HP 40gs

Graphing Calculator
This ideal classroom graphing tool uses Computer Algebra System (CAS), familiar algebraic entry-system logic and displays answers in symbolic, numeric, and graphing views. Create and store Aplets with 2.25MB total memory**.
Enhanced classroom power Math and science students will benefit from algebraic entry-system logic and easy-to-use interactive tools. Perform complex arithmetic and calculus functions with Computer Algebra System (CAS) Improve problem solving and learning opportunities with symbolic, numeric and graphic views Easily create and use Aplets to assist in learning Review and work with your data using interactive history, notes and sketch capabilities Complex problem solver Complex problem solving is easier on a large, dynamic split screen with adjustable contrast and 2.25MB of total memory**. Easy readability on dynamic split screen with adjustable contrast Get outstanding performance and ample storage with 2.25MB of total memory (2MB Flash + 256KB RAM)** Tackle tough problems with over 750 built-in functions plus powerful HP solvers and applications Use a built-in library of 29 constants and easy metric unit conversions for math and science Designed to be efficient Access online applications and share data through a variety of connectivity options. Improve accuracy with HP click-style keys. Download and share data with PCs and other devices using USB and serial ports Reduce keying errors and improve accuracy with unique HP click-and-rotate keys Increase protection and improve portability using slide-on hard cover Get added flexibility using on-screen dynamic menu options HP quality and support Have confidence that every time you turn on your HP calculator, every calculation you make, results in dependable, worry-free performance and accurate results. Rely on HP quality and award-wining support online and by phone Get the most from your calculator, visit www.hp.com/calculators for downloads, tutorials and more

Specifications

The HP 40gs Graphing Calculator includes all the features of the HP 9G plus: Computer Algebra System (CAS) Symbolic, numeric and graphic views Linear equation solver and triangle solver 2.25MB total memory (2MB Flash ROM + 256KB RAM)** Enhanced connectivity with serial port, USB Adjustable contrast for greater readability Built-in constant library Slide-on hard cover included
HP Part Number CPU Display size Display Type Connectivity Contrast Entry-system logic Built-in functions Menus, prompts, etc. Internal precision Memory Keyboard Power Power off memory protection Auto power off Size (L x W x D) Enclosure material Key top material Weight What's in the box Warranty Subject suitability Permitted for use on
F2225AA 75Mhz ARMx 64 pixels (7 lines x 33 characters + 2 line header + 1 line menu) LCD USB and serial ports for connectivity to PCs, other HP 40gs calculators and peripherals Adjustable Algebraic Over 750 Yes 15 digits 2.25MB total memory (2MB Flash + 256KB RAM)** Alphanumeric AAA x 4 + CR2032 Yes 5 minutes 18.7 x 9.4 x 3.1 cm (7.4 x 3.7 x 1.2 inches) Plastic Plastic Approximately 249 g (8.8 oz)
Calculator, slide-on protective cover, batteries, user manual, USB cable, unit-tounit cable and CD with connectivity software, Aplets and advanced user manual
1-year warranty (may vary by region) General mathematics, Algebra, Trigonometry, Statistics, Geometry, Biology, Chemistry, Physics, Earth Sciences SAT Reasoning and SAT Subject TestsTM in Math 1 & 2, ACT, PSAT/NMSQT, AP Chemistry/Physics, AP Calculus/Statistics, PLAN, EXPLORE*
2007 Hewlett-Packard Development Company, L.P. The information contained herein is subject to change without notice. The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services. Nothing herein should be construed as constituting an additional warranty. HP shall not be liable for technical or editorial errors or omissions contained herein. *ACT, PLAN and EXPLORE are registered trademarks of ACT, Inc., which was not involved in the production of and does not endorse this product. For more information, go to www.act.org. AP Calculus requires a graphing calculator. Any scientific or graphing calculator (Excludes models with QWERTY (i.e. typewriter) keyboards, electronic writing pads, and pen-input/stylus-driven devices) is permitted for the following College Board tests: AP Chemistry, AP Physics, AP Statistics (a graphing calculator with statistical capabilities is expected), PSAT/NMSQT, SAT Reasoning and SAT Subject Tests in Mathematics Level 1 and Level 2. For more information, go to www.collegeboard.com. Policies are subject to change. AP and SAT are registered trademarks of the College Board. PSAT/NMSQT is a registered trademark of both the College Board and National Merit Scholarship Corporation which were not involved in the production of and do not endorse this product. **Flash ROM memory is for system upgrades only and is not available to the user.

To learn more, visit www.hp.com/calculators

4AA1-0863ENUC, June 2007

For example the standard PLOT screen provides a standard graph covering the whole screen, but the VIEWS menu lets you use a split screen such as shown right. Information on the VIEWS menu is given in the chapter dealing with the Function aplet.
In its second role, the VIEWS key also has a critical purpose when using aplets which have been downloaded from the Internet. When a programmed aplet is created for the hp 39gs or hp 40gs, a menu is provided by the programmer to let you control and use it. During the programming this menu is tied to the VIEWS key, replacing the menu normally found on the key.
For example, the snapshot shown right is of a VIEWS menu taken from an aplet designed to analyze and graph Time Series data.
The next important key is the HOME key. It allows you to change into the HOME view from wherever you are. Above it is the MODES key, accessed by pressing SHIFT first. More detailed information on these two views follows later.
The VARS key The VARS key is used, mainly by programmers, as a compact way to access all the different variables stored by the calculator including aplet environment variables.
Shown right are two views of the VARS screen, the first from the HOME list showing the graphic variables (memories) G1, G2. and the next from the APLET list showing some of the variables in the set controlling PLOT.
The VARS key is not generally used much, and you may not have followed this explanation. This is not important as it is a key that is very rarely used by the average user. A few uses for the average user are detailed in the Function aplets Expert User section on page 62.
The MATH key next to VARS is far more important and provides access to a huge library of mathematical functions. The more common functions have keys of their own, but there is a limit to the number of keys that one can put on a calculator before it takes too long to find the key required. Hence the MATH key.
The MATH menu lists all those functions that would not fit onto the keyboard plus some which also appear on the keyboard. Shown in the screen snapshot right is a small selection of the total list. For a listing of almost all the functions, with examples of their use, see the chapter entitled The MATH Menus on page 165.
As is usual with all calculators, most of the keys have another function above the key. The hp 39gs and hp 40gs get twice the action from each key by having this second function.
The second function is accessed via the SHIFT key on the left side of the calculator. Although this book will sometimes tell you explicitly to press this key, in most cases it will be assumed that you are intelligent enough to work out for yourself when it is necessary to press it.

The ALPHA key gives access to the alphabetical characters, shown below and right of most keys. Pressing SHIFT ALPHA gives lower case.
Calculator Tip If you press and hold down the ALPHA key you can lock alpha mode, although this doesnt work for lower case. Many people use this to type in functions by hand rather than going through the MATH menu. Some views, such as the Notepad, also offer a screen key function that lets you lock either upper or lower case alpha mode.
The SETUP views The SETUP views, above PLOT, SYMB and NUM, are used to customize their respective views. For example, the PLOT SETUP screen controls things like axes, labels etc. Their use changes in different aplets, so for more information see the explanations in the chapters dealing with the various aplets, particularly in the Function aplet on page 50.
The SYMB SETUP key is only used in one place, which is to choose the data model for bivariate statistics in the Statistics aplet. It is not available in the other aplets and trying to access it will result only in a quick flash of an exclamation mark on the screen to say Youve done something wrong!.
Information on the use of the SKETCH and NOTE views (located above the APLET and VIEWS keys) can be found in the chapters Working with Sketches and Working with Notes & the Notepad on pages 222 & 217.
The main use for the SKETCH and NOTE views is in aplets downloaded from the Internet. Instructions for using the aplet are sometimes included with the aplet in note form, and sometimes as an accompanying sketch.
The MODES view The MODES view (see right) controls the numeric format used in displaying numbers and angles in aplets. At the bottom of the screen you will see that one of the screen keys has been given the function. Pressing this key pops up a menu of choices from which you can select the option which suits you. The default angle setting is radians.
Calculator Tip If you dont want to use the menu then, rather than pressing , highlight the field and then press the + key repeatedly. This will cycle through the choices without popping up a menu. This can be much faster if the menu has only a few choices.

+1 dx is read as:

the integral from 1 to 2 of

x 2 +1

& entered the same way:

2, X + 1 , X )

A similar path was taken with the differentiation function, so that:
d X 2 , which is read as the derivative. with respect to X.of X2 dx
and entered as it is read as X ( X 2 ).
Note that although I have used X as the variable of integration in the examples above, this is not a requirement. The integration example could be done as

( 1, 2,

A2 + 1 , A ) with the same result.
Integration: The algebraic indefinite integral Algebraic integration is also possible (for simple functions), in the following fashions:
If done in the SYMB view of the Function aplet, then the integration must be done using the symbolic variable S1 (or S2, S3, S4 or S5). If done in this manner then the results are satisfactory, except that there is no constant of integration c. The screenshot right shows the results of defining
F1( X ) = X and then F 2( X ) = ( 0, S1,

X 2 1, X ) , together

with the results of the same thing after pressing the
(the result is placed in F3(X) only for convenience of viewing).
All that is now necessary is to read -S1+S1^3/3 as x + or as it should be read as

x3 x+c. 3 x3 , 3

If done in the HOME view, then S1 must again be used as the variable of integration.

i.e. x 1 dx

is entered as

( 1, S1, X2 - 1, X ).

. The This is shown above, together with the results of highlighting the answer and pressing result may seem odd but is caused by calculator assuming that X itself may be a function of some other variable and integrating accordingly as a partial integration. While mathematically correct, this is not what most of us want. The way to simplify this answer to a better form is to highlight it, it, and press ENTER again, giving the result shown
right. This is the result of the calculator performing the
substitutions implied in the previous expression.
A caveat when integrating symbolically This substitution process has one implication which you need to be wary of and so it is worth examining the process in more detail. The expanded version of what is happening is shown below.

The disadvantage of the previous method is that it is not very visual. An alternative is to use an aplet downloaded from the web. An aplet that will automate the process and provide a visual display of the chord diminishing in length can be found on the authors website at http://www.hphomeview.com.
Finding and accessing polynomial roots The POLYROOT function can be used to find roots very quickly, but the results are often difficult to see in the HOME view due to the number of decimal places spilling off the edge of the screen, particularly if they include complex roots. This can be dealt with easily by storing the results to a matrix.
For example, suppose we want to find the roots of f ( x) = x3 3x 2 + 3. We will use the POLYROOT function and store the results into M1.
The advantage of this is that you can now view the roots by changing to the Matrix Catalog (SHIFT 4) and. See page 209 for pressing more detailed information on matrices.
In addition to this, you can access the roots in the HOME view as shown. This method works equally well for complex roots. See page 309 for details on finding roots of real and complex polynomials using the CAS on the hp 40gs.
Calculator Tip This trick is particularly helpful if you are working with complex roots. 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.

10 THE VIEWS MENU

In addition to the views of PLOT, SYMB and NUM (together with their SETUP views), there is another key which we have so far only used very fleetingly - the VIEWS key.
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.
The contents of the VIEWS menu changes slightly according to which aplet you are currently using. The Function aplet contents are covered here but the others differ in only small ways.
Aplets downloaded from the Internet, however, will usually have a radically different VIEWS menus created by the person who wrote the program for the aplet. See page 257 for more information on this process if you intend to program the calculator. The first image shown right shows the contents of the VIEWS menu for an aplet called Coin Toss which investigates probability.

Tn = 3n 1.. Tn = n Tn = 2
{2, 5,8,11,14,..} {1, 4, 9,16, 25,..} {2, 4,8,16, 32,..}

(implicit/recursive)

Tn = 2Tn;T1 = 2 Tn = 5 Tn1 ;T1 = 2 Tn = Tn1 + Tn2 ;T1 = 1,T2 = 1
{2, 3, 5, 9,17,..} {2, 3, 2, 3, 2,..} {1,1, 2, 3, 5,8..}
As with most aplets, the Sequence aplet starts in the SYMB view when you enter formulas. The Sequence aplet uses the terminology U(N) rather than the other commonly used Tn for its definitions in order to avoid having to use subscripts which would not show up well on the screen. All functions of this type are assumed to be defined for the positive integers only ie. for N = 1,2,3,4 First, second & general terms Each definition has three entries - U1(1), U1(2) and U1(N) (see above) but it is not always necessary to supply all three.
For example, if the sequence is non-recursive then only the U1(N) entry needs to be filled in, with the other two entries calculated automatically from the definition as shown in the sequence of two screens shown right.
If the definition is recursive but only involves value for U1(2).
Tn1 rather than both Tn1 and Tn2 then you need not enter a
For example, for the sequence
Tn = Tn1 + 3; T1 = 2 you need only
enter the value 5 into U1(1) and the expression U1(N-1)+4 into U1(N). The value of U1(2) will be ignored in the SYMB view but filled in by the calculator automatically in the NUM view.
Convenient screen keys provided There are a number of very convenient extra buttons provided at the bottom of the screen when entering sequences.
and - are available as soon as the cursor Two of these moves onto the U(N) line (see right). Pressing either will enter the appropriate text into the sequence definition.
The rest become visible once you have begun to enter the sequence definition.
For example, suppose we enter the Fibonacci sequence into U2 by defining U2(N) as U2(N-1) + U2(N-2). Rather than having to type all of this we can use the buttons provided, pressing:
This is a very convenient feature, and worth remembering.
mark next to the definition yet, since the sequence is There is no defined recursively and no values have yet been given for U2(1) and U2(2). Type in a value of 1 for both of these and then press the NUM button to switch to the NUM view.
As you can see in the screenshot right, the NUM view shows the actual values in the sequence as a table. If you move the highlight into the U1 button and see the sequence and U2 columns, you can press the rule. You can experiment for yourself and see the result of pressing the button is also button (see next page for an example). The available as usual, but it is easier to use other methods.
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 dont realize 2.1475E9 is computer speak for 109.

Move the highlight to V and enter the value , then to U and enter and finally to D and enter 100.
Now move the highlight back to A (the value youre trying to find) and button. You should find that you obtain the answer to press the our problem of m/s2.
The INFO report process has finished, you can obtain a report on it by When the button. The result in this case may not seem very pressing the informative but there is more about these messages on page 106. The information they supply can be critical and you should develop the habit of checking them.
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 to the estimate.
Example 1 The volume of a cylinder is given by V = 2 r ( r + h ). Find the radius of a cylinder which has a volume of 1 liter and a height of 10cm.
Enter the equation into E1 as shown right. When you are entering the equation, ensure that you put a * sign between the R and the bracket. See page 79 for more information on the reason for this.
Change to the NUM view and enter the known values, remembering that 1 liter=1000cm3. Position the highlight over R, enter a positive value as to find the solution shown right of your estimate, and press 8.57cm. The equation is a quadratic in R which means two solutions are possible. If you enter an initial estimate of -10 you will obtain the negative solution, which is physically invalid in this case.
Example 2 If f ( x ) = x 3 2x 2 5x + 2 find all values of x for which f ( x ) = 1.
Although you may have a clear picture in your mind and can provide Solve with the estimates it needs, Ill assume that, like me, you would find it helpful to see a graph first.
It is also possible to solve this in the Function aplet, which offers more powerful tools. The PLOT view in the Solve aplet, although powerful, can be deceptive if you dont understand it and I sometimes find it easier to work in the Function aplet. In this case we will continue to work in Solve. Graphing in Solve In the SYMB view, enter the equation Y=X^3-2X2-5X+2 into E1. In the NUM view, enter the known value of Y=1, ensure that the highlight is on X, making it the active variable, and then press PLOT. If your view does not look like this then you may not have had the highlight on the X, or your axes may not be set the same as mine in PLOT SETUP.

(Y = b X )

( Y = aX + bX + c )
- a*X^3+b*X^2+cX+d ( Y = aX + bX + cX + d ) - L/(1+a*exp(-b*X)) (Y =

L ) 1+ a e bX

This fits the data to a logistic curve where L is the saturation value. See tip below. Exponent - b*m^X (Y = b m )
This model is essentially the same as the
Exponential version but without the use of e. This caters for students who have been exposed to exponential equations but not to the extent of e. Trigonometric - a*SIN(b*X+c)+d (Y

= a sin(bx + c) + d )

This model fits a possible trigonometric curve to the data. Because the sine curve is periodic the answer will not be unique. User Defined - discussed on the following page. Calculator Tip 1. If you want the value of L calculated automatically for the Logistic model then store a value of zero into L in HOME. If the value is known, you can store a positive real value into memory L prior to the curve fit and this will be used. 2. If you calculate a line of best fit and want to remove the resulting equation from the SYMB display and return to the m*X+b display then just position the highlight on the relevant Fit: line and press the DEL key. When you do this, the will be removed and will have to be reset.
The User Defined model When you set the model to user defined it means that you are expected to supply the complete equation, including the values of any coefficients. The calculator will not calculate the values of any variables you include. For example, if you were to supply an equation of A/(XB) as your model then the calculator would use the values of A and B currently in memory. By repeatedly adjusting the values of A and B in HOME you could find the best version of the curve for the data. This may seem to be a useless model but it can be quite useful if you want to experiment with a model that is not one of those supplied with the calculator.
Connected data One of the settings on the second page of the PLOT SETUP screen can be useful for some types of data. For example, one of the common tasks in many mathematical courses is the analysis of time series data. Unlike most bivariate data, time series values are usually plotted as a line graph - i.e. as connected points. This facilitated by Connect. For example: The sales of an ice-cream shop are shown as quarterly sales figures for the

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.
28 THE TRIG EXPLORER TEACHING APLET
Rather than being a multi-purpose aplet like most of the others covered so far, this is a teaching aplet specialized to the single use of exploring the graphs of trigonometric functions. As such it does not have the normal SYMB, NUM and PLOT views, but only a single multi-purpose view. The SYMB and PLOT keys do have meanings but not the normal ones. Objectives Using the Trig Explorer aplet, the student will investigate the behavior of the graph of y = a sin(bx + c) + d as the values of a, b, c and d change. This can be done both by manipulating the equation and seeing the change in the graph, or by manipulating the graph and seeing the change in the equation. , they will see the main screen of the When the student presses aplet, shown right. Like the Quadratic Explorer, this aplet has only one screen, rather than the usual PLOT, SYMB and NUM views. If the aplet has been used before then it may be necessary to press the screen key to go back to the opening view shown. SIN vs. COS (or ) key can be used to toggle between the The (or y = sin ( x ) curve and the y = cos ( x ) curve. The ) key
can be used to toggle between radian measure and degree measure. The markings on the horizontal axis adjust accordingly (see right and below right). SYMB vs. GRPH mode The Trig Explorer aplet can be used in two modes:

INVERSE(<matrix>) This function produces the inverse matrix of an n x n square matrix, where possible. A fully worked example of the use of an inverse matrix to solve a 3 by 3 system of equations is given in the chapter on Using Matrices on page 211 and in Appendix A on page 302. An error message is given (see right) when the matrix is singular (det. zero).
Note: Some people write the inverse matrix as a fraction (one over the
determinant) multiplied by a matrix, so as to avoid decimals and fractions within the inverse matrix. The calculator does not do this. If you want the matrix with the determinant factored out, then evaluate DET(matrix) first, record the fraction and then evaluate DET(matrix) * INVERSE(matrix) to obtain (usually) a non-fractional matrix.

A= A = 2

Remember that the inverse matrix is not just the matrix, but the fraction times the matrix. See also: RREF, DET
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.
If you want to separate these matrices for later use then you should store them into a list variable. For example, if M1 was [[1,2,3],[4,5,6],[7,8,9]] then 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.
LSQ(<matrix1>,<matrix2>) The least squares function displays the minimum norm least squares matrix (or vector).
LU(<matrix>) This LU Decomposition function is similar to the LQ function on the previous page. It factors a square matrix into three matrices, returning them in the form of a list variable. {[[lower triangular]],[[upper triangular]],[[permutation]]} The upper triangular has ones on its diagonal. The matrices can be separated in the same method outlined for the LQ function.
MAKEMAT(<expression>,<rows>,<columns>) The MAKEMAT function is used, mainly by programmers to manufacture a matrix with dimensions rows columns, using the supplied expression to calculate each element. Eg.
MAKEMAT(0,3,3) returns a 33 zero matrix,
Note: If the expression contains the variables I and J, then the calculation for each element substitutes the current row number for I and the current column number for J during the calculation.

4 MAKEMAT(I+J,3,3) returns the matrix 5 6
QR(<matrix>) The QR function is similar to the LQ function on the previous page. It factors an m x n matrix into three matrices, returning them in the form of a list variable. {[[mm orthogonal]],[[mn uppertrapezoidal]],[[nn permutation]]}
RANK(<matrix>) This function returns the rank of a rectangular matrix.
ROWNORM(<matrix>) Finds the row norm of a matrix: the maximum, over all rows contained in the matrix, of the absolute values of the sum of the elements in each row. 3

Eg. For the matrix M 1 =

6 , the row with the largest absolute sum of 15 is row 2.
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.
x 2 y + 3 z = 14 Eg. The system of equations 2x + y z = 3 4 x 2 y + 2 z = 14 is written as the augmented matrix
which is then stored as a 3x4 real matrix M1.
We now use the function RREF to change this to reduced row echelon form and store it as M2.
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 cant 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.
x + y + z = 5 2x y = y + 2 z = 13
If we solve this in the same way as before, the matrix which results is:
The final line of [0 1] indicates no solution. See the chapter Working with Matrices for more examples. See also: INVERSE, DET
SCHUR(<matrix>) This function returns the Schur Decomposition for the square matrix supplied. The result is two matrices stored in a list. If the supplied matrix is real, then the result is: {[[orthogonal]],[[upper-quasi triangular]]}. If matrix is complex, then the result is: {[[unitary]],[[upper-triangular]]}.
SPECNORM(<matrix>) This function returns the Spectral norm of a matrix.
SPECRAD(<matrix>) This function returns the Spectral radius of a matrix.
SVD(<matrix>) This function performs a Singular Value Decomposition on an m n matrix. The result is two matrices and a vector: {[[m m square orthogonal]],[[n n square orthogonal]],[real]}.
SVL(<matrix>) This function returns a vector containing the singular values of the supplied matrix.

The final button allows you to delete a Note. Pressing it will result in a pop up dialog box asking you if you are really sure you want to do this.
38 PROGRAMMING THE HP 39GS & HP 40GS

The design process

An overview Although you can choose to simply create programs, it should be remembered that the whole point of working on the hp 39gs or hp 40gs is to use aplets. Working with an aplet means that you inherit its abilities such as auto setting of axes in the PLOT screen and so on. A program shares none of these and must re-create them when needed. This chapter will concentrate on the process of creating aplets which, in addition to their native abilities, possess enhanced powers provided by attached helper programs. Part of this process will involve the creation of these helper programs, and some readers may choose to concentrate solely on that aspect. Whilst this is obviously easier in the short term, the results are far less powerful than the creation of aplets. The key to the entire process of creating completely new aplets is the VIEWS menu and its controlling command function SETVIEWS. This function allows you to override the normal behavior of an aplet and superimpose new properties by linking in a set of programs written by you. This is the single most important point in the process and should be kept in mind. It is mildly deceptive to call these aplets new, as they always derive from one of the standard ones, but the modification of the VIEWS menu means that their final appearance and behavior can be very different to the aplet they derive from. Essentially the process involves the following stages
Choose the parent aplet, based on what abilities you want the child aplet to have; Analyze the behavior you require the aplet to have and design the VIEWS menu; Write the helper programs and attach them to the aplet using the SETVIEWS function; Add supporting documentation. This last point is often overlooked but in many ways it is as important as the programming itself. Your user must be able to use the aplet or else why did you write it?
Choosing the parent aplet The first stage in the creation process is to decide which of the standard aplets you wish to make the parent of your new child aplet. For some aplets this may not matter, but for others this can be a very important choice. All the abilities of the parent are inherited by the child so the parent choice is crucial if your aplet requires particular abilities. The most commonly used parent aplets are the Function and Statistics aplets, whereas the Quadratic and Trig Explorers would probably not make good parent aplets, since they are specialized teaching aplets without the flexibility of the others.

This is the most complex of the programs. See right for an explanation.
.MSG.SV, severing the aplets link to its current VIEWS menu which was inherited from its parent the Function
Having created all of the programs that make up the aplet Message, we can now run the program
aplet, and substituting this new menu. Before you do this, check that you are still in the correct aplet. Press the SYMB key and check that the title at the top still says MESSAGE SYMBOLIC VIEW. If it doesnt show the aplet again to ensure that it is the active one and so the one whose VIEWS menu will be this, then changed. This step is critical you do not want to change the VIEWS menu for the wrong aplet!
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:

For this to activity work you need to sabotage their efforts in advance via a scale which does not have hole. A good scale is -1 to 6 on both axes and you can rationalize the choice by telling them that it focuses well on the point were interested in. They may still sabotage this by choosing their own axes when zooming.
When discussing the concept of a domain, the NUM view can be very useful in developing this (see right). ing the In the SYMB view, enter the functions shown right, un first two non-composite functions. In the NUM view shown, I have used the NUM SETUP view to set the scale to start at -1 and increase in steps of 0.25. Obviously discussion will now center on why f ( x) = x 2 is not the
same as f ( x) = x , and why f1 ( f 2 ( x ) ) is not the same as f 2 ( f1 ( x ) ) for x<0.
Composite functions can easily be defined, as can be seen in the examples to the right.
In the first screen shot, F1(X)=X2-X and F2(X)=F1(X+3) have been entered into the SYMB view.
The second, substituted view is obtained by moving the highlight to F2(X) and pressing the button.
If desirable, you can further simplify using POLYFORM. With the. Move the highlight to the start of highlight on F2(X), press the expression and use the MATH button to enter POLYFORM(. Now move to the end and add ,X) to the expression and press. Pressing again now will give the result shown right.

Gradient at a Point

This is best introduced using an aplet called Chords downloaded from The HP HOME View web site (at http://www.hphomeview.com), but you can also use the Function aplet. If you use the aplet you will find that there is a worksheet supplied with it. To do it in the Function aplet, enter the function being studied into F1(X). To examine the gradient at x=3, store 3 into A in the HOME view as shown right, then return to the SYMB view and enter the expression shown right into F2(X).
Change to the NUM SETUP view and change the NumType to Build Your Own.
You can now enter successively smaller values for X in the NUM view, since X is taking the role of h in the expression

f ' ( a ) = lim

f (a + h) f (a) h
To investigate the gradient at a different point, change back to the HOME view, enter a new value into A and then return to the NUM view. The disadvantage of the previous method is that it is not very visual. As mentioned before, an alternative is to use the Chords aplet.
VIEWS menu to allow students to
In this aplet, a menu is provided via the
choose from a list of predefined functions or enter their own.
Once the function has been graphed, the Show slopes option will display an animated series of chords of diminishing length, with the gradient displayed at the top of the screen. As the chord shortens the student can see how this affects the approximation to the gradient at the point chosen.

Gradient Function

Once the concept of gradient at a point has been established the next step is to develop the idea of a gradient function. This can be Slope function which done via the Function aplet by using the gives the gradient of the graph at the position of the cursor (see page 58). If the teacher has the student enter a function in the SYMB view they can then have the student explore the value of the slope at various values using the the cursor precisely.