HP 39GS HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p
HP 39GS - Graphing Calculator Manual
UPC - 808736931328
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- HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 1
hp 39gs and hp 40gs graphing calculators Mastering the hp 39gs & hp 40gs A guide for teachers, students and other users of the hp 39gs & hp 40gs Edition 1.0 HP part number F2224-90010 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 2
, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE. HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE OF THIS MANUAL OR THE - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 3
the keyboard 19 Angle and Numeric settings 28 Memory Management 30 Fractions on the hp 39gs and hp 40gs 33 The HOME History ...37 Storing and Retrieving Memories 39 Referring to other aplets from the HOME view 40 A brief introduction to the MATH Menu 41 Resetting the calculator 42 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 4
Statistics Aplet - Bivariate Data 123 The Expert: Manipulating columns & eqns 133 The Inference Aplet ...141 The Expert: Chi2 tests & Frequency tables 147 The Linear Solver Aplet 190 The 'Loop' group of functions 193 The 'Matrix' group of functions 195 The 'Polynomial' group of - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 5
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 The - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 6
Rectilinear Motion...321 Limits...321 Piecewise Defined Functions 322 Sequences and Series 322 Transformations of Graphs 323 Appendix C: The CAS on the hp 40gs 324 Introduction ...324 Using the CAS ...327 Examples using the CAS 341 The CAS menus ...358 On-line help ...361 Configuring - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 7
where a CAS has long been an expected ability for calculators used by high school students. The hp 39gs has infra-red communication, similar to that of a TV remote control, which allows easy transmission of programs and aplets between calculators. The hp 40gs does not and uses a cable instead. 7 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 8
case with the hp 39gs & hp 40gs: the internal chips are different and there is no way to 'convert' one into the other using an aplet or program. For more information on the CAS, see page 324. This manual will cover, for the most part, the features which are shared by both calculators with the CAS - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 9
As can be seen on the previous pages, the keyboards for the hp 39gs and hp 40gs are exactly the same except for the different color schemes. These keys are the ones which control the operation of the calculator - most others are simply used to do calculations once the important keys have set up the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 10
- used to graph the function. (The PLOT SETUP view sets the axes.) The NUM key showing a tabular view of the function. (The NUM SETUP view sets table parameters.) The APLET key is used to choose which aplet is active. There are 12 aplets provided with the calculator and more can be downloaded from - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 11
5 KEYS & NOTATION CONVENTIONS There are a number of types of keys/buttons that are used on the hp 39gs and hp 40gs. The basic keys are those that you see on any calculator including scientific ones, such as the numeric operators and the trig keys. Most of these keys have two or more functions, - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 12
the ENTER key. Your screen should look like the one on the right. You have now stored the value 12 into memory D. Each alpha key can be used as a memory. Note that memories X, T and θ are regularly overwritten by the normal operation of the calculator and should be used with caution. 12 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 13
You can also use these memories in calculations. Type in the following, not forgetting the ALPHA key before the D.... (3+D)/5 ENTER The calculator will use the value of 12 stored earlier in D to evaluate the expression (see image). In case you haven't worked it out for yourself, the / symbol comes - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 14
of inferential statistics via hypothesis testing and confidence intervals. The Linear Solver aplet (see page 150 ) This aplet is used to solve simultaneous linear equations in two or three unknowns. The Parametric aplet (see page 92) Handles x(t), y(t) style graphs. Can also be used to help - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 15
& 123) Handles descriptive statistics. Data entry is easy, as is editing. It analyzes univariate and bivariate data, drawing scatter graphs, histograms and box & whisker graphs and finding lines of best fit, linear and non-linear. The Triangle Solve aplet (see page 152 ) This aplet solves for sides - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 16
about the programming language, there is no reason why you should worry about it. The standard aplets will cover all of your normal requirements in mathematics. However one of the great strengths of the hp 39gs and hp 40gs is their ability to "download" additional aplets from other calculators and - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 17
and software were provided with your hp 39gs and hp 40gs which you can use to connect your PC to your calculator via the USB port and then download aplets from the computer to the calculator or to save your work to the computer. If you have an earlier model such as the hp 38g, hp 39g or hp 40g then - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 18
in the following order: • Exploring the Keyboard • Angle and numeric settings • Memory management • Fractions on the hp 39gs & hp 40gs • The HOME History • Storing and retrieving memories • Referring to other aplets from the HOME view • An introduction to the MATH menu • Resetting the calculator 18 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 19
yourself with the mathematical functions available on the keyboard. If we examine them row by row, you will see that they tend to fall into two categories - those which are specific to the use of aplets, and those which are commonly used in mathematical calculations. The screen keys The first row of - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 20
written by other programmers. Once these are downloaded into your calculator they can also be accessed via the APLET key. For more detail on this type of aplet, see the brief summary later in this section, and the chapter entitled "Programming the hp 39gs & hp 40gs" on page 255. The SYMB, PLOT - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 21
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 22
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 23
Calculator Tip If you press and hold down the ALPHA key you can 'lock' alpha mode, although this doesn't work for lower case. Many people use 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 24
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 25
Fixed 4, Scientific 4 and Engineering 4. Calculator Tip If you have Labels turned on when you in (or out) on a graph or choose a Trig scale then 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 26
that the hp 39gs and hp 40gs do not treat a negative as being the same as a subtract. If you want to calculate the value of (say) −2 − (−9) then you must use the times too. A common error by new users is to enter a value into the PLOT SETUP view using subtract instead of negative. This will usually - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 27
keyboard. This serves as a backspace key when typing in formulas or calculations, erasing the last character typed. If you have used the left/right arrow keys to move around within a line useful in the PLOT SETUP view. The remaining keys of LIST, MATRIX, MEMORY, NOTEPAD and PROGRAM have special chapters - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 28
use of the hp 39gs and hp 40gs that you understand how the angle and numeric settings work. For those few who may be upgrading from the original hp different. On the hp 39gs and hp 40gs, when you set the angle measure or the numeric format in the MODES view, it applies both to the aplet and to the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 29
the hp 39gs and hp 40g, if we now change to the HOME view, retrieve the root and perform the calculation shown right, we expect that the answer should be zero, as indeed it is. However, this is only the case because the angle measures of HOME and the Function aplet agree. The problem was that - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 30
an aplet or reset the calculator then the default setting will return. Memory Management One of the major complaints about the original hp 38g was its memory - mainly the lack of it at only 23Kb, but also the inability to easily control or manage it. This problem has been addressed on the hp 39gs - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 31
. Downloaded aplets & memory If you use teaching aplets that you download from the internet via the Connectivity Kit, or which are supplied to you by your teacher via the infra-red link on an hp 39gs or the cable on an hp 40gs, then you need to bear in mind that most of them have 'helper' programs - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 32
hp 39g was a much slower calculator and the games may simply run too fast to be playable. • Some games were written using programming commands specifically aimed at the hp 39g chip. When these commands execute on an hp 39gs or hp 40gs they may cause the calculator to lock up and/or lose user memory - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 33
to a fraction, others, such as recurring ones, are not so easy. Most calculators opt for the easy option of switching to a decimal answer in any mixture of fractions and decimals. When making the hp 39gs and hp 40gs HP took a very different approach. Once you select Fraction mode, all numbers become - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 34
second point to remember involves the method the hp 39gs and hp 40gs use when converting decimals to fractions, which is this is determined by the '4' in Fraction 4. Very roughly explained, the calculator will use the first fraction it finds in its process of approximation which matches the decimal - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 35
the approach taken by the hp 39gs and hp 40gs it is capable of producing results which are closer to what was probably intended by the user in entering 0.66666. You may have noticed that all the results so far have been improper fractions. For example the first calculation shown right gives the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 36
the hp 39gs and hp 40gs is the setting of Mixed Fraction in the MODES view. The results of this new setting can be seen in the image to the right. Using the setting of Mixed Fraction the result is 4+1/7 ( 4 1 ) whereas 7 the answer of 29/7 is obtained using the old Fraction setting. Calculator - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 37
the whole 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 39gs & hp 40gs have. You can calculations and results from any number of different lines in building your new expression. 37 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 38
an expression the way you would write it on the page rather than in the somewhat difficult to read style that is forced on the calculator when it must show the whole expression on one line. This works anywhere the label appears, not just in HOME. Some examples... 38 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 39
B, and then finally the result... As another example, suppose we were evaluating 3x − x2 + 7 for the value x = −3 . We can store -3 into the memory X and then use that symbol in the calculation as shown right. The advantage of this is that if we now wanted to evaluate that expression for other - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 40
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 181). Note: This type of work is actually far more easily done in the Function aplet, where QUOTE is - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 41
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 a list of topics. Scroll through the topics until you find the one you want, then use the right arrow key to move into the list of functions for that topic. For example: The - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 42
crash! The hp 39gs and hp 40gs can sometimes do this due to the very complex and flexible operating system they use. 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. Calculator Tip If you are a user of external - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 43
used by engineers to test the calculator's components. There is nothing wrong with experimenting with it but it is of no use to the average user press repeatedly.) Use ON and to lighten the screen. • Change the batteries for new ones. Try this more than once because sometimes batteries are dead - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 44
remaining power from the internal capacitors. Leave the calculator overnight and re-insert fresh batteries. • If this happened when running a game or aplet that you've downloaded from the internet then consider that this may be the source of the problem. Backup anything that you want to keep to - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 45
settings may change if you change aplets in the APLET view. • Numbers are stored in memory using the key labeled . The stored values can then be used by simply putting the letter in the expression in place of the number. • You can easily reboot the calculator if it locks up, generally without - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 46
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 The first step for any aplet is to choose it in the APLET LIBRARY. Press the APLET key and you will - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 47
