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hp 39g+ graphing calculator Mastering the hp 39g+ A guide for teachers, students and other users of the hp 39g+, hp 39g & hp 40g

10 The ‘Polynomial’ group of functions...277 POLYCOEF...

100 TTHHEE PPAARRAAMMEETTRRIICC AAPPLLEETT This aplet is used to graph functions where x and y are both functions of a third independent variable

101 The effect of TRng The X and Y ranges control the lengths of the axes. They determine how much of the function, when drawn, that you will be abl

102 Calculator Tip ! Decreasing TStep beyond a certain point will only slow down the graphing process but not smooth the graph further. ! Since trig

103 TTIIPPSS && TTRRIICCKKSS -- PPAARRAAMMEETTRRIICC EEQQUUAATTIIOONNSS FFuunn aanndd ggaammeess Apart from the normal mathematica

104 VVeeccttoorrss The Parametric aplet can be used to visually display vector motion in one and two dimensions. Example 1 A particle P is moving

105 Example 2 Two ships are traveling according to the vector motions given below, where time is in hours and distance in kilometers. Illustrate the

106 TTHHEE PPOOLLAARR AAPPLLEETT This aplet is used to graph functions of the type where the radius r is a function of the angle θ (theta). As w

107 TTHHEE SSEEQQUUEENNCCEE AAPPLLEETT This aplet is used to deal with sequences, and indirectly series, in both non-recursive form (where Tn is

108 As they do, marks appear on all three, but ing or un- ing any one does the same for all three. Convenient screen keys provided There are a numb

109 The NUM SETUP view offers more useful features. Change to that view now and change the NumStep value to 10. If you then swap back to the NUM vie

11 Appendix C: The hp 40g & its CAS ...310 Introduction...

110 TTIIPPSS && TTRRIICCKKSS -- SSEEQQUUEENNCCEESS && SSEERRIIEESS Defining a generalized GP and the sum to n terms. If we d

111 Population type problems are also easily dealt with in this way. For example, “A population of mice numbers 5600 and is growing at a rate of 1

112 Modeling loans I need to see the progress of a loan of $10,000 at a compound interest of 5.5% p.a., starting Jan. 1 1995, with a quarterly repaym

113 TTHHEE SSOOLLVVEE AAPPLLEETT This aplet will probably rival the Function aplet as your ‘most used’ tool. It solves equations, finds zeros of

114 Suppose you had the problem: “What acceleration is needed to increase the speed of a car from 16 67⋅ m/s (60kph or ~38mph) to 27 78⋅ m/s (100k

115 Multiple solutions and the initial guess Our first example was fairly simple because there was only one solution so it did not much matter where w

116 Graphing in Solve In the SYMB view, enter the equation Y=X^3-2X2-5X+2 into E1. In the NUM view, enter the known value of Y=1, ensure that the

117 Referring to functions from other aplets The Solve aplet can be used in conjunction with any of the functions available through the MATH menu, and

118 A detailed explanation of PLOT in Solve The PLOT view in the Solve aplet is a little more complex than most others, since the active variable (x,

119 Move the cursor near to the left hand intersection and then change back to the NUM view. When you do so, the approximate value you chose with the

12 IINNTTRROODDUUCCTTIIOONN This booklet is intended to help you to master your hp 39g+ calculator but is also aimed at users of the hp 39g and hp

120 The meaning of messages On pages 115, the values used were V=27 78⋅, U=16 67⋅ and D=100 and we were solving for A. Thus: 222vu ad=− becam

121 TTIIPPSS && TTRRIICCKKSS -- SSOOLLVVEE Easy problems Have you ever thought “There has to be an easier way!” when confronted in a t

122 TTHHEE SSTTAATTSS AAPPLLEETT -- UUNNIIVVAARRIIAATTEE DDAATTAA One of the major strengths of the hp 39g+ is the tools it provides for deali

123 Looking at the bottom of the screen you will see a series of tools provided for you. is not really worth bothering with. It is generally easier

124 Functions of columns Let's create a second column of data, and cheat by making all its values double the values in the first column. We can

125 You may be wondering why the SYMB view is organized around histograms H1, H2..H9 rather than simply around the columns C1, C2..C9. The reason is

126 Plot Setup options The setting of Statplot controls what type of graph is drawn. There two choices are Hist (short for histogram) or BoxW (Bo

127 The effect of HRng The effect of HRange is rather different. It controls what range of data is analyzed in calculating the frequencies, and is no

128 However this can be fixed by using the setting HWidth. This variable controls the width of the columns, with the initial starting value and en

129 TTIIPPSS && TTRRIICCKKSS -- UUNNIIVVAARRIIAATTEE DDAATTAA New columns as functions of old You have already seen the use of one tri

13 HHOOWW TTOO UUSSEE TTHHIISS MMAANNUUAALL It has been attempted to design this manual to cover the full use of the hp 39g+ calculator. This

130 The expression INT(RANDOM*6+1) will simulate one roll of the die. This means that MAKELIST(INT(RANDOM*6+1),X,1,500,1) will simulate 500 rolls of a

131 Example 4: Simulate 100 obs. on a normal N(µ=80, σ2=50). Ensure that MODES is set to radian measure and type: MAKELIST(80+ 50*( (-2*LN(RANDOM))

132 TTHHEE SSTTAATTSS AAPPLLEETT -- BBIIVVAARRIIAATTEE DDAATTAA As mentioned in the Univariate section, one of the major strengths of the hp 3

133 Move the highlight into column C1 and enter the xi values, pressing the ENTER key after each one. Now do the same for the yi values in C2. Enter

134 If you have more than one data set displayed on the screen then the up/down arrows move from one set to the other, unless the fit line is also sh

135 Choosing from available fit models On the hp 39g+ the Statistics aplet is the only one which has a SYMB SETUP view, and even then only in mode.

136 This may seem to be a useless model but it can be quite useful. For example, suppose you had collected a set of data using a data logger and a mo

137 Calculator Tip If you have trouble seeing the small dots that the hp 39g+ uses in its scatter-graphs by default then you will be interested in th

138 Enter the data into the NUM view and then switch to the SYMB view. Make sure that S1 (data set 1) is set to C1 and C2, ed, and that the fit is l

139 In the SYMB view (see right) the equation is given to so many decimal places that it doesn’t fit onto the screen. The simplest way to see the ent

14 means and to display histograms. In the MATH menu, read about the functions ROUND, POLYFORM and POLYROOT. Make sure you know how to save and tran

140 We can make predictions from our line of best fit in two places - the HOME view and the PLOT view. The hp 38g was able to do this only from the H

141 There are two methods of dealing with this. The first is to use another measure of goodness of fit. The second is to ‘linearize’ the data (discus

142 The curve which results in the PLOT view is exactly what is required and the equation comes out as 1 (0.693147 )YEXP X=⋅ This “EXP(“ is the ca

143 TTIIPPSS && TTRRIICCKKSS -- BBIIVVAARRIIAATTEE DDAATTAA New columns as functions of old As with univariate statistics, you can us

144 As you can see on the right, the values of the mean and standard deviation are given in the screen to 12 significant digits. If we now switch t

145 Obtaining coefficients from the fit model Coefficients can be obtained from the chosen fit model algebraically. The function PREDY from MATH give

146 Correct interpretation of the PREDX function The PREDX function in the MATH menu simply reverses the line of best fit. For example, the equation

147 Assigning rank orders to sets of data It is occasionally handy to be able to assign rank orders to a set of data. You might be running a Quiz Co

148 Using Stats to find equations from point data eg. 1 Find the equation of the quadratic which passes through the points (1,5), (3,15) and (-5,71

149 Either use the VIEWS Auto Scale option, or change to the PLOT SETUP view and adjust it so that it will display the data. This is not really needed

15 WWHHEERREE’’SS TTHHEE OONN BBUUTTTTOONN?? Let’s begin by looking at the fundamentals - the layout of the keyboard and which are the important

150 TTHHEE IINNFFEERREENNCCEE AAPPLLEETT This aplet is a very flexible tool for users investigating inference problems. It provides critical val

151 The values can be seen by changing to the NUM view. In the MATH menu, Probability section, there is a function called UTPC (Upper-Tailed Probab

152 Sample t value is outside rejection Choose the test and the alternate hypothesis in the SYMB view of the Inference aplet. In this case we are

153 The test value for the Student-t and the sample mean are listed in the middle of the screen and the rough position of these values is shown by a v

154 As before, a more visual display can be seen in the PLOT view. Thus the sample data indicates in our two examples that: ! we can be confident

155 We are dealing with two independent samples in this case and so we need to choose from those tests which involve two samples. Since we know

156 Hypothesis test: Z-Test 1-µ A teacher has developed a new teaching technique for hearing-impaired students which he believes is producing signif

157 Enter the values for the mean and standard deviation of the standardized test, and the significance level of 0.05 (5%). If we now change to the

158 TTIIPPSS && TTRRIICCKKSS -- IINNFFEERREENNCCEE Importing from a frequency table The import ( ) facility of the Inference aplet has

159 Now change into the Program Catalogue and the program you created. Assuming that it has no errors you will see a running count as it creates th

16 SSOOMMEE KKEEYYBBOOAARRDD EEXXAAMMPPLLEESS Shown below are snapshots of some typical screens you might see when you press each of the keys sh

160 TTHHEE FFIINNAANNCCEE AAPPLLEETT This aplet is designed to allow users to solve time-value-of-money (TVM) and amortization style problems qui

161 PV - This is the present value of the initial flow of cash. In a loan, this is the amount of the loan. In an investment, the amount invested.

162 Annuity An engineer retires with $650,000 available for investment. She invests the money in a portfolio which is expected to have an average ret

163 Amortization The second page of this aplet allows amortization calculations in order to determine the amounts applied towards the principal and i

164 TTHHEE QQUUAADD EEXXPPLLOORREERR TTEEAACCHHIINNGG AAPPLLEETT Rather than being a multi-purpose aplet, this is a teaching aplet specialized

165 As can be seen in the screen shots right, the bottom half of the screen shows the roots (if any), the value of the discriminant and the equation i

166 The + and - keys are disabled in mode, since their effects are controlled instead by the ↑ and ↓ keys once the highlight is on the ‘a’ coefficie

167 TTHHEE TTRRIIGG EEXXPPLLOORREERR TTEEAACCHHIINNGG AAPPLLEETT Rather than being a multi-purpose aplet like most of the others covered so far

168 The operation of the two modes is summarized below. PLOT mode The underlying concept in PLOT mode is that the graph controls the equation. Th

169 The c coefficient is shown as a multiple of π in radian mode rather than as a decimal. The currently active coefficient is highlighted and can b

17 KKEEYYSS && NNOOTTAATTIIOONN CCOONNVVEENNTTIIOONNSS There are a number of types of keys/buttons that are used on the hp 39g+. SSoo

170 UUSSIINNGG MMAATTRRIICCEESS OONN TTHHEE HHPP 3399GG++ The hp 39g+ deals very well with matrices. It offers many powerful tools as well as

171 If you look at the list of screen keys on the bottom of the view, you will see one labeled . This determines which way the highlight will move (a

172 Another method is to store the result into a third matrix and then to view it through the Edit screen of the MATRIX Catalog. This is shown below

173 The method for doing this on the hp 39g+ is as follows… Step 1. Enter the MATRIX Catalogue. Use SHIFT CLEAR to erase all matrices. Step 2

174 Finding an inverse matrix Eg. 2 Find the inverse matrix 1A− for the matrix 21411324 1A=−− The first step is to store the matrix A i

175 The dot product Eg. 4 Find the angle between the vectors (3,4)a= and (4,1)b=. Using the formula that ..cosab abθ•= where ab• is the

176 UUSSIINNGG LLIISSTTSS OONN TTHHEE HHPP 3399GG++ A list in the hp 39g+ is the same mathematically as a set. As with a set, it is written a

177 There are also a number of special functions available for list variables which are contained in the List group of functions in the MATH menu. See

178 UUSSIINNGG TTHHEE NNOOTTEEPPAADD CCAATTAALLOOGG The hp 39g+ provides access to Notes which can be either attached to an aplet or created as

179 If you the menu and press NOTE then you would see the Note attached to the aplet. This is common with these aplets. Since they are non-standard

18 The ALPHA key The next modifier key is the ALPHA key. This is used to type alphabetic characters, and these appear in orange just below most keys.

180 Transferring notes using IR Notes can be shared between friends since they can be transmitted over the infra-red link in the same way as can be do

181 SSooffttwwaarree For the hp 38g, hp 39g & hp 40g The HP Connectivity Kit, called HPGComm, is discussed in detail on page 204. It allows us

182 CCrreeaattiinngg aa NNoottee Let’s create a small Note containing some commonly used formulas. Press SHIFT NOTEPAD (not SHIFT NOTE ) and you

183 Use the keys discussed above to type in the screen shown on the right. The arrow keys can be used to move around in the text and insert or delet

184 UUSSIINNGG TTHHEE AAPPLLEETT SSKKEETTCCHHPPAADD If you have not already done so, read the previous chapter. As is explained there, every ap

185 There are two font sizes available via the key, with the default size being large. If you press the key then it will change to . Although ther

186 CIRCLE The circle command is similar. You should position the cursor at the center of the proposed circle. Pressing , move the cursor outwards

187 Move down through the menu until you reach Graphic and across to the particular GROB you chose. Now also press the key labeled and then press

188 Having pasted it into the Sketch page, you can now modify it by adding text and other information. One has to question however whether the time

189 UUSSIINNGG,, CCOOPPYYIINNGG && CCRREEAATTIINNGG AAPPLLEETTSS Before you read this chapter, you should be reasonably familiar with t

19 Try this… If you haven’t already, out of the menu from the previous screen. Press the HOME key to see the screen on the right. Yours may not b

190 CCrreeaattiinngg aa ccooppyy ooff aa SSttaannddaarrdd aapplleett.. Imagine either of these two scenarios…. (i) you are a student and you

191 Our student’s newly created copy of the Function aplet is now totally independent of its parent aplet. She can now (if she wants to) the origin

192 Indeed, if the students have access to the Internet and a Connectivity Kit themselves, then there is no reason that the teacher could not post the

193 E6: P=e^-(K*A)-e^(-K*B) E7: P=UTPN(M, S2,X) E8: P=1-UTPN(M,S2,X) E9: P=UTPN(M,S2,A)-UTPN(M, S2,B) E0: P=UTPN(M,S2,M-K)+ UTPN(M,S2,M+K) These form

194 Equation E6 gives ()Pa x b≤≤ for an exponential distribution. Equations E7 to E0 concern the Normal distribution, with E7 giving ()PX x≥ , E8 g

195 The result is a triangle with corners at (1,1), (2,1) and (1,3), along with its image after reflection in the x axis. We can now matrix M1 so

196 To use a different shape you need only change the points in matrix M2. If your new shape has more than three vertices you will need to change the

197 CCooppyyiinngg ffrroomm hhpp 3399gg++ ttoo hhpp 3399gg++ vviiaa tthhee iinnffrraa--rreedd lliinnkk.. Any aplet can be copied from one

198 To send an aplet, both calculators should be showing the APLET view, with the highlight on the aplet you wish to send. Now press the key on the

199 Time out If you see a message saying that there has been a “Time-out”, it may mean that you did not line the calculators up precisely enough or pr

2 Table of Contents Introduction...12 How to use this Ma

20 You should now be back HOME, with the function ROUND( entered in the display as shown right. You can also achieve the same effect by using AL

200 Apart from curiosity, there is one important respect in which you need to know about these programs, and that is when it comes time to delete an a

201 Generally you will be able to click on a link for each aplet and see a summary on screen, together with a link that lets you download that aplet a

202 For example, at my school I set up a structure containing directories for each of the courses being run. In each of these directories I then set

203 Software for the hp 39g+ At the time of writing the hp 39g+ had only just been released and new software was in the process of being developed. An

204 The HPGComm Connectivity Program At this stage I will assume that you have an hp 38g, hp 39g or hp 40g and you have installed the Connectivity so

205 The first task is to tell the program where to find the aplet. Press the Change Directory button and use the window that pops up to select the dir

206 Using downloaded aplets If you press the VIEWS key on your hp 39g+ you will see a list of options which vary according to which aplet is currentl

207 Deleting downloaded aplets from the calculator As was mentioned earlier, most of the aplets you download will have ‘helper’ programs associated w

208 Saving notes, aplets and sketches via the Connectivity Kit The following information applies to the HPGComm program for the hp 38g, hp 39g or hp

209 If the directory is currently empty, then the calculator will display the image shown right. Calculator Tip The meaning of the question abo

21 EEVVEERRYYTTHHIINNGG RREEVVOOLLVVEESS AARROOUUNNDD AAPPLLEETTSS!! A set of “aplets” is provided in the APLET view on the hp 39g+. This eff

210 Capturing screens using the Connectivity Kit One of the most powerful abilities of the Connectivity Kit is its ability to capture images of the c

211 A variation of this capture process is useful if you want to retain the image on your calculator. Pressing ON+PLOT stores the image into graphics

212 PPRROOGGRRAAMMMMIINNGG TTHHEE HHPP 3399GG++ TThhee ddeessiiggnn pprroocceessss An overview Although you can choose to simply create prog

213 If your new aplet is going to be concerned with analyzing data then your best choice for a parent would probably be the Statistics aplet. On the

214 Planning the VIEWS menu It is very important to the usefulness of your aplet that you carefully plan the VIEWS menu to be clear, concise and user

215 You should therefore also think about what you want the user to be looking at once the program they have triggered stops running. Do you want the

216 The linking process performed by the SETVIEWS command (or by the ADK) is also important in that it tells the calculator which programs are to be t

217 The ‘Start’ entry It is a very good idea to include a “Start” entry, since it will be automatically run when the user presses and it thus allows

218 Spend a moment to go through the code and ensure that you are clear in your own mind the menu it will create, the programs it will run, and the vi

219 Swap back to the Program Catalog, position the highlight on the program .MSG.SV and the program. Apart from the screen going blank for a moment

22 The Quadratic Explorer aplet (see page 164) This is a teaching aplet, allowing the student to investigate the properties of quadratic graphs. The

220 The next option in the menu is ‘Input value’. Choosing this option will create an input screen. The statement controlling this was: INPUT N;&qu

221 The final option is ‘Show function’. The program this runs is a little more complex than the ones shown so far and illustrates a useful technique

222 Example aplet #2 If you haven’t already, read pages 194 which explain how to create a copy of the Parametric aplet to explore geometric transform

223 .TRANSF.SHAPE .TRANSF.MAT This program (left) uses the CHOOSE command to offer a list of options. Note the need to pre-load a value into

224 In the next example we will use the Aplet Development Kit (ADK) to re-create the same ‘Transformer’ aplet used in example 2. This will allow us t

225 Click on “View 1” in the View List window. Change the prompt to “Change matrix”, the Object name to “.TRANSF.MAT” and the Next View to “7: Views”

226 The final stage is to use the ADK to create the two special files HP39DIR.CUR and HP39DIR.000. In the File menu, choose Aplet Library. You wi

227 In the Note view, enter the text shown right. Our VIEWS menu will only have three entries, so use the View - Custom views… command to display t

228 Save the aplet and use the File - Aplet library facility to create the two special files for the directory which allow the calculator to download

229 The 2nd and 3rd lines are there to insert a function. We need a function when the axes are plotted or the normal error message will be displayed

23 The PLOT view is used to display the function as a graph… The key gives access to a number of other useful tools allowing further analysis of t

230 Still referring to the code on the previous page, you will see that it refers to PageNum. The sketches in the hp 39g+’s SKETCH view are numbered 1

231 The DISPXY command allows you to place a string of text at any position on the screen using two different fonts. Until this command was added to

232 If the left or right arrows have been pressed (keys 34.1 or 36.1) then the line is ‘twisted’ by changing the value of M. If the up or down arrows

233 PPRROOGGRRAAMMMMIINNGