List group of functions....190
The Loop group of functions...193
The Matrix group of functions....195
The Polynomial group of functions...202
The Probability group of functions...205
Working with Matrices...209
Working with Lists....215
Working with Notes & the Notepad...217
Independent Notes and the Notepad Catalog..219

Creating a Note....220

Working with Sketches...222

The DRAW menu....223

Copying & Creating aplets on the calculator..226
Different models use different methods to communicate..227
Sending/Receiving via the infra-red link or cable..228
Creating a copy of a Standard aplet...230
Some examples of saved aplets...232
Storing aplets & notes to the PC...237

Overview....237

Software is required to link to a PC...238
Sending from calculator to PC...239
Receiving from PC to calculator....244
Aplets from the Internet....245
Using downloaded aplets...249
Deleting downloaded aplets from the calculator...250
Capturing screens using the Connectivity Kit..251
Editing Notes using the Connectivity Software...252
Programming the hp 39gs & hp 40gs...255
Alternatives to HP Basic Programming...281

Flash ROM....284

The design process....255
Planning the VIEWS menu....257
The SETVIEWS command....259
Example aplet #1 Displaying info...262
Example aplet #2 The Transformer Aplet...268
Designing aplets on a PC...270
Example aplet #3 Transformer revisited...272
Example aplet #4 The Linear Explorer aplet..274
Programming Commands....286
The The The The The The The The

Aplet commands....286

Branch commands....287

Drawing commands....289

Graphics commands....291

Loop commands...291

Matrix commands....292

Print commands...293

Prompt commands....294
Appendix A: Some Worked Examples...298
Finding the intercepts of a quadratic...298
Finding complex solutions to a complex equation..299
Finding critical points and graphing a polynomial..300
Solving simultaneous equations...302
Expanding polynomials...304
Exponential growth....305
Solution of matrix equations...307
Finding complex roots....308
Complex Roots on the hp 40gs....309
Analyzing vector motion and collisions...310
Circular Motion and the Dot Product...311
Inference testing using the Chi2 test...312

Press the left arrow 5 or 6 times to see a similar display to that shown right. Pressing up or down arrow moves from function to function.
The order used when moving from graph to graph is not related to the physical location of the graphs on the is turned off then the cursor screen but rather to the order that they are defined in the SYMB view. If is free to move anywhere on the screen.
Defn (short for Definition). You will find that the Press the key labeled equation is now listed at the bottom of the screen.
The up/down arrows will move the cursor from F1(X) to F2(X), with the definition changing as it does so. If will not work correctly, nor will various other useful tools. is switched off then
However, it does have the advantage that the cursor can be freely moved around the screen with the current coordinates displayed at the bottom of the screen. For this aspect to work properly you really need to choose a scale where the pixels are on nice numbers. Multiples or fractions of the default scale are best for this.
Goto This function allows you to move directly to a point on the graph without having to trace along the graph. It is very powerful and useful.
Suppose we begin with the cursor at x = 0 on F1(X) as shown right.

and then

to see the input form shown right.
Type the value 3 and press ENTER. The cursor will jump straight to the value x = 3, displaying the (X,Y) coordinates at the bottom of the screen.
key is that it will jump to values A very nice feature of the which are not on the current screen, or which would be inaccessible for the current scale.
For example, we can jump to the value x = 100 and see the (X,Y) coordinate displayed, with the cursor positioned at the far right side of the screen. Similarly, you could jump to the value x = 2 despite this value being inaccessible for the scale chosen, since the cursor will normally only move to the values defined by the dots on the screen.
Calculator Tip The key will also accept calculated values. You could, for example, jump to a value such as e2+2. If you had recently found an intersection, then jumping to a value of Isect would return the cursor to that point. This is useful when finding areas between functions. See page 58 for information on Isect. See page 70 for an example of. finding areas between curves using
The Zoom Sub-menu. Pressing the key under The next menu key well examine is pops up a new menu, shown right.

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. This will give you the default axes, probably not showing the graph very well.
Place the cursor so that it is in the center of the area you are most interested in.
menu to adjust the view. You Use the may choose first to change the zoom factors to something other than 4x4, and to ensure ed. The PLOT view that Recenter is on the right is the result of setting 2x2 and recenter.
The advantage of doing it this way is that if you zoom in or out by a factor of 2 or 4 or 5, the cursor jumps will stay at (relatively) nice values allowing you to trace more easily. In this case, the cursor now moves in jumps of 0.05, which is ideal for most purposes. If you are not interested in tracing along the graph then this may not be important.
The disadvantage of this method is that you need to have at least some of the graph showing on the screen before you can zoom in or out to show more! Auto Scale can sometimes give you this first step.
Composite functions The Function aplet is capable of dealing with composite functions such as f ( x + 2 ) or f ( g ( x ) ) in its SYMB view. The and keys are particularly helpful with this.
For example, if we define F1( x) = x and F 2( x) = x , then we can use these in our defining of F3(X),
F4(X). See the screen shot on the left below.
If the highlight is now positioned on each of these in turn, and the performed. The result is shown in the right hand snapshot.
key pressed then the substitution is
Notice that the calculator is smart enough to realize in F3(X) that
1 is the same as x 1 , although
not, unfortunately, smart enough to keep track of the implications for the domain, which are that F3(X) should be defined only for non-negative x.
There is a limit to this however. If you define F1( x) = x 2 x 1 and then

F 2( x) = F1(

x +1) , then the
routine will not simplify

( x +1) ( x + 1) 1

to x + x 1.
On the other hand there is a way to further simplify the expression. the result and enclose it with the POLYFORM function as shown. right, adding a final ,X as shown, then highlight it and press The calculator will expand the brackets and gather terms.
Calculator Tip These functions can all be graphed but the speed of graphing is slowed first. This is because the composite function is if you dont press internally re-evaluated for each point graphed. The hp 39gs and hp 40gs are fast enough that the result is still satisfactory but if you have an old 39g or 40g they are slowed to the point of being unusable.

A related effect happens when investigating the behavior of the commonly used
1 calculus limit of lim 1 + . One of the common tasks given to students in introductory calculus classes is n n
to evaluate this expression for increasing values of n to see that it tends towards e. This can easily be done in the Function aplet using the NUM view but there is a trap in store for the unwary!
Begin as follows: 1. Entering the function into the SYMB view as F1(X)=(1+1/X)^X 2. Change to the NUM SETUP view and choose Build Your Own

in the NumType field.

3. Now change to the NUM view enter increasingly large values

for X.

The convergence towards e can also be seen graphically in the PLOT view but is very slow to reach high accuracy.
The trap mentioned earlier lies in the fact that the slow convergence will mean that people will often try to graph this function for very large values of X. The first graph on the right shows the graph of this function for the domain of 0 to 100. The second graph shows how instability develops in the domain 0 to 1E11 ( 11011 ).
This apparent instability is caused by the internal rounding of the calculator. It works to 16 bits accuracy, which means that it can store 12 significant digits (for reasons only of interest to programmers). This means that when you invert a really large number and add it to one, you lose a lot of accuracy.
For example, if X = 1010 then 1/X is 10-11. When you add 1 to this, the calculator is forced to discard all but the last decimal place because it can only store 12 significant digits. Thus 1 + 1/X
becomes 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 numbers) the expression (1+1/X)X is equivalent mathematically (on the HP) to 1.00000000003X. This produces a short section of an exponential graph, which only looks linear because you don't see enough of it.
Eventually the calculator reaches a value on the x axis which is large enough that it rounds off to a smaller number than 1.00000000003, which is 1.00000000002. This produces the sudden drop in the graph as the plot changes from a section of a 1.00000000003X graph to a section of a 1.00000000002X graph (which has a shallower gradient).

mode, the equation in y=ax2+bx+c form, its roots As with the and its discriminant are shown on the right half of the screen.
The + and - keys are disabled in
mode, since their effects are
and keys once the highlight is on the a controlled instead by the key controls the sign of a. coefficient. The Test mode. This key will present the student with a The final key is labeled series of graphs for which they must supply the equation. The type of graph is governed by the current setting. For example, if the current setting of was at Y = X 2 + v then the test graphs would also of only use the v parameter instead of a, h and v simultaneously. The setting of can be changed within screen using the key supplied. the
There are two levels of questions denoted by the keys and on the screen. An question will be in the main screen ( one can be anywhere in the 5 to 5 on each axis), whereas a also affects the difficulty larger screen (see right). The setting of but you can substitute of the question. The first is always or. another by pressing
mode you must use the arrow keys to change the parameters In a, h and v until they match the graph shown. The accuracy of your , which answer can be checked by pressing the key labeled appears as soon as you begin to change the values. The number of attempts is monitored and displayed.
An incorrect answer is shown as an animated graph on the screen , flashing repeatedly between the required graph when you press and your incorrect guess. This has to be seen to be appreciated - a screen shot cant do it justice. If your guess and the required graph cant be shown on the same screen then this animation may not be possible. will display the If you are unable to find the answer, pressing correct parameters.
When you are successful, or when you give up, press either return to the main screen.

for a new graph, or

If you go to HPs 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.

rather than , from the options at the bottom Change into the sketch view, press VAR and select of the screen. Move the highlight to Graphic and then into the right-hand column and find G0. Press the key and then press ENTER. Unlike the previous example where the pasted GROB now had to be located on the sketch page, the captured screen in this case is a full size image and so will be pasted in as a fresh page rather than replacing part of an existing one. Having pasted it into the Sketch page, you can now modify it by adding
text and other information.
One has to question, however, whether the time needed to do this and the crudity of the result make the whole
process worthwhile. If youre intending to do this to produce a set of cheat notes for your next test or exam,
you would do better to spend the time studying!
Calculator Tip The screen capture facility demonstrated here can be used to capture any screen as a GROB, not just a PLOT screen. Pressing ON+PLOT at any time will store an image of the current screen into G0. See page 251.
34 COPYING & CREATING APLETS ON THE CALCULATOR
This chapter assumes a reasonable degree of familiarity with the majority of the built-in aplets.
As has been discussed before, the designers of this calculator provided a set of standard aplets for you to use, changing the capabilities of the calculator as you change aplet. These standard aplets will cover most, if not all, of your requirements but to a certain extent you can also modify them to suit your needs and copy them for your friends. No programming is necessarily required at the lowest level and so, unless you want to learn about the programming language of the hp 39gs & hp 40gs, there is no reason to worry about it unless you want to produce highly enhanced aplets.
In this chapter we will cover the creation of aplets and, to a lesser extent, programs and notes on the calculator together with the ability to transfer them to another calculator via cable (hp 40gs) or infra-red (hp 39gs). Generally this will involve making small modifications to the standard aplets and saving them under a new name. In a chapter which follows we will cover the use of software on a PC to do this.
As well as this you can download additional aplets and programs written by people who do enjoy programming. These aplets come via the Internet, but you may be able to obtain them from your teacher, from other users, or from a PC onto which they have been copied. Once aplets have been copied from the Internet the USB cable provided with your calculator can be used to download the aplets to the calculator. This will also be covered in a subsequent chapter on page 245.

During the file transfer process the calculator will also show various pop up boxes to show progress. Their contents depends on what is being transmitted. The filename that is used on the PC to store the object is normally contracted as shown in the screen to the right. This is not important since, thanks to those two small files mentioned in the previous paragraph, the full name will be recorded and restored when transferred back to the calculator. The reason for the contraction is that the original hp 38g from which the hp 39gs and hp 40gs are derived was released for an earlier version of Windows that did not allow long filenames. This has never been changed on later models.
Time out If you see a message saying that there has been a Time-out, it means that communication with the PC has been lost. This can be due to low batteries. Communication with the PC is very power intensive and problems may occur before the low battery indicator lights up at the top of the calculator screen. It can also be due to problems with the communications software. The USB connection seems to be quite unstable and you may find that you need to close the program and re-start it at times to restore communications.
Attached programs If your aplet is one that has been given to you by someone else such as your teacher, rather than simply a copy of one of the standard ones, then it may have one or more helper programs associated with it. For example, almost all the aplets available from the Hewlett-Packard web site come with sets of up to 6 or 7 programs to do the work, and without which they are totally useless. 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. This can greatly increase the transmission time and it is important that you dont interrupt the process early. If you want to see these helper programs, press SHIFT PROGRAM to see a list of the programs currently on your calculator. Even if there are no other programs currently stored, you will always see the Editline entry. It contains a record of the last calculation you did in the HOME view and cant be deleted.

In general, any aplet which is suitable for the older HP39G, HP40G or hp 39g+ will also work on the new hp 39gs and hp 40gs. Some games may not be for two reasons. Firstly the earlier models used a slower chip and this means the older games sometimes run so fast that they are unplayable. Secondly, some of them directly access the calculators chip. If the address on the chip they reference has changed from the old model to the newer one then running the aplet may cause the calculator to lock up or spontaneously reset. The worst result will be loss of user memory. None of the aplets designed for the earliest model, the HP38G, will work on older models.
If you own a calculator then you will already have the required cable with which to download from the internet. If you bought yours second hand without a cable then youll need to purchase a cable from an electronics store. The mini-USB cable required is the same as that used by many digital cameras.
Downloading an aplet from the web is very simple. Any site will present you with a page which may be similar to the one on the previous page. It may contain either programs or aplets or both. Generally you will be able to click on a link that lets you download that aplet as a compressed ZIP file.
A ZIP file is a special type of file which contains one or more files in compressed. The reason for the compression is simply to allow you to download them from the Internet as one single file instead of having to download each one of the collection separately. The ability to expand these ZIP files is built into Windows XP and you should de-compress them as soon as you have them on your PC. Just double click on the file and it will open as if it is a folder. You should then move or copy them into a normal folder (one that isnt a compressed file).
The HP39DIR files The software that sends the files to the calculator cant work on them if they are inside a compressed file so you must expand them before using them.
Calculator Tip It is critical that you decompress each aplet into a separate directory. Each aplet has two special files called HP39DIR.000 & HP39DIR.CUR which always have this same name. Decompressing two aplets into the same directory will cause these two special files from the first one to be overwritten by those of the second. The aplet itself will not be harmed by this but the effect is to render it invisible to the calculator, since these two special files contain information telling the calculator about the aplet.
Organizing your collection Shown below and right is the contents of one directory in part of my collection.
If youre only going to download a few aplets then organization will not be as important. If you are a teacher or if you are intending to download lots of aplets then you might consider setting up a logical structure of directories to contain them. For example, a teacher might choose to set up a structure containing directories for each of the courses being run, with further directories containing all the aplets which were relevant to that course. Again, it must be stressed that each aplet must be in a separate folder!

the Swap back to the Program Catalog, position the highlight on the program.MSG.SV and 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. Press VIEWS to check. You should find that your new menu appears. Press to exit.
Providing that you have done everything correctly, this is now the end of the process - the aplet is now ready or ENTER to run to be run. In the APLET view, make sure the highlight is still on the aplet and press and the program.
it. If you get an error message at any time then you may have to
When you do this, the aplet will run the program.MSG.S which will

display a MSGBOX.

The line in the SETVIEWS command controlling this was:
"Start";".MSG.S";7;
Since the triplet ends with a view number of 7, this means that after the ), the VIEWS menu will program terminates (when you press display.
If you choose the option Message 1, then this will cause the program.MSG.1 to be run, displaying the screen on the right. This line in the SETVIEWS command also terminated with a view number of 7 so when you press the VIEWS menu will display again.
The program line for this was:
MSGBOX "Hello world! 3+4 = " 3+4:
Items in quotes are displayed as they appear, while expressions outside them are evaluated before being displayed. This means that the 3+4 inside the quotes appears as exactly that, while the one outside is evaluated to 7. Expressions can include variables and calls to functions.
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. Note the suggested value of 20, and note also that the prompt of Please enter N. was too long to be displayed. See the PROMPT command for an alternative that is simpler but less flexible.
When you enter a number into the input screen and press ENTER, the next line in.MSG.IN will display this , the view number of 7 specified in the relevant line of value in a MSGBOX. When you then press.MSG.SV will cause the VIEWS menu to be displayed again.
Notice that the input window is still displaying in the background. To stop this happening, you could have included in.MSG.IN a line of ERASE: , which is a command to erase the display screen. Try editing the program, inserting this line before the MSGBOX line, and running it again.

.TRANSF.SHAPE

.TRANSF.MAT
(continued) Since the default contents of any variable is zero and there is no zeroth option on a list this means a program bug waiting to happen unless you preset the value. Options 1 and 2 load preset matrices while option 3 allows the user to edit their own. Note the check to ensure the matrix they entered has a valid size. The number of columns is then extracted and used to reset the value of Tmax. The new image matrix is also recalculated. Note: The indenting used is not required and is there simply to make the program easier to read. The amount of memory take up by a few extra spaces is minimal but well worth it in terms of readability.

CHOOSE command to offer

This program uses the
a list of options. Note the need to pre-load a value into C. This value determines which option is initially highlighted when the menu appears. If a list has only three options but the highlight is set to some other value than those three then it can crash the program.
This program puts up a message instructing the user and then allows them to edit the transformation matrix in M1. The size of the matrix is checked to ensure it is 2x2, with the DOUNTIL loop ensuring that the user cannot exit without a valid matrix entered.
the.TRANSF.SV program to create the new altered VIEWS menu then you Assuming that you have the aplet first to ensure that the new VIEWS menu is can now test the aplet. Dont forget that you must attached to the right aplet. Its operation should be familiar to you if you have already examined its cousin on page 234.

Designing aplets on a PC

The software used on the PC to edit and create Notes, programs and aplets was in the process of being written at the same time as this book. Consequently the explanations given here may tend to be a little vauge. Screen images and explanations may be different on the final version you are using. However the process should be substantially correct. At the time this book was being written the sofware was called The Connectivity Kit but this too may have changed. Look for the latest version on HPs website or on The HP HOME view (at http://www.hphomeview.com). In the next example we will use The Connectivity Kit to create small program and then to re-create the same Transformer aplet used in example 2. This second example will allow us to concentrate fully on how to use the The Connectivity Kit rather than the programming task since the programming has been discussed in great detail earlier.

Please note

Example program Log X (base b) This is a small program that will find the log of any number to any base using the change of base law. Clearly this is not terribly useful but it does illustrate the process in a simple way. Begin by creating a folder to hold the program or choosing an existing one if thats what you want. Start the Connectivity Kit and select the folder in the initial Folder/Transfer tab.

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.
Pressing the PLOT button will result in the menu shown in the second screen.
If you choose the Function aplet then you will be asked to nominate a destination. The current contents of each function is shown to allow you to choose whether to overwrite or not. All you need then do is exit the CAS and enter the Function aplet. You will then need to manually the new function if you want to PLOT it. See page 342.
Evaluating algebraic expressions When an expression is highlighted, pressing ENTER will cause it to be algebraically evaluated and any functions to be applied accordingly. For example, if you highlight (2x+3)^3 as shown right then pressing ENTER will give the result shown.
Further examples are shown below. In each case it is only the highlighted expression which is evaluated. Depending on the settings of the CAS configuration there may or may not be intermediate steps displayed between those shown.
Notice the lack of a +c indefinite constant in the integration result. Here, this is because we are using the definite integral (see page 73 and the page following). A better alternative is to use the INTVX function as shown below, even though it still does not add the +c (see page 73 for reasons).
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! The amazing abilities of the CAS are such that even the entire results of something like 200! can be seen.

Examples using the CAS

In these examples we will begin with exercises which demonstrate the basic abilities of the CAS to simplify expressions and then move on to the use of the functions available through the various menus. In the initial examples the exact keystrokes will be supplied but in later ones this may not always be the case.

Example 1: Simplifying a fraction with working Suppose you are required to simplify the expression shown right, giving your answer as a proper fraction. i. Begin by entering the top pair of fractions:

3 SHIFT

4 SHIFT 2 3
At this point the screen should appear as shown above right. ii. We will now simplify selectively in order to be able to record working, beginning with the denominator:
Because the entire denominator is selected, will now pressing select the numerator. To evaluate this, press ENTER again:
Now press SHIFT ENTER to evaluate it:
to select the entire expression and then
To obtain a mixed fraction we use the function PROPFRAC, designed to transform improper fractions to mixed. The fraction is already selected, so choosing the fraction now will apply it:

SHIFT CMDS 7 ENTER ENTER

Note: The 7 above causes a jump to the first function beginning with a
P, the letter on the 7. The
arrows within any menu cause a
page down. The alternative is just to scroll to the function.
Example 2: Simplifying surds Simplify the surd expression: i. Begin by entering the expression:
2 SHIFT 18 SHIFT SHIFT 75 SHIFT 72

72 + 75

Now simplify each surd in turn (assuming working is desired):

ENTER

Finally, select the entire expression with SHIFT

ENTER to simplify:

and press
If you want the result as a decimal, press NUM. Pressing SHIFT NUM will cause the calculator to analyze the decimal and re-instate the surd.
There are two ways that functions can be used in the CAS. The first is to use them as the expression is entered. In this method the order is to choose the function and then to fill in the parameters required. The second is to apply a function to all or part of an expression that has perhaps resulted from a previous calculation or been typed in first. If you highlight an expression and then choose a function the expression will appear as the first parameter in the function. A list of the functions in their various menus is given on page 358.

Example 3: Using lim

Find lim

x x 35. x7

The sequence of keys for this is scroll to lim and press

ENTER ENTER

Find lim
The sequence of keys for this is
- 2 scroll to lim then ENTER 1 scroll to QUOTE ENTER 2 - 0 MATH SHIFT ENTER ENTER

Some notes:

1. The limit approached from above would be entered as QUOTE(2 + 0). 2. The use of the QUOTE function forces the CAS to treat the 2 - 0 as an algebraic entity rather than immediately evaluating it as simply 2. Thus the result of . 3. The two functions LIMIT and lim are the same. On the old model hp 40g the only function was LIMIT but lim was added on the 40gs. Because it was a late entry it appears one way in some menus and as the alternative in the others. Functionally there is no difference so why it was added is not clear.

Example 9: Investigation of a complex function Rewrite the function
z + z in parametric form and graph it. Show 2 that it is symmetrical about the x axis and evaluate f as an exact surd. 3

f ( z) =

The first step is to enter the function.

ALPHA Z

ALPHA Z
We now transform it into exponential form by using the SUBST function to replace z with
SHIFT ALPHA Z SHIFT = SHIFT SHIFT i SHIFT ALPHA t

SHIFT

ENTER ENTER x

within the menu

The reason for pressing is to jump to the first function starting with an S, the letter on the
key. Pressing it again jumps to the next function starting

with S, which is SUBST.

Next we linearize it

ENTER ENTER ENTER

is used
1. As in the previous case, the to jump to the first function that starts with
an L, the letter on 2. The hp 40gs will probably ask if it should
turn Complex mode on, assuming it is in
its default configuration. One of the ENTERs

is to tell it Yes.

And, having linearized it, we store it as a variable M in case we need to refer to it again.

ALPHA M ENTER

When the STORE command is executed the expression is echoed back to the screen. Press SHIFT ALPHA CLEAR to clear the screen. At this point, any reference to M will be equivalent to the expression shown right. Note that the screen image above is in small font purely to allow the entire expression to be seen. Your screen will not be unless youve selected small font earlier.
We now separate the real and imaginary parts of M into separate functions, storing them as X1(t) and Y1(t).

ALPHA M MATH ENTER ENTER

SHIFT =
ALPHA X 1 ( SHIFT ALPHA T
The parameter order must now be changed before the function is applied

SHIFT SHIFT ENTER

Clear the current contents of the screen using SHIFT ALPHA CLEAR. Then perform the same definition assignment for Y1(t) as the imaginary part of M.

ALPHA M MATH ENTER ENTER

Note: As before, the
button jumps to the first function with that letter (L), in this case IM.

hp calculators hp 39g+ & hp 39g/40g The MATH menu The MATH menu
The purpose of this section of the tutorial is to introduce MATH menu, demonstrating the use of a selection of useful functions.
Using the menu The REAL functions The TRIG functions The LIST functions The MATRIX functions The POLYNOMIAL functions The PROBABILITY functions The COMPLEX functions
The materials presented on this page are adapted from material published by Applications in Mathematics. Materials presented on this page are licensed exclusively to Hewlett-Packard Co.(HP ) by Applications in Mathematics, solely for viewing in this form and on this HP web site. Printing, reproduction or re-transmission in any other form or venue is prohibited. 2003 Applications in Mathematics. All rights reserved.

hp calculators

hp 39g+ The MATH menu & hp 39g/40g

Using the menu

The mechanics of accessing the MATH menu is very simple. It is illustrated here using the function POLYFORM from the Polynomial group, covered in more detail later. Change into the HOME view and then press the MATH button. You will see the screen on the right. The menu appears first with the Real functions highlighted. It is possible to 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 7 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 - Polynomial and Probability. To reach Probability just press the P key again or scroll down. Once in the correct group, press the right arrow key to move into the list of functions belonging to that group. Once again you have a choice of using the arrow keys or the button corresponding to the first letter of the function. Pressing the right arrow key again will move down the functions a page at a time. In this case, since every single function in the Polynomial group begins with a P, and there is only one page of them, there is no difference between the methods. Move the highlight down to POLYFORM and then press the ENTER key. Your HOME view should now look like this You will notice that the first bracket has already been inserted for you. This is the normal practice. Press ON to clear the edit line.

The REAL functions

These are the functions which deal with real numbers, rounding, exponents, conversions and so on. Some examples are given below but you should see the manual for the complete list. DEG RAD(degrees) This fgunction converts degrees to radians. Eg. DEG RAD(30) = 0.5235 DEG RAD(180) = 3.1415926
ROUND(num,dec.pts) This function rounds to a number of decimal places (d.p.). Eg. 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. To do this, simply put a negative sign on the number of places. Eg. Round 32345 to the nearest thousand. Use: ROUND(32345,-2) = 32000 Round 3405.63475 to 6 sig.fig. Use: ROUND(3405.63475,-6) = 3405.63

The TRIG functions

This group, together with the associated Hyperbolic group of functions, covers the less commonly used trigonometry functions which were not put on the keyboard. They are used in exactly the same way as the normal SIN, COS and TAN functions, together with their inverse functions (above the keys) of ASIN, ACOS and ATAN.
On the face of the calculator you will find: Function SIN (sine) COS (cosine) TAN (tangent) Inverse function ASIN (arc-sine) ACOS (arc-cosine) ATAN (arc-tangent)
In the Trig. group of functions you will find: Function COT (cotangent) CSC (cosec/cosecant) SEC (secant) Inverse function ACOT (arc-cotangent) ACSC (arc-cosec) ASEC (arc-secant)
In the Trig. group of functions you will find (among other specialized functions): Function SINH (hyperbolic sine) COSH (hyperbolic cosine) TANH (hyperbolic tangent) Inverse function ASINH (arc-hyperbolic sine) ACOSH (arc-hyperbolic cosine) ATANH (arc-hyperbolic tangent)

The LIST functions I

A list is the same as a set. It is separated by commas and enclosed with a pair of curly brackets. Eg. {2,5,-2,10,3.75} The most useful of the functions in the List category is the MAKELIST function covered below. MAKELIST This function produces a list of the length specified using a rule of your choice.

The syntax is: MAKELIST( expression, variable, start , end, increment ) where expression is the mathematical rule used to generate the numbers. variable is the variable used in the expression. start is the first value that variable is be given. end is the largest value that variable is to take. and increment is the amount by which variable should be incremented.
Eg. 1 MAKELIST( X2,X,1,10,2) L1 produces { 1, 9, 25, 49, 81 } as X goes from 1 to 3 to 5 to and also stores the result into L1. Eg. 2 MAKELIST(RANDOM,X,1,10,1) produces a set of 10 random numbers. The X in this case serves only as a counter. Eg. 3 MAKELIST(3,X,1,10,2) produces the list {3,3,3,3,3,3,3,3,3,3}.

The LIST functions II

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). Thus MAKELIST(RANDOM<0.75,X,1,10,1) will return a list of 1s and 0s corresponding to the simulated Bernoulli trials. Example 1: Simulate 100 observations on a continuous U[10,15] distribution.
In HOME type: MAKELIST(5*RANDOM+10,X,1,100,1) C2 Example 2: Simulate 50 observations on a discrete uniform random variable U[3,7] In HOME type: MAKELIST(INT(5*RANDOM+3),X,1,50,1) C2 Example 3: Simulate 50 observations on a Binomial random variable with n=20 & p=0.75. In HOME type: MAKELIST( (I=1,20,RANDOM<0.75),X,1,50,1) C2 Note: The and the = are both on the keyboard. Each element of the 100 in the list will be the sum of 20 Bernoulli trials. This will be a relatively slow calculation because it involves evaluating 1000 random numbers (50 x 20). Example 4: Simulate 100 observations on a normal distribution with =80 and =50. In HOME type: MAKELIST(80+ 50*( (-2*LN(RANDOM))*sin(2*RANDOM)),X,1,100,1) C2 (ensure MODES is set to Radian measure first)

The MATRIX functions

This very extensive group of functions is provided to deal with matrices. One of the most useful is the RREF function which is used to convert augmented matrices into reduced row echelon form. See Using Matrices for more details on this. The scope of functions and abilities covered in this group is vastly greater than would be required by the average school student or teacher. Consult the manual for details. Two small examples are given below. DET(matrix) This function finds the determinant of a square matrix. Eg. If

A= 1 5

then find det(A).
LQ(matrix) This function takes an mxn matrix, factors it and returns a list containing three matrices which are (in order): an mxn lower trapezoidal matrix an nxn orthogonal matrix an mxm permutation matrix. To separate these matrices for later use, store them into a list variable. For example LQ(M1) L1 would store the three resulting matrices into list variable L1. In the HOME view you could now enter L1(1) M2 to store the first of the result matrices into M2 and so on.

The PROBABILITY functions I
This group of functions manipulates probabilities and probability distribution functions.
RANDOM This function supplies a random 12 digit number between zero and one. If you want a series of random numbers, just keep pressing ENTER after the first one. Eg. Produce a set of random integers between 5 and 15 inclusive. Use the expression INT(RANDOM*11)+5 The RANDOM*11 produces a range from 0 to 10.999999. This is then dropped down to the integer below by the INT function, giving a range of integers 0,1,2,3,.,10. The final adding of 5 gives the correct range.
Tip: If you enter RANDOM on two calculator taken straight from their boxes the results will be the same random set! To stop this happening you need to seed the internal algorithm with a different value on each calculator. The simplest way to do this is to type RANDSEED(Time) in the HOME view. Since the internal clock will have a different time for each calculator this will mean that everyone will get different values. This will need to be re-done if you reset the calculator.
The PROBABILITY functions II
COMB(n,r) This function gives the value of nCr. Eg. Find the probability of choosing 2 men and 3 women for a committee of 5 people from a pool of 6 men and 5 women.
Tip: The reason for the single COMB(6,2) above the main calculation is to save time. Rather than using the MATH menu for every entry of the COMB function, you can enter it once and then it repeatedly, changing the parameters.
UTPN(mean, variance, value) This function, the Upper-Tail Normal Probability, gives the probability that a normal random variable is greater than or equal to the value supplied. Note that the variance must be supplied, NOT the standard deviation.
Eg. 1. Find the probability that a randomly chosen individual is more than 2 meters tall if the population has a mean height of 1.87m and a standard deviation of 10.4cm
x = 1.87m, = 0.104m 2 = 0.010816
As shown right, Pr(height>2m) = 0.1056
The POLYNOMIAL functions I
These functions are all ones which you will use regularly. Some are outlined below. POLYCOEF([root1, root2, ]) Returns the coefficients of a polynomial with roots x1, x2 , x3 ,. The roots must be supplied in vector form, which for the hp 39g+ means putting them in square brackets. The function f ( x) above has roots 2, -3 and 1. The screen shot to the right shows the POLYCOEF function giving the required coefficients as 1, 0, -7 and 6 for a final polynomial of f ( x) = xx + 6.
POLYFORM(expression, variable, 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. If the expression contains more than one variable then any others are treated as constants. Eg. 1 Expand

( 2 x 3)

( x 1)2
Result: 8xx4 + 134 x3 171x2 + 108x 27 The resulting polynomial is shown both as it appears in the HOME view and as it appears after pressing the key.
The POLYNOMIAL functions II

Eg. 2 Expand ( 3a 2b )

This function contains two variables, A and B, which must be expanded separately. The first expansion, treating A as the variable, is POLYFORM((3A-2B)^4,A) (see right).
Pressing , it can be seen that the expansion of the expression in terms of A has been done, but the terms involving B are not fully evaluated.
The solution is to use POLYFORM again. Use the MATH menu to fetch the POLYFORM function to the edit line, then move the cursor up to the partially evaluated expression that was the result of the previous POLYFORM. Copy it into the edit line, add a comma, a B and an end bracket. Pressing ENTER will now evaluate the terms involving B.
After pressing ENTER the for the second evaluation, the result is shown right (after pressing ).

The COMPLEX functions I

Complex numbers on the hp 39g+ can be entered as they are commonly written in mathematical workings as a + bi with the i obtained using SHIFT ALPHA to get lowercase, or as an ordered pair (a,b). As soon as you press ENTER, the calculator immediately converts the a + bi form into an ordered pair. The exception is when a complex number is entered in rcis form using the (angle) sign on the keyboard. See the edit line to the right to see how it was entered with the results shown above. When you do this the calculator converts to a more explicit rcis format as shown right, and gives the result as an ordered pair. This behaviour only happens in Radian mode. Complex numbers can be used with all trigonometric and hyperbolic function, as well as with matrices, lists and some real-number and keyboard functions. There are 10 special memories Z1,Z2.Z9,Z0 which are provided to store complex numbers.
ABS(real or complex) - found on the keyboard and the MATH menu The absolute function returns the absolute value of a real number. When you use ABS on a complex number a + bi it returns the magnitude of the complex number a 2 + b2.

The COMPLEX functions II

SIGN(real or complex) This function is part of the Real group but is more useful with complex numbers. Given a vector/complex number (a,b), SIGN will return another vector/complex number which is a unit vector in the direction of (a, b). i.e. SIGN((A,B)) returns

a b , 2 a + b2 a +b

ARG(complex or vector) - found on the keyboard and the MATH menu This function returns the argument of the complex number. For example, as shown right, ARG(4+2i) would be 26 565o. The reason for the double brackets in the screen shot right is that every function used by the calculator uses brackets (hence the outer pair) but so too do complex numbers (hence the inner pair). Using ARG(a+bi) avoids this.
IM(complex) and RE(complex)
These functions return the imaginary and real parts of the complex number supplied. If you enter a + bi then IM((a,b)) = b and RE((a,b)) = a.