where you are (if you didn't already). Calculator Tip Pressing ENTER rather than would have had the aplet you are in. Let's use that key to produce a graph of the quadratic we dealt with in the earlier section on the HOME view. Using the up/down arrows, move the cursor (if necessary) to the line - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 48
. The PLOT view Now press the PLOT key. The graph you'll see will not be a terribly useful one (see right) because the axes will not be function whose shape is not known in advance is to let the calculator suggest a suitable scale using the Auto Scale option in the VIEWS menu covered on the next - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 49
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 the axis tick marks are so close together that it looks like a solid line. To tidy this up you must change to the PLOT SETUP view. If - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 50
Enter the value -4. Calculator Tip Don't use the subtract key to enter a negative. You MUST use the negative key labeled (-). Similarly, don't use a (-) when you mean dot. This is quicker but may make some graphs appear less smooth, particularly graphs with steep gradients. There are two pages to - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 51
. Connect The second option Connect controls whether the separate dots that make up a graph are connected with lines or left as dots. This is very seldom of use. 'Y') and a scale are put on the axes. The only time this causes problems is if the scale is an odd one, causing the labels to have too - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 52
graph, of course, and has nothing to do with your choice of scale. Once the scale changes, the size of the jumps from dot to dot are often not a useful while the left/right arrows move along the currently selected function. Calculator Tip Pressing SHIFT right arrow or SHIFT left arrow will jump the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 53
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 screen but rather to is switched off then will not work correctly, nor will various other useful tools. However, it does have the advantage that the cursor can be - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 54
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 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 55
' scale, this will preserve it, while perhaps showing a more interesting section of graph. In/Out These two options zoom in or out by adjusting the scales by the first corner. If you use the arrow keys to move the cursor to one corner of a rectangle containing the part of the graph you want to zoom - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 56
the axes or let you switch off the labels option. Alternatively you could use the MODES view to set two decimal places. Rather than doing any of check mark next to an option called Recenter. If this is ed then the graph will be redrawn after zooming in or out with the current position of the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 57
you can see on the right, this key gives you access to a number of useful tools. If you leave the highlight on Root (as shown) and press ENTER ( means moving it past the turning point. Move to about this position. Calculator Tip If you are working with a function which has asymptotes then make - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 58
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. See "The Expert" on page 75 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 59
the hp 39gs or hp 40gs 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. What has actually been calculated is the definite integral - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 60
area under one. Again, note that the result will be a signed area (definite integral) not a true area. See page 75 for a simple method of finding true 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 users should be - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 61
given by a simple definite integral then we must take into store the values of the roots as A, B, C... These values can then be used in the calculation to retain full accuracy. Extremum The final item in the menu is the Extremum tool. This is used to find relative maxima and minima for the graphs - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 62
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 you can PLOT and then zoom in or out. • If the graph is part of a test or an examination then the wording of the question will often give a - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 63
right. This would be ideal for answering questions on the domain stated. Another possible strategy for graphing which works quite well and, perhaps importantly, always gives 'nice' scales is to use . Enter your graphs into the SYMB view. Remember that Auto Scale only works on the first ticked - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 64
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 65
will expand the brackets and gather terms. Calculator Tip These functions can all be graphed but the speed of graphing is slowed if you don't press first. This is because the composite function is internally re-evaluated for each point graphed. The hp 39gs and hp 40gs are fast enough that the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 66
the Function aplet as shown in store a specific value into the memory X beforehand. In the example shown right, the answer of 3 is the value of the derivative 2x −1 at the value of x = 2. But what of algebraic differentiation? It is possible but not very convenient to do this in the HOME view using - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 67
is to define your function as F1(X) and its derivative as F2(X) (see below)... press Calculator Tip Doing your differentiation in the Function aplet is much easier and offers the additional advantage of being able to graph the two functions. Circular functions There are two issues that influence the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 68
screen shots right are an example of two images of the same graph x2 + y2 = 9 using two slightly different scales. You can see that the second example that when the calculator draws the graph it does so by 'joining the dots'. For the default scale of -6.5 to 6.5 this is not a problem since the edges - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 69
2.953846 and 3.046154. This means that the calculator can't draw anything past 2.953846 because the next missing piece is a problem to you then the solution is to use scales which allow the functions If you intend to the graph of a trig function and you are using radian measure then you should - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 70
ways to access these values: o The first and simplest is via the value stored in memory X. If you move from the PLOT view to the HOME view without moving been found then they will return zero. This trick is particularly useful when calculating areas under or between curves. See page 75. The NUM - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 71
for X. Typing in the values of (for example): 3 ENTER (-) 2 ENTER 5 ENTER ... will give... In this situation the function values are being calculated as you input the X values. This can be quite useful if you are wanting to evaluate the behavior of a function at selected points. ZOOM If you now - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 72
. As with differentiation, the results for algebraic integration are better in the Function aplet. The ∫ symbol is obtained via the keyboard. The syntax of the integration function is: ∫ (a,b, function, name) where: a and b are the limits of integration and function is defined in terms of name - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 73
: • 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 caused by calculator assuming that X itself may be a function of some other variable and integrating accordingly as a 'partial integration'. While - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 74
⎝3 ⎠ = S13 − S1 3 The potential problem lies with the second line, where the substitution of zero results in the integration, so perhaps this extra constant will help you to remember the '+c'! Calculator Tip There are strict limits to what the hp 39gs can integrate. For example, ∫ on the hp 39gs - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 75
, Area, and Extremum are stored for the other tools. You can access these names by typing them in using the ALPHA key, or by using the VARS key. Press VARS and you will see a list of the HOME variables. If you press SK2, labeled (not the APLET button on the keyboard), then the display changes - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 76
graphs. memory variable A. We then do the same thing for the second intersection, storing the result into B. We can now calculate the area in the HOME view, using f1 − f2 for the first and f2 − f1 for the second. Use to duplicate the first integral and edit it to adjust the functions and limits - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 77
Piecewise defined functions It is possible to graph piecewise defined functions using the Function aplet, although it involves literally splitting the function into pieces. For example: ⎧x +3 f (x) = ⎪ ⎨ x2 − 2 ⎪⎩3 − x ; x < −2 ; − 2 ≤ x ≤ 1 ; x ≥ 1 To graph this we need to enter it - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 78
the screen is exactly 0.1 apart. There are other scales, basically multiples of these numbers, that also give nice values if you want to along the graph. For example, halving each of -6.5 and 6.5 will place the dots 0.05 apart. To zoom out instead of in simply double the values, producing dots that - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 79
or subtracting a constant from each end of the axes will produce a graph where the y axis is not centred. Use of brackets in functions One problem commonly encountered by new users is misinterpretation of brackets. The hp calculator will correctly interpret F1(X) = X2(X+1) as X2*(X+1) but will not - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 80
limits In evaluating limits to infinity using substitution, problems can be encountered if values are used which are too large. For example: ex lim x →∞ 2e x + 6 It is possible to gain an idea of the value of this limit by entering the function F1(X)=e^X/(2*e^X+6) into the Function aplet - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 81
common tasks given to students in introductory calculus classes is 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 82
quite important that they have some understanding of these ideas if they use an hp 39gs to numerically evaluate limits. Because of the CAS on the hp 40gs this situation is less likely to be a problem for that model. The solution to all problems of this type is to simply be aware of their existence - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 83
the limit for x=3 is the value 6. To investigate the gradient at a different point simply 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. An alternative is to use an aplet downloaded from - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 84
storing the results to a matrix. For example, suppose we want to find the roots of f (x) = x3 − 3x2 + 3 . We will use the POLYROOT function and store 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 85
, 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 page 89) and this is probably the one most used. The other options are also very useful at times. Shown on the right is the graph of F1( X ) = X 2 −1 . - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 86
the result on the right allowing easy comparison of 'before' and 'after' views. The left hand graph is always the active one, with results of actions shown on the right. We can now use the left graph again to zoom in on another section of interest, or alternatively, press the key under the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 87
one to another. In this case, with only one, it centers the table. Let us switch now to a graph of the two functions F1( X ) = X 2 −1 and F 2( X ) = X 3 + 2X 2 − 5X − 4 . This is shown on the right, using an XRng of -8 to 8. Choosing Plot-Table gives the result shown left. As you can see, the scale - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 88
problem. Overlay Plot Another possibility from the VIEWS menu is Overlay Plot. This option can be used to add another graph aplet. This could be used to show, for example, the enclosing curves for conic sections. You can also use this technique to overlay functions on top of statistical graphs - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 89
Auto Scale Auto Scale is an good way to ensure that you get a reasonable picture of the graph if you are not sure in advance of the scale. After using Auto Scale you can then use the PLOT SETUP view to adjust the results. It is important to understand two points about how Auto - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 90
in. The example right uses zoom factors of 2x2 with Recenter: ed. 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 stored - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 91
of the interval, the type of calculation and the number of rectangles to be used. The rectangles are drawn on the screen. A worksheet introduces the idea of integration to find areas. Linear Programming This aplet visually solves linear programming problems, finding the vertices of the feasible - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 92
11 THE PARAMETRIC APLET This aplet is used to graph functions where x and y are both functions of a third independent variable T. It is generally very similar to the Function aplet and so we will look mainly at the ways that it differs. An example of a graph from this aplet is: x(t) = 5cos (t ) - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 93
of: As you can see above, changing the T range from 0 ≤ t ≤ 2π to 0 ≤ t ≤ 5 gives a graph that appears only partially drawn. Of course, what constitutes "fully drawn" depends on the function used. TStep controls smoothness The value of the parameter TStep controls the jump between successive values - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 94
Calculator Tip Decreasing TStep beyond a certain point will slow down the graphing process without smoothing the graph any further. Using 0.05 is generally enough. Since trig functions are often used Y1 both derive from T. As with the Function aplet, it is possible to change the starting point - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 95
: An easy way to vary A and B is to store values to memories A and B in the HOME view and enter the equations exactly as shown. New graphs can then be created by changing back to HOME and storing different values to A and B. The example shown uses A=4, B=2.5 and has axes set with TRng of 0 to - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 96
Vectors The Parametric aplet can be used to visually display vector motion in one and two dimensions. Example 1 A particle P is moving in a straight line. Its velocity v (in ms plots, the speed is slow enough to show its progress. The graph makes it plain that it doubles back twice in the first two - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 97
the active variable must be an X in the Function aplet instead of the T of the Parametric aplet but you can still refer to the Parametric functions X1 and Y1 even within the Function aplet. Graphing this function in the PLOT view of the Function aplet will allow you to find its minimum value. In - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 98
13 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. Some examples of - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 99
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 the other two entries calculated automatically from the definition as shown in the sequence of two screens shown right. - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 100
in the SYMB view but filled in by the calculator automatically in the NUM view. Convenient screen keys provided as soon as the cursor moves onto the U(N) line (see right). Pressing either will enter the than having to type all of this we can use the buttons provided, pressing: This is a very - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 101
been pressed. Due to the type of problems one is usually trying to solve with sequences, the NUM view rather than the PLOT view is often more useful in this aplet, but let's have a look at the change to the PLOT view and you should see a graph similar to the one shown below right. The second type of - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 102
it. If we define our GP using memory variables then it becomes far more using a similar method. Note the reference to U1 in the definition of U2. Once U2 is defined in this way you can change both U1 & U2. by simply storing new values into A and R from the HOME view. Solving sequence problems - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 103
type problems are rule, the two initial values of 5600 and 6300 will be automatically calculated when you enter the rule into U1(N). All we need do now in the Solve aplet. For example if we use the Sequence aplet to define U1(N)=2^(N-1) as before, then we can change to the Solve aplet and enter - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 104
compound interest of 5.5% p.a. calculated each quarter, starting Jan. 1 1995, with a quarterly repayment rate of $175. This problem can be modeled by a problem is more easily handled in the Finance aplet (see page 155). The Finance aplet has abilities that are specifically aimed at financial problems - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 105
16 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 106
values are showing on your screen will depend on what happens to be in the memories V, U, A and D at the time. Pressing SHIFT CLEAR will zero all values and press the button. You should find that you obtain the answer to our problem of 2 ⋅ 47 m/s2. The INFO report When the process has finished - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 107
powerful, can be deceptive if you don't 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 108
answer (eventually) of 2.4495. The delay is caused by the repeated integrations as the calculator searches for better solutions. It is important to remember that the calculator does not use algebra in Solve - it uses an algorithm which is essentially a more sophisticated version of "guess, check - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 109
upper-tailed probability. The syntax is UTPN( mean, variance, value). In the Solve aplet, set E1 to P=UTPN(M,V,X). Enter the NUM view press to obtain 201.35cm There are many more ways in which the Solve aplet can be used in conjunction with the functions available in the MATH menu. The MATH menu - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 110
aplet line and the reason for this lies in how Solve interprets your equation. When you select B by highlighting it, the calculator substitutes the supplied values in the NUM view into all other variables except B and graphs linear. In this case there are clearly two points where the graphs intersect - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 111
Now press and you will see the calculator find the nearest solution to your guess. Finish by that A* B2 + C = ⋅5* B becomes 0 ⋅ 4 + C = 0 ⋅ 5 . In this case both sides are linear and this is shown in the PLOT view. Notice that the axis label is now C. This would have only one solution and there - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 112
The problem uses a square root or a logarithm and you began from a value involving a negative. • Constant? - no solution was found. The value of the function was the same at every point tested and wasn't the value you wanted. Calculator aplet, since it allows you to see clearly whether or not there - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 113
way!" when confronted in a test with something like: ( x −1) −1 = 2 − (3 − x) 3 94 If you're sure there is only one answer to a problem, as there is in view we can use these as initial guesses. This will give solutions of -2.56 and 1.56. In this case the problem shown will graph easily on the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 114
the major strengths of the hp 39gs & hp40gs is the tools they provide for dealing with statistical data. The Statistics aplet and its companion the Inference aplet provide very powerful yet easy to use tools with which to analyze statistical data. The calculator treats univariate and bivariate data - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 115
right are used with bivariate aplet before beginning this process. If the SYMB view defines columns which don't actually have any data in them then errors will result. As you can see in the screens above right, the calculator gives not only the standard statistics that any scientific calculator - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 116
' column of data by using the SYMB view. Simply enter an expression giving the new column as a function of the old one. Although the 'virtual' column will not be displayed in the NUM view (and does not consume memory), it can now be graphed and analyzed statistically. You may be wondering why - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 117
of , and . They all behave in the normal manner as was discussed in detail in the Function aplet chapter. The tool can be quite useful by displaying information on which columns make up each graph if you lose track. Looking again at the screen shot of the first page of PLOT SETUP (near - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 118
displayed on the graph, regardless of what axes are used. It is normally classes. For example, suppose we want to analyze the set of grouped data in the table on the left. As with most calculators, the hp 39gs & hp 40gs provide only limited methods to deal with data of this form. Summary statistics - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 119
example, the data set below produces the graph to the right of it using Auto Scale. You may have noticed that the download an aplet from the author's website called "Grouped Data". This will calculate the values of the medians and quartiles using linear interpolation and will also allow calculations - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 120
using the HOME view, and the command would give exactly the same results. The advantage of this is that it takes much less memory if both columns need not be stored the rolling of dice. This can be simulated in the Statistics aplet using the MATH menu function MAKELIST. (For more detail see page - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 121
We therefore need only store the resulting list into a Statistics aplet column to analyze and graph it. This is of various sorts. This can also be done using the MATH menu function MAKELIST. See the previous the keyboard. This will be a relatively slow calculation because it involves evaluating 1000 random - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 122
As an illustration, the result of this particular simulation is shown graphically on the right. Its mean turned out to be 2.067 (3 decimal places.). Yours will be different of course - after all, that's the point of using random numbers! Calculator Tip The RANDOM function is not truly 'random' any - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 123
strengths of the hp 39gs & hp 40gs is the tools they provide for dealing with statistical data. Unlike the others, the Statistics aplet begins in use the set of data left to show the use of the bivariate features of Statistics. We will obtain all the usual statistics on it, and draw a scatter graph - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 124
which to choose, or you can use the ALPHA key to type in the column name. Entering data as ordered pairs Calculator Tip You can enter the xi that are to be used in plotting the points, allowing you to choose different markings for different data sets if you are graphing multiple data sets. Set - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 125
. The screen above shows the default setup when you the aplet in the APLET view. It specifies that columns C1 and C2 are paired and that a linear fit (m*X + b) is to be used when calculating a line of best fit. If you intend to use other columns then you must register them in the SYMB view - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 126
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 127
1, 2, 3, 4 we can't use them that way because it would result in 1992 Qtr 1 being graphed on top of 1993 Qtr 1. The graph on the right was produced by entering values of 1992, 1992.25, 1992.5, 1992.75 etc. This is not the end of the story though. When you activate Connect the calculator will always - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 128
If you have trouble seeing the small dots that the calculator 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 then you will see the menu shown below - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 129
the key and you will obtain the results listed in the screens shown below. Calculator Tip Make sure that your data set is defined and ed in the SYMB and ed. Showing the line of best fit If you now press the PLOT key you will see the graph shown right. If there is no line of best fit on - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 130
from the Stat-Two section of the MATH menu. The functions PREDX and PREDY use whatever was the last line of best fit calculated. It is up to you to ensure that the one you want used was the one last graphed. If I want to predict a y value for x = 3, then I simply type PREDY(3) into the HOME - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 131
2 of 2.806. If there is more than one data set (and fit lines) graphed then the up arrow will move progressively from one to another and finally back is to use another measure of goodness of fit. The second is to 'linearize' the data (discussed on the next page). The calculator provides an - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 132
to zero for the exponential model (rounding error may result in something non-zero). The alternative to using RelErr is to graph column C1 against ln(C2) which also straightens the data. 'Linearizing' will cause problems if some of the data points are outside the domain of the function you - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 133
statistics can be investigated in this way by storing, for example, -2*C2+3 into C2. You can even combine columns in this way, such as storing C1+C2 into C3. Using values from in calculations It is often useful 5, 55} One possible test for outliers is to calculate the mean and standard - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 134
using the ALPHA key, or you can use the VARS key instead. If you press VARS and then the screen key labeled then, assuming the Statistics aplet using SHIFT +. Calculator Tip The values of the mean and standard deviation retrieved are those of the last set calculated calculation of used use - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 135
y value using the last line of best fit that was calculated. This means that you must use the SYMB view use the PLOT screen and the key to ensure that your set of data was the last one graphed aplet, highlight it and press . The equation will be transferred and can then be analyzed using - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 136
transfer it to the Function aplet by entering F1(X)=PREDY(X) into the Function aplet, highlighting it and then pressing hp 39gs & hp40gs are unusual in this odd interpretation. Most calculators' equivalent of the PREDX function behave in the same manner. The formula for the slope b in the line - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 137
, then you should change to the SYMB view and enter a new data set S2 which uses C2 and C1 in reversed order, avoiding the need to re enter the data. Now use PREDY for the second fit line rather than PREDX. As you can see in the screen below, the result of PREDX - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 138
choices (see page 126). Change to the PLOT view using the VIEWS Auto Scale option and press the key. Don't worry that the scale is not good because we don't care about the graph. It only needs to be drawn in order to calculate the fit equation. Finally, change back to the SYMB - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 139
? i. Find N0 and k. Start up the Statistics aplet, set it to and enter the data given. Change to calculated even if the data doesn't show. Now change to the PLOT view and press draws. . Wait while the line Change to the SYMB view, move the highlight to the equation of the regression line - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 140
fit are not directly accessible but can be retrieved using the PREDY function (see page 135). This is shown in the screen shown right. Store the results into memories A and K. This saves having to re-type them from the screen. Now switch to the Solve aplet and enter the equation to be solved - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 141
concepts of hypothesis testing. In the Inference aplet the SYMB view is used to choose the test to be applied. 22 The NUM SETUP view is used to enter the information required to apply the test. These results can either be entered by hand or imported from the Statistics aplet using the button - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 142
line shows the equivalent critical sample mean range. The test value for the Student-t and the sample mean are also listed in the middle of the screen. The regions for rejection of the null hypotheses are shown at the very top of the screen by the ' R' and 'R '. ( ) We assume, by statistical - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 143
SYMB view and the method of Conf Interval. The type of interval is converted to the equivalent type of T-INT: 1 µ. In the NUM SETUP view use the import facility as before to import the values from our sample data. The default confidence level is 99% so you will need to change - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 144
Hypothesis test: T-Test µ1 -µ2 A farmer compared the 15- Statistics aplet. 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 145
and a standard deviation of 12.2%. When he applies this test to his class of 23 students their scores are shown below. The teacher believes C1 of the Statistics aplet. Changing to the Inference aplet, we choose a Hypothesis test using Ztest: 1 µ, since we know the population standard deviation. 145 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 146
standardized population (µ > µ0 ) . Change to the NUM SETUP view, you can use the import facility to import the summary statistics from the Statistics aplet. 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 147
to look at a simple inferential problem which can be solved using only the Statistics and Solve aplets. Using the Chi2 test on a frequency table "Four coins columns of the Statistics aplet (right). We now need to calculate the expected values based on our null hypothesis. The expected values - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 148
value of 9.488 we conclude that we must reject the null hypothesis and judge that the observed values do not follow this binomial change to the NUM SETUP view of the Inference aplet and try to use the import facility you will find that you can program on the next page will do this for you. 148 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 149
hundreds or even thousands of values then the program will take a long time to complete. In the case of thousands of values you may even exceed the calculator's memory in the MAKELIST command. It might be easier to use the Statistics aplet to calculate the required mean and standard deviation in the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 150
THE LINEAR SOLVER APLET This is a very easy aplet to use. It is designed to solve simultaneous linear equations in 2 or 3 As you may be able to see, this is a pair of parallel lines and so has no solution. To see this on the calculator we must first change to the 2x2 view, meaning 2 equations in 2 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 151
system of equations corresponds to a 'spindle' of planes in 3-space as shown in the diagram above right. This situation allows infinite solutions anywhere along the line of intersection of the three planes. As you can see right, the calculator has correctly indicated the situation. 151 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 152
it is actually only necessary to supply 2 values despite what is stated. 115° 7cm 15cm Example 1 Solve the triangle shown right. Use the Aplet view to select and the aplet. The second is to ensure that we are working in degree mode. Change to the MODES view and choose Degrees. Now press - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 153
will result in the remaining 3 values The calculated values are highlighted for convenience. Example 2 12 doesn't really matter what angle mode the aplet is set to. If you worked the previous will remove the remaining values from the previous problem. Use the arrow keys to move to the A and - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 154
the values shown right. Notice that as soon as sufficient information has been entered the message "Solution Found" appears. Press and the calculator will fill in the missing values. The additional button label of will appear to announce that an alternate solution is available. 6 cm Pressing - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 155
money". TVM problems involve the use of the idea that the value of money changes with time - a dollar today is worth more than the same dollar some years from now. For example, that a dollar invested today can generate more money than the same dollar invested later. The calculator manual contains - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 156
60. The view on the right shows the problem on the calculator. The button has been pressed to give a future value FV of $1816.70. Calculator Tip As can be seen above, the designers of this aplet chose to display money to 2 decimal places and using comma separators. This choice is independent of the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 157
for 20 years. What income can be withdrawn? The PV for this problem is negative because, from the point of view of the engineer, the of monthly payments. On this basis the monthly annuity can be $4289.71 Loan calculations You wish to purchase a car by taking out a loan. The current interest rate - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 158
Amortization The second page of this aplet allows amortization calculations in order to determine the amounts applied towards the principal and interest in a payment or series of payments. Suppose we borrow $20,000 at an - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 159
does not have the normal SYMB, NUM and PLOT views, but only a single multi-purpose view. Objectives Using the Quadratic Explorer aplet, the student will investigate the behavior of the graph of y = a ( x + h)2 + v as the values of a, h and v change. This can be done both by manipulating the equation - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 160
labeled will change the emphasis from the graph to the equation in the right hand half of the screen. Pressing PLOT on the calculator, or the key labeled will change the emphasis from the equation back to the graph. SYMB mode The alternative to graphical mode is symbolic mode. In directly and - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 161
you are successful, or when you give up, press either or return to the main screen. for a new graph, or to 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 162
Objectives Using the Trig Explorer aplet, the student will investigate the behavior of the graph of aplet and the aplet has no SETUP views. The ranges for the x and y axes are preset and cannot be changed. In both modes the original shape of the sine or cosine graph is left visible as a dotted line - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 163
point of control for the graph. It is only visible in PLOT mode. When in PLOT mode the graph is changed using the arrow keys. The effects is that the equation controls the graph. The user has control of the coefficients and any changes are reflected in the graph. All four coefficients are shown at - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 164
by ) -3 to 3 in steps of 0.1 If you go to Hewlett Packard'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. The - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 165
the hp 39gs this screen key is blank and typing the command manually will result in an 'unknown user function' error. Since they are not relevant for both calculators, the CAS commands are covered in the section on the CAS for the hp 40gs. The following pages will cover: • how to use and - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 166
*X^4+40*X^3+71*...etc There are two ways of seeing the complete result. You can move the highlight up to that line and it. You could then move back and forth through the line using the arrow keys to see it in full. A better method is to press the screen key labeled . This gives - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 167
statement will aid a normal user of the calculator, since these syntax statements are usually more suited to a programmer type than to a student. However they may be enough to trigger your memory. One piece of terminology that will be used in this section of the manual is 'argument'. The arguments - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 168
: • Chemistry • Physics • Quantum Physics The contents are simply the numerical values of various physical constants that are useful in calculations and formulae. Chemistry • Avogadro's number • Boltzmann's constant • Molar volume • Universal gas constant • Standard temperature • Standard pressure - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 169
and percentage functions. - bivariate statistical functions. - functions for manipulating equations and symbols. - used in programming more than normal work. - contains the trig functions not found on the keyboard. E.g. sec, cosec. - integration and differentiation - functions to manipulate - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 170
as the mathematical function 'greatest integer' which is studied in many mathematical courses. If you want to graph the greatest integer function then you will need to use the PLOT SETUP view to turn off CONNECT first, since the graph is supposed to be a discontinuous step function. The result with - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 171
It's a lot easier to use the Solve aplet. This is a tool for programmers so that they can access the Solve abilities within programs. You need to tell it involves more than one variable then whatever values are currently in memory are used for the other variables. See also: QUAD, POLYROOT FRAC(< - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 172
to decimal time. The calculator can convert a value such as 45D23′17′′ if you put it into the form 45.2317 and then use the HMS function. E.g. 5D3′7′′ ) would be COS(HMS (5.0307)) This function, together with HMS, can also be used to deal with time. E.g. What time will it be 1 hr 34 min. and 15 sec - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 173
you feed it when transformed into scientific notation. It would be used with the XPON function, which returns the power part of the is not needed in your normal calculations, since you could just look at the numbers, but a programmer will be writing a program which deals with numbers not known - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 174
It is considered to be an mathematical operator in the same way that a plus, minus, times or divide sign is. Because of this it does not need = 0 -14 MOD 5 = 1 % function(,) To find x% of y, use the function %(X, Y). Eg. 10 % of $400 = $40 is shown right. See also: %, %TOTAL, %CHANGE 174 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 175
discount as a percentage of the usual price? Use: %CHANGE(6.50,5.95) See also: %, %TOTAL %TOTAL(,) To find out what percentage X is of Y, use the function %TOTAL(Y,X). Note the reversed order. Eg. What percentage is a score of 53 out of 81 on a test? Use: %TOTAL(81,53) What percentage - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 176
.pts>) This function rounds off a supplied number to the specified number of decimal places (d.p.). Eg. Round 66.65 to 1 d.p. Use: ROUND(66.65,1) = 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 177
to get 5 ⋅ 087 ×10−4 . MANT(0.0005087) = 5.087 XPON(0.0005087) = -4 This function could be of use to you if you are just learning scientific notation, but is of more use to people writing programs. A normal user would just look at the number and see the answer, but a programmer would not know in - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 178
in the Statistics aplet. This is discussed in more detail in the section covering the Statistics aplet, but graphed in the PLOT view and that the FIT screen key has been used to plot the line indep.) value of 3 ⋅ 5 . Calculator Tip The line of best fit used in the function PREDY is whichever one was - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 179
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. It's easier to obtain the = sign directly from the keyboard. The reason that it is found in the MATH menu is that the original calculator, the hp 38g, had less - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 180
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. Eg. Suppose we use the expression AX 2 − B + 4 If X is the variable and A and B are - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 181
not work but F1(QUOTE(X)) will. No-one ever promised consistency! See Example 1 on page 262 in the chapter "Programming on the hp 39gs & hp 40gs" for an example of use in writing code. The | function written as: | (var1=value,var2=value,...) This is called the 'where' function. The - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 182
more about programming is to download aplets from the internet and dismantle them to see how the code produces the results. The 'Trigonometric' & 'Hyperbolic' groups of functions These two groups of functions cover the Trigonometry functions, plus others, which are less commonly used and which - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 183
available on the face of the calculator but give more accurate answers. They would primarily be of use to those people, such as architects look at the screen opposite will show you. As you can see, the normal keyboard function e^ gives an answer to e0.0000003 of 1.0000003. This gives the impression - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 184
taken from the current memory values. Symbolic integration can be done in two ways. Firstly by replacing one of the limits of integration with a symbolic variable in memory. For example, if X currently has the value of 3 then the result is as shown right. When done in the Function aplet, or using a - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 185
expression> supplied is approximated with respect to by terms of a polynomial up to power. The screen shot on the right shows the calculator deriving the Taylor polynomial for sin(x) up to the 7th power. The SIN(X) function can be approximated by taking terms from the polynomial: x3 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 186
hp 39gs & hp 40gs can be entered in either of two ways. Firstly, in the same way as they are commonly written in mathematical workings: a + bi. Secondly, as an ordered pair: (a,b). For example, 3 + 2i could be entered into the calculator exactly as it is written, with the 'i' obtained using SHIFT - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 187
returns ⎜⎜⎝ a, a2 + b2 b a2 + b2 . y This is very useful, not just in complex numbers, but also in vector problems. 6 See also: SIGN (in the Real group),IM,RE,ARG,CONJ 4 ARG() or ARG() This function, also found on the keyboard, returns the size of the angle defined by - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 188
number supplied. See also: CONJ,ARG,RE Note: As mentioned earlier, a very useful function ( ) can be found on the keyboard as the SHIFT function for . If you enter a complex number in (r, ) form as shown right, then the calculator will display it in the form r cos(θ ) + r sin(θ ) from, and as an - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 189
is capable of dealing, and are there for use by programmers as a check to ensure that calculations within a program have not overflowed the capacity of the calculator. 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 190
L1 would add another element of value 5 onto the end of list L1, storing the resulting longer list back into L1. ∆LIST() This function produces a of the length specified using a rule of your choice. It is very useful, not only in programming but in statistical simulations and modeling. The - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 191
and also stores the result test is false). Thus: MAKELIST(RANDOM - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 192
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 193
>,) This function evaluates an expression in terms of a variable, starting with a supplied initial value, for a specified number of iterations. Each iteration uses the answer to the previous evaluation as the value for the variable in the next evaluation. Eg. ITERATE(X2 - 1, X, 2, 5) gives an - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 194
>,) and it must be stored into a sequence such as U1,U2..U9,U0 for it to have any meaning. Σ (,,,) This function, also available on the keyboard, offers a way of calculating the results of summation notation problems. The syntax of the function is ordered - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 195
more detail than the manual of what the function is used for would occupy many pages to no real useful gain. Consequently although some Matrices" on page 209. COLNORM() Finds the column norm of a matrix: the maximum, over all columns contained in the matrix, of the absolute values of the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 196
containing the eigenvalues. IDENTMAT() This function creates an n x n square matrix which is an identity matrix. For example, IDENTMAT(4) would produce a 4x4 identity matrix for use or storage. This is a function that is probably of more use to programmers than to the average user. 196 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 197
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 198
. MAKEMAT(,,) 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 3×3 zero matrix, Note: If the expression contains the variables - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 199
. x − 2 y + 3z = 14 ⎫ Eg. The system of equations 2x + y − z = −3 ⎪ ⎬ 4x − 2 y + 2z = 14⎭⎪ is written as the augmented matrix ⎡1 −2 3 14⎤ ⎢⎢2 1 −1 −3 4 −2 2 14⎦⎥ 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 200
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 201
is two matrices and a vector: {[[m × m square orthogonal]],[[n × n square orthogonal]],[real]}. SVL() This function returns a vector containing the singular values of the supplied matrix. TRACE() This function finds the trace of a square matrix. The trace is equal to the sum of the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 202
functions This group of functions is provided to manipulate polynomials. We will use the function shown right to illustrate some of the tools in the Polynomial For normal users it is probably more efficient to enter the function into the SYMB view of the Function aplet and then either use the NUM - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 203
of A has been done, but the terms involving B are not fully evaluated. The solution to this 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 204
roots of the polynomial whose coefficients are specified. The coefficients must be input as a vector in square brackets. Eg. Using our earlier function of f (x) = (x − 2)(x + 3)(x −1) = x3 − 7x + 6 we can for details on finding roots of real and complex polynomials using the CAS on the hp 40gs. 204 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 205
avoid this and give accurate answers. 3. If you are solving for the value of N, such as in a Binomial probability calculation then you must use N!/((N-R)!*R!) rather than COMB. The ! function The factorial function finds the number of possible permutations of an entire collection of n objects - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 206
between 5 and 15 inclusive. Use the expression INT(RANDOM*11)+5 The uses a 'seed' number to produce them. Unfortunately, when taken straight out of the box, two calculators will produce exactly the same sequence of "random" numbers! This can be a problem. For example, a class set of calculators - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 207
a standard deviation of 14%. What two scores will cut off the top and bottom 10% of students? 0·1 0·1 65% i.e. Find x0 such that P(x > x0 ) = 0 ⋅1 Using the Solve aplet (right) we can reverse the normal direction of the UTPN function. Enter the expression to be solved for into the SYMB view as - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 208
it. Final answer... 47.06% and 82.94% are the cut-offs. Calculator Tip The normal order for the arguments in the UTPN function is UTPN(mean, variance value supplied. See page 147 for an example of this function's use. UTPF(,,) This is the Upper-Tailed Snedecor's - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 209
cables supplied, one being a mini-USB for use with a PC and the other being a mini-serial for inter-calculator communication. On the hp 39gs only the mini-USB cable is supplied for use with the PC since inter-calculator communication is done using the calculator's infra-red link. We'll begin by - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 210
on the keyboard the highlight will move back to the first element in the second row. 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 211
4 13 ⎥⎦ where the inverse matrix is... ⎡x⎤ ⎡ 2 ⎤ which gives a final answer of ⎢ ⎢ y ⎥⎥ = ⎢⎢−3⎥⎥ ⎢⎣ z 1 ⎥⎦ ⎡2 3 −1⎤−1 ⎢⎢1 −3 1 ⎥ ⎥ ⎢⎣3 −1 4 ⎦⎥ The method for doing this on the calculator is as follows... Step 1. Enter the MATRIX Catalogue. Use SHIFT CLEAR to erase all matrices if - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 212
of which are acceptable to the hp 39gs or hp 40gs), and store the result into M3. (a) M1-1*M2 (b) M2/M1 (c) INVERSE(M1)*M2 The best of these is probably the first. The inverse x-1 function is on the keyboard and this makes it more convenient to use. The only problem with the second method is that - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 213
matrix Eg. 2 ⎡2 1 4⎤ Find the inverse matrix A−1 for the matrix A = ⎢ ⎢ 1 1 3 ⎥ ⎥ ⎢⎣−2 4 −1⎥⎦ The first step is to store the matrix A into M1. If you now simply store format in the MODES view. This will give a matrix of fractional values which can be seen more clearly using . 213 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 214
dot product 5 Eg. 4 Find the angle between the vectors 4 a = (3, 4) and b = (4,1) . 3 Using the formula that a • b = a . b .cosθ 2 1 -5 -4 -3 -2 -1 -1 -2 -3 The calculations are shown in the two screen shots on the right. Remember to change into degree mode first. The list of matrix - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 215
WITH LISTS A list in the hp 39gs or hp 40gs is the equivalent of a mathematical set. As with a set, it is written as numbers separated by commas and enclosed with curly brackets. Eg. {2,5,-2,10,3.75} The list variables Using the HOME view these lists can be stored in special list variables. There - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 216
the memory it uses. using the CONCAT function discussed on the next page. Lists can be sent from one calculator to another using the infra-red link on the hp 39gs or using the supplied mini-serial cable with the hp 40gs. The procedure is the same as that for sending aplets from one calculator - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 217
key. This is not a standard aplet. Unless you download this aplet yourself you will not find it on your calculator! When this aplet is run, the first thing visible is the VIEWS menu. This menu is set up by the programmer to control the aplet (see "Programming the hp 39gs & hp 40gs" on page 255). 217 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 218
On the hp 39gs & hp 40gs, as programmers become used to having plenty of memory to use, aplets have become larger and more powerful. An example is shown above right of a sketch from one of the aplets available from HP's web site called 'Periodic'. If you installed this aplet on your calculator then - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 219
on how to do this. Transferring notes using IR Notes can be shared between students in the same way as can be done for aplets, lists, matrices and programs. It is worth pointing out that this will not help you in a test situation since, on the hp 39gs the strength of the infra-red link is - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 220
Notes to or from another calculator (or a computer). A Note is deleted using the DEL key, while the up by the indication of how much memory is used. When you press ENTER after typing in keyboard. Use the keys discussed above to type in the screen shown on the right. The arrow keys can be used - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 221
calculator. • If you own an hp 39gs then use keyboard above the divide button. The reason for this odd transposition is based in the history of the calculator. The original hp 38g only had the function INVERSE(...) and the -1 operator was added for convenience sake in the hp 39g problem users stored - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 222
for the standard aplets start blank but you may find that an aplet that you download from the Internet computer drawing package. Adding text to a sketch When you first enter the Sketch page on your calculator you will see the same size as the text will be. Using the arrow keys you can now move the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 223
to a computer drawing or painting program. DOT+ The small cursor (cross) in the middle of the screen can be moved around using the arrow keys. If you LINE Moving the cursor to one end of a proposed line, you can now press the key and move the cursor to the other end of the line. When the line - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 224
. Finally, press to leave the drawing tools view. Cut and paste images Using the key you can capture part of the screen and store it into any of ten graphics memories G1,G2..G9,G0 (called 'GROBs', which is short for graphics objects). When you press the message you see on the right will - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 225
you're intending to do this to produce a set of 'cheat notes' for your next test or exam, you would do better to spend the time studying! Calculator Tip The screen capture facility demonstrated here can be used to capture any screen as a GROB, not just a PLOT screen. Pressing ON+PLOT at any - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 226
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 227
to connect to data-loggers and other possible peripherals. Mini-serial port Infra-red port Mini-USB port If you are using the cable on an hp 40gs then alignment of the calculators is obviously not a problem. For infra-red, of course, it is. Look at the keyboard side of the calculator, near the HP - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 228
a copy of the highlighted aplet to any other calculator. These and keys also appear in other views. If using the infra-red on the hp 39gs then you should begin by putting the two calculators top to top with the calculators no more than 8 -10 cm apart and line up the arrows. The best separation - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 229
calculator. On an hp 39gs this will be "HP39 (IrDA)" and on an hp 40gs it will be "HP39/40 (Ser)". • Press on both calculators and the transmission process will begin. Calculator Tip If you begin to receive "Time Out" messages when transmitting aplets or notes then this means that the connection - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 230
Statistics aplet and then watch while they all use different axes and get totally different graphs. In either of those two cases, the solution is to make a copy of the aplet concerned. You can make as many copies of any of the standard aplets as you wish. The only limit is the calculator's memory - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 231
Sets". If desired, you can the original Statistics aplet afterwards, ready for next use. This saved aplet can now be downloaded to all the students' calculators using the infra-red link in the case of an hp 39gs or using the cable in the case of the hp 40gs. This ensures that each student has - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 232
be obtained from the keyboard on the zero button using ALPHA. Change into the MODES view and set the angle mode to Degrees (unless you want to use another mode). By changing into the NUM view you can now use this to solve problems in right triangles. Some users choose to use the letter D for degrees - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 233
distribution function and use it to find P ( x ≤ 1.2) " Use it by substituting whatever function is in use for the one currently entered. As this formula involves the integration function, each use of the solve process will require the calculator to perform multiple integrations. Because of this - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 234
technique of first of identifying whether the problem is discrete or continuous. The Transformer aplet This aplet is based on the Parametric aplet and allows students to investigate geometric transformations using 2x2 matrices. In the APLET view, the Parametric aplet and it under the new name - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 235
great power of this aplet is its use as a teaching and investigative tool. Simply continue to matrix M1, repeating the HOME calculation, and re-PLOTing their matrices on the board as they discovered them. For a less able class you might hand out a list of matrices they should investigate. Perhaps - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 236
-red. Plus, if the class is not to regard this as 'magic' then it helps if they understand how the aplet works. This is best accomplished by having them set it up themselves. You might even consider allowing them to first play with drawing shapes of their own invention using a single matrix and only - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 237
notes and aplets onto a PC using the supplied cable and software. By doing this you free up space on your calculator and, more importantly, you ensure that the material is backed up onto a PC and is safe from accidental loss. In addition to this, one of the nice features of the hp 39gs and hp 40gs - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 238
will transfer information, notes, aplets and programs to and from the calculator it does not let you edit them in any way. To do that you need to use a program called the ADK. This can also be found at the author's website together with instructions. For the hp 39g+, hp 39gs and hp 40gs As stated - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 239
for an hp 40gs is shown right. An hp 39gs is identical except that the space between the two ports contains the electronics for use in infra red communications. Sending from calculator to PC Any aplet, note, program, matrix or list can be copied from a calculator to a PC using the supplied - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 240
Try closing the program and re-starting it with the calculator already turned on. Sometimes it can take up to 10 seconds for the connection to stabilize. iii) The batteries may not be sufficiently fresh. Communication with the PC uses a lot of power and problems may occur with low battery power even - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 241
is to use the software to transmit the aplet, list, matrix or note to the PC. The instructions which follow apply to the transmission of an aplet via the APLET LIBRARY view but the process is the same for any other view which has and keys such as the List view, Matrix view, Program view and - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 242
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 243
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 244
press ENTER. To download multiple objects use the button to select them. Calculator Tip The displayed list will contain only objects that are appropriate for the current view of the calculator. The folder may contain many aplets or programs but if you press in the Matrix view then you will - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 245
which are 'standard'. Finding aplets The Hewlett-Packard site is one possible starting point and can be found at http://www.hp.com/calculators. From that point you can follow the links to collections of material for the hp 39gs and/or hp 40gs as well as to software and utilities. Other sites can - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 246
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 calculator's chip - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 247
folder! Having downloaded an aplet from the web to the computer, we now have the task of transferring it from the computer to the calculator via the HP Connectivity Software. To do this, of course, you need the mini-USB cable that came with your calculator (see page 239) plus some software. 247 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 248
the newly downloaded aplet from the PC to the calculator is exactly the same as it is for an aplet which you have saved to the PC yourself. The instructions for this can be found on page 244. It is important to realise that most sites contain both aplets and programs. Aplets are stored in the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 249
Using downloaded aplets Normally if you press the VIEWS key on your hp 39gs or hp 40gs then you will see a list of options which vary according to which aplet is currently active. The VIEWS menu for the Function aplet is shown right. Any aplet that has been created by a programmer, such as the Curve - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 250
If your calculator only contains one aplet with programs linked, then it is faster to use SHIFT CLEAR to delete all programs at once. The Program Catalog view has no key. If you store a large number of aplets then you may find that you start to have trouble telling what program belongs and what - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 251
Capturing screens using the Connectivity Kit One of the more useful abilities of the Connectivity Software is its ability to capture images of the calculator screen. These images can be pasted into a document or into a Paint program for further processing. This allows teachers to create worksheets - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 252
the calculator to the PC, the Connectivity Software will also allow you to edit it once it is on the PC. On previous models this was done using a separate piece of software called the ADK but with the release of new software with the hp 39gs and hp 40gs this ability was integrated into one program - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 253
. You can now type your text into the Note using the normal computer keyboard. The special characters that are normally available from the are on the calculator itself. When you've finished editing you can use the Connectivity Software to transfer the result back to the calculator. The process so - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 254
used to record the Notes on the PC are not terribly imaginative, as can be seen to the right. You must not change these names! They are recorded in the special files HP39DIR.CUR and HP39DIR.000 and the calculator manner to anything desired. Calculator Tip The Connectivity software will allow you to - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 255
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 256
the hp 39gs & hp 40gs this means buying a cable. For the hp 39gs & hp 40gs the mini-USB cable required is included in the package with the calculator. In this chapter we will begin by creating our first two aplets entirely on the calculator. We will then look at two more examples using the software - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 257
in your 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 calculator. When the 'helper' program terminates the calculator drops into whatever view you as the designer choose - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 258
called "Curve Areas" which finds the areas under curves using various approximations and is used to introduce the definite integral. Because it deals with functions and graphs its parent is the Function aplet. Some of the 'helper' programs for this aplet are shown below. As you can see, their names - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 259
a graph, with the program being 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 via infra-red link. Only programs named in the SETVIEWS command (or linked by the software) will be transmitted with the aplet - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 260
in the line will be transmitted with the aplet. This can be handy if you have a program which is a subroutine. In other words, one which is not directly called from the menu but which is called by other programs which are in the menu. If there is a particular piece of code which is used repeatedly - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 261
smoothly. You should always bear in mind that the user may make changes to any axes you set or store their own values into variables as part of some other calculation, not realising that you've used them as part of your aplet. The results can be very unfortunate if you don't bear this in - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 262
the SETVIEWS command to create a simple (and totally useless) aplet, which illustrates a few of the concepts useful in programming the hp 39gs or hp 40gs. We'll call it the 'Message' aplet and create it as a child of the Function aplet. Change into the APLET view, move the highlight to the Function - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 263
up. The command GROB in the program left, stands for "Graphic Object" and creates a GROB from the F1(X) expression stored in the The SETVIEWS command is discussed in detail on the previous pages. SYMB view, storing it in the graphic memory G1, using the font specified (0, 1, 2 or 3). The - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 264
it. If you get an error message at any time then you may have to and the program. 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 265
on the right and notice the connection between the various parts of the line of ERASE: , which is a command to erase the display screen. Try editing the program, inserting this line before the MSGBOX line up into 7 lines (1 - 7) on which you can display data. For example, suppose memory A contained - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 266
1: in order to it or it would not graph. You may wish to edit the .MSG.SV and.MSG.FN program to try this. The next lines display the expression using the four options available. The line: GROB G1;F1(QUOTE(X));0: converts the expression F1(X) into a Graphic Object (GROB). The number at the end - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 267
use of Xmin, Xmax, Ymin and Ymax in the LINE command. These are the minimum and maximum limits of the current PLOT view and using them instead of fixed values means that the line visible to the user and not immediately replaced by the next view. FREEZE resumes execution of the program as soon as any - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 268
not essential. The user may want to use a rotational matrix and can choose their own settings for this. This program changes the value of 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 calculator into thinking that the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 269
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. This program puts up a message instructing the user and - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 270
Please note The software used on the PC to edit and create Notes, programs and aplets was in the 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 271
the user click on a "Save" button. So... if there is a "Save" button or an option on the File menu of "Save" then use this now to save your code. If there's no such option then go on to the next step. Change back to the Folders/Transfers and download your program to the calculator for use - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 272
revisited Run the Connectivity Kit and use the File menu to create a new folder called "Transformer", and highlight that folder to hold your aplet. In my experience it is a very good idea to store each aplet in a separate folder but this is not strictly necessary. Change to the Aplet tab view to - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 273
the far left is enabled. Clicking on this changes the focus from the Aplets tag to the Program tag, allowing you to enter the code for the program. You should practice this process now by re-creating the Transformer aplet which was used as Example #2 on page 268. You will find the code listed on - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 274
calculator's APLET view. This aplet will be somewhat similar to the Quad and Trig Explorer aplets, except that it will explore linear equations. Its parent is the Function aplet. As with the previous example, begin by creating a directory to hold the aplet and then run The Connectivity Kit. Select - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 275
If you have done this correctly then your VIEWS menu have three entries shown right when it is transferred to the calculator. The text for the 'helper programs' associated with each menu entry is shown below: 275 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 276
the aplet works if you see it in action first so you may wish to download the aplet from The HP HOME View user presses the first thing they will see after this code executes is the VIEWS menu. The variable G is being used here as a flag. A 'flag' is a programming term for a variable that is used - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 277
linear function, a horizontal line, which is guaranteed to be off-screen for the entire domain no matter what axes are used vertically. Clever, eh? The next program view is stored in the aplet's sketch view and then retrieved and modified using the various graphics commands. The program is broken - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 278
the actual sketch page itself is called Page. Thus the two lines after ELSE are telling the program to store the PLOT view into the first page of the SKETCH view using the command PLOTÆ. This command stores the PLOT view into whatever graphics variable you specify. In this case into Page. The PLOT - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 279
part of the line extends off the screen there is no problem - the excess is clipped by the calculator. The next section of code below waits until the user presses a key (GETKEY) and stores the key's code into the variable K. A CASE statement is then used to check for the use of the arrow - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 280
Finally, add a line to display the current increment size at the top right of the screen using the DISPXY command. Be careful that your display does not go off the screen. The explanation so far should help you in understanding the programming process on the hp 39gs & hp 40gs. The aplet structure is - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 281
. Additionally, while a crash in HP Basic will simply cause the program to stop unexpectedly, a crash in sRPL may well cause the calculator to lock up or reset with complete loss of user memory. For those interested in learning HP Basic a series of tutorials can be found on the author's website - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 282
chip ran out world wide in about 2003 and so the hp 39g+ took a different route. Instead it uses an extremely fast ARM processor (slowed down slightly to save battery power) and simply emulates the Saturn 5. That is, it runs a special program on the ARM processor in machine code that 'pretends' to - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 283
more sophisticated graphical calculator aimed at university and professional use. Support for the hp 39gs & hp 40gs was added later. At the time of writing this information in early 2006, HPG-CC had reached Version 2.0 but subsequent to this version the support for the hp 39g+, hp 39gs & hp 40gs had - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 284
The process of performing an update is somewhat similar to that of downloading an aplet. It is accomplished using the Connectivity software (see right). Full instructions will be given in the package that you will download from HP but the process is outlined briefly below. One stage requires three - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 285
to save all your aplets, programs and notes to a PC before the update. A concern to educators may be whether an hp 39gs user can load the operating system of an hp 40gs and thereby gain access to a CAS. This is not possible because the hp 39gs has less flash ROM installed than the hp 40gs. The - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 286
the hp 39gs and hp 40gs are supplied with a simple and easy to use programming language called HP Basic. All programming commands can by typed in by hand but, as with the MATH commands, can also be obtained from a menu. Press SHIFT CMDS to display this. During the course of using the calculators in - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 287
internal IF clauses. IFFERR THEN [ELSE ] END This can be used to error trap programs where there is a possibility of something going wrong which would normally crash the program, such as evaluating a function at a point for which it is undefined. By trapping the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 288
afterwards. If a particular piece of code is used repeatedly then this can be used to reduce memory use by placing the code in a separate program and calling it from different locations. See the SETVIEWS command for information on how to link a program to an aplet when it does not appear on the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 289
This command erases the current display screen. FREEZE This command halts execution until the user presses any key. Execution resumes on the next line of the program. LINE ;;; This draws a line on the screen using (x1,y1) and (x2,y2) as the ends. The coordinates are relative to the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 290
of all pixels. This means that it can be used to erase previously drawn lines. If you would like to see this command in action, download the aplet called "Sine Define" from the author's website The HP HOME view (at http://www.hphomeview.com). This aplet contains extensive use of this command. 290 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 291
commands See the chapter "Programming the hp 39gs & hp 40gs" beginning on page 255 for examples illustrating some of the graphics commands that I have used regularly. Consult the manual for more. The Loop commands FOR = TO [STEP ] END - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 292
the HP Basic language. The Matrix commands EDITMAT This command pops up a window in which the user can edit or input a matrix with an bottom. When the user presses , execution resumes after the EDITMAT statement. key at the REDIM ; This command is very useful if - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 293
the battery operated HP infra-red thermal printer that is designed for use with any of the 39g family. This printer was originally designed for the first calculator in this family, the hp 38g, released in 1995. Very few of them sold because it was far easier to simply use the connectivity software - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 294
, varying by up to 5% from one calculator to the next and depending also on the temperature. If you want accuracy then use a piano! The volume is also not very loud because of concerns with interruptions to tests and examinations. Any frequency can be produced using the BEEP command but most people - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 295
existing line and 'edit' material already present. The DISPXY command should be used for this purpose but is a little more complex to use. the screen position specified using the font specified. An extensive example can be found in the chapter "Programming the hp 39g & hp 40gs" on page 274 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 296
the correct time and date set has no effect on the operation of the calculator! GETKEY This pauses the execution until the user presses a key and stores the code for the key into the variable for later use. See the manual for how the value of the key changes according to whether it is - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 297
WAIT This command pauses execution for the specified number of seconds. Execution resumes at the next statement after the WAIT command. 297 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 298
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 has the advantage that you can see the graph clearly. Note: Using the Root method does not depend on the graph being on the screen. The algorithm will - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 299
alternative method is to use the POLYROOT function and store the results to a matrix. This offers the advantage of being able to examine the result more easily by ing the matrix, and also of being able to access each root by referring to the matrix elements in a calculation (eg M1(1), M1(2) etc - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 300
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. Step 2. Use setting is also found in the menu. Now use the pop-up menu to find the Extremum ( - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 301
the menu again, retrieving this time from the VAR menu the variable called 'Root' and perhaps storing that into memory C. We will evaluate the integral in the HOME view where you can use the accurate values you stored in Step 4. It needs to be done in two parts and added (subtracted actually to - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 302
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 = ...... and store them into F1(X) and F2(X) in the SYMB view of the Function aplet. Switch to the PLOT view and use - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 303
calculation M1-1*M2. The result is the (x,y) coordinate of the solution displayed as a matrix. A similar method can be used to solve the second 3x3 system of equations. The matrix M1 and the result are shown right. Method 3 - Using the Linear Solver aplet This method uses an aplet called the Linear - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 304
the key to examine the result. Result: 16x4 + 96x3 + 216x2 + 216x + 81 (ii) Use POLYFORM((3A-2B)^5,B) to expand the polynomial as a function of B. Then use the polynomial function again, ing the result from the first expansion and expanding this time as a function of A. The key can then be - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 305
it take for the number of colonies to double? (i) Find N0 and k using the calculator. Step 1. Start up the Statistics aplet, set it to and enter the data given. Change to the SYMB SETUP view and specify an Exponential line of best fit for the data. Step 2. Press VIEWS and choose Auto Scale - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 306
is currently off screen. Alternatively, change to the HOME view and use the PREDY function. Result: 268 269 colonies. (iii) Find t so that N = 1 2 N0 . Step 1. Find the values of N0 and k and store N0 into memory A and k into memory K, so that it is un-necessary to re-type them. See - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 307
of A and B into M1 and M2 respectively. A(1− 2X ) = B 1 − 2 X = A−1 B −2 X = A−1 B − I ( ) X = −1 A−1B − I 2 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. In this case the result is - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 308
second POLYROOT calculation in the screen shot right. In this case the results are unlikely to be integers so we store them into M1. The result is shown below and right. The edit line shows the highlighted element to a greater degree of accuracy. Unfortunately there is no way on the hp 39gs to get - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 309
roots of z5 = 32 . On the hp 40gs you can obtain exact roots for polynomials using the CAS function SOLVEVX. The instructions following assume that the CAS is in its . A similar result can be found for the second equation. The calculator will ask you if you want to turn "Approximation mode" on. - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 310
are other methods based purely on calculations. Firstly enter the equations for the ships' paths into the Parametric aplet using the first equation pair for appear on the screen will show visibly that they do not collide. The graph is shown on the right just before closest approach. However we need - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 311
graph the particle's path. We go into the Parametric aplet and enter the rule into the first equation X1, Y1. After setting TRng to 0 to 6 and then using this is a circle and we can copy this diagram onto our test paper as the required graph. Note the gap at the bottom because the TRng stops at 6 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 312
40 40 40 120 Enter the observed and expected frequencies into columns C1 and C2 of the Statistics aplet. In the HOME view, perform the calculation shown right. This calculates the individual χ 2 values ready for summing as per the formula ∑ χ 2 = (O − E )2 , where O and E are the observed and - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 313
Changing into the Solve aplet we can enter a formula which will allow us to calculate values from the Chi2 distribution using the UTPC function. With a 3x2 contingency table the number of degrees of freedom value is 5.99 and so we would accept the null hypothesis and conclude no relationship. 313 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 314
graphical calculator. Some of them are listed below: Investigating the graphs of y=xn for n an integer This is a task often given to introductory calculus classes along the graph they will obtain 'nice' values. This aplet can now be sent to each student's calculator at the end of a lesson using the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 315
the idea of limits? However - there is a trick to this! If you use the default axes of -6.5 to 6.5 then there will be a hole (see right) because X=2 falls on a pixel point and so, because it is undefined, the calculator leaves it out. The missing value means that there is no connection to the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 316
(see right). In the SYMB view, enter the functions shown right, un ing the 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) = x2 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 317
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 318
can be fitted using the ( ) d xn Statistics aplet and this should be using an aplet downloaded from The HP HOME View web site (http://www.hphomeview.com) called "Tangent Lines". This aplet will add a moveable tangent line to an existing graph, as shown in the screen shot above, allowing the user - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 319
The Chain Rule If desirable, an aplet is available from The HP HOME View web site (at http://www. such a box, choosing for themselves what size square to cut out. They can then explore, using the Function aplet, what cut-out size will produce the maximum volume. As can be seen above & right - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 320
using an aplet from The HP HOME View web site (at http://www.hphomeview.com). This aplet, called "Curve Areas" will draw rectangles either over or under a curve or use trapezoids. A number of curves are supplied pre-set but the user 'description' of the function stored in F1(X). The screen shots - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 321
of { } domains and this is usually extended to graphing intersecting regions such as ( x, y) : y ≤ 0.5x +1∩ y ≥ x2 −1 . Although the hp 39gs & hp 40gs do not have the in-built ability to plot inequalities, the process is easily handled using an aplet from The HP HOME View web site (at http://www - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 322
on the keyboard above the button. Sequences and Series Through the Sequence aplet the hp 39gs & hp 40gs provide very flexible tools for the investigation of sequences. These can easily be adapted to investigate series as well. Information and worked examples of using the calculator for evaluation - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 323
manual for more information. Transformations of Graphs This topic can be handled in a number of ways. One of these is to use the Function aplet into the calculator. Both of these aplets allow the student to explore the effect of changing parameters on the shape of the graph, one using a quadratic - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 324
calculating power of the hp 40g (or hp 40gs). It can be found at Hewlett Packard's web site (http://www.hp.com/calculators) or on the Help page of The HP seconds to solve. If you do this then you can watch the calculator work. In the Solve aplet, enter the equation (0, A, X2, X) = 1000 as shown - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 325
calculators there is no way to obtain this exact answer because the calculator doesn't use algebra. However, the CAS or Computer Algebra System on the hp 40gs does use and HP 40gs calculators. The HP CAS system offers the user a vast array of functions and abilities as well as an easy user interface - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 326
program since it simply does not exist on the chip to be activated. It is also not possible to download the hp 40gs operating system into the flash ROM on the hp 39gs because the extra space required by the CAS means that it physically won't fit into the smaller memory ROM installed on the hp 39gs - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 327
Using the is the variable that is entered when you press the button on the keyboard. There are certain functions, such as SOVLEVX, which assume that you the other contents of the VARS screen, read the CAS manual that came with your calculator. It is not advisable to change entries in this view - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 328
(FRED) will remove the variable and release the memory it takes up. Alternatively, you can enter the VARS screen and use the (purge) command, which is one of the screen buttons in that view. Just highlight the variable and press . The functions STORE and UNASSIGN can both be found in the menu - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 329
To re-use the previous command press and highlight the FACTOR(X^2+20) line as shown right. Press to copy it to the screen, replacing the highlighted material currently on the screen. Alternatively, since this was the last operation applied you could simply press SHIFT MEMORY - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 330
move the highlight from one component of the expression to another and how to use special keys to manipulate the expression. In the HOME view press and then follow once. Press up arrow three times & finally press 2. (DO NOT use the X2 button for this.) 3, then press Notice that in each case - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 331
5 S P C ^ 81 The new tree is shown below with nodes R and S added above A. B * Although it is not strictly necessary for you to understand or use D this concept of a tree of operations you may find that it will ^ help you to follow why the highlight behaves as it does as it - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 332
, exit the CAS by pressing HOME. B * 2Q D Note: There can be a problem with the way that the X2 ^ button is handled. If you try going back through the F 2 G 3 and edit the power because the X2 operation is stored differently. This is purely a personal preference generally. x2 + 4x + - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 333
stores the character to a buffer and allows you to continue selecting more. You can then either press ON to exit or use Using the CHARS view is not the most convenient method and some commonly used characters are provided via special keyboard useful when working with limits or integrals. 333 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 334
commands - Undo, multi-select & swap Unlike most calculators the CAS editing screen has an undo function. If you have performed some operation that was incorrect then pressing SHIFT MEMORY will undo the operation. Unlike programs on the PC which have more memory to work with and so allow multiple - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 335
term and then extended the selection using SHIFT right: as shown ... then pressing SHIFT will result in: The main use for this is when you and are having trouble removing it, then you can highlight and edit an expression 'in-line' as if you were entering it in the calculator's normal HOME view - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 336
at node E, deleting first the node's contents then the operation (multiply) which connected it to the tree. Try it and see. This process is best seen with expression then the best method may be to use the 'Edit Expr.' command in the menu. The tree structure used by the editor means that although it - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 337
to the view on the right, with all previous calculations and results recorded. As with the normal History it is worth deleting the contents regularly by pressing if the memory is not to be gradually used up. Alternatively you can access the Memory Manager (see page 30) and clear the CAS History - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 338
the variable and this may cause problems later. In general the PUSH command is not really very useful. 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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 339
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 340
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 341
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 and then ENTER to evaluate it: v. To obtain a mixed fraction we use the function PROPFRAC, designed to transform improper fractions to mixed. The fraction - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 342
entire expression with SHIFT ENTER to simplify: and press iv. 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. 342 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 343
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 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 344
2 x iii) Find lim x→∞ 2 x + 5 Limits to infinity are also permitted using the lim function, with infinity entered using the shortcut SHIFT 0. scroll to lim and press ENTER ENTER 344 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 345
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. The sequence of keys for this is... Expansion - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 346
Now use the SOLVEVX function, typing: The SOLVEVX function assumes that the active variable is being used. brackets incorrectly accordingly. Alternatively you can use X+Y=-3 AND X=Y-1 instead of the expressions : (X=-2) AND (Y=-1) LINSOLVE can be used for any number of simultaneous variables. - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 347
The LINSOLVE function can also be used to solve problems with symbolic coefficients such as the one 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. - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 348
that it is a probability distribution function we know that 4 ∫1 f ( x ) dx = 1 . We can use this to get the first expression in terms of a and b. As can be seen above, the initial integration gives an equation involving a fraction. This can be simplified by multiplying both sides by - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 349
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 and to highlight the linear expression again as shown right. Now, while the entire expression is highlighted, as shown above, press - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 350
Example 8: 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 prime function f ( x) = 22x +1. Note that the sequence of keys is: ENTER ALPHA F ( SHIFT = 2 2 + 1 ENTER The - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 351
We can now test to see if this is a prime number by using the ISPRIME? function from the MATH menu. This is found in the Integer section of the CAS function list as shown right. It returns a value of 0 (false) indicating that it is not a prime number. Using the FACTOR function from the are - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 352
with an S, the letter on the key. Pressing it again jumps to the next function starting with S, which is SUBST. iii. Next we linearize it... ENTER ENTER ENTER Note: 1. As in the previous case, the is used to jump to the first function that starts with an L, the letter on . 2. The - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 353
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 v. We now separate the real and imaginary parts of M into separate functions, storing them as X1(t) and Y1(t). ALPHA M MATH 9 ENTER ENTER ENTER SHIFT - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 354
Purely for convenience we will display X1(t)=X1(-t) and evaluate each side. The = is not used to solve anything but just to display both at once for comparison so that it can be seen that Y1(t)= -Y1(-t) has been met. Therefore we can conclude that the graph is symmetrical about the x axis. 354 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 355
SHIFT ALPHA CLEAR ALPHA X 1 ( ALPHA T + SHIFT 1 ALPHA Y 1 ( ALPHA T SHIFT ENTER Now store to the aplet using the PLOT button on the keyboard, choosing X1,Y1 in the Parametric aplet. PLOT ENTER ENTER Note: The reason that we used capital T instead of lower case t here is because that is the - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 356
aplet doesn't seem to properly accept the functions. If you press PLOT now you will receive the "Undefined Name" error. The trick is to highlight each function in turn and press . Don't make any changes, just press ENTER or . This seems to make the calculator you may wish to use PLOT SETUP to - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 357
Example 10: First order linear differential equation In order to illustrate the use of the CAS help pages obtained by pressing VIEWS and cutting and pasting in a Paint program to obtain a wider result. The 'd1Y(X)' is used to represent the first derivative. Highlighting this and pressing ENTER will - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 358
335. The others each pop up a menu of functions that are the most commonly used ones in each category but there are others that you can access via the MATH their categories below: Algb. COLLECT DEF EXPAND FACTOR PARTFAC QUOTE STORE | SUBST TEXPAND UNASSIGN Diff. DERIV DERVX DIVPC FOURIER IBP - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 359
shown right because they are the ones most often used in the HOME view but there are other menus accessible as follows: Algebra COLLECT DEF EXPAND FACTOR PARTFRAC QUOTE STORE | SUBST TEXPAND UNASSIGN Complex i ABS ARG CONJ DESOLVE ISOLATE LDEC LINSOLVE SOLVE SOLVEVX Tests ASSUME UNASSUME > ≥ < ≤ - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 360
DIV2MOD CHINREM EXP2HYP CYCLOTOMIC GAMMA DIV2 HORNER IABCUV IBERNOULLI ICHINREM ILAP LAP LIMIT PA2B2 PLOT PLOTADD PSI Psi REORDER SERIES SEVAL SIGMA SIGMAVX STURMAB TSIMP the previous pages. The manual supplied with your calculator is generally quite clear on their use and abilities. 360 - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 361
the hp 40gs 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 , as you can see to the right, but generally contains an extremely useful summary. An example is always given and pressing will cause this example to - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 362
given here. One method is via the configuration line (CFG) at the top of each menu. The line shown right of CFG R= X S means that the calculator is set to exact-real mode, that X is the current variable Modular calculations are carried out in Z/13Z (p = 13) You are working in Rigorous mode (that is - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 363
right is that the lower one is harder to use and contains one option not available on the upper configuration view. The information supplied in the manual on the various configuration states is quoted below example, definite integrals, square roots, etc.), will be calculated numerically. When this - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 364
the main display. The comment lines will appear in the top lines of the display, but only while the operation is being calculated. [Default: unselected.] Comment: I've never found the comments to be particularly helpful. The methodology and algorithms that the CAS uses internally are not those that - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 365
choice here really depends entirely on the problem at the time. Simplify non-rational I suggest that this is generally more desirable! Calculator Tip Changing the configuration can have a profound you read carefully the relevant information in the manual and/or the information in Renée de Graeve - HP 39GS | HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 366
calculator HOME screen, you can use the MODES view to change this default but this does not affect the CAS. • Step by step mode might appear to be quite useful for students but is quite limited can use the integration symbol provided on the keyboard it has disadvantages outlined on page 74. Use the
hp 39gs and hp 40gs graphing calculators
Mastering the hp 39gs & hp 40gs
A guide for teachers, students and other
users of the hp 39gs & hp 40gs
Edition 1.0
HP part number F2224-90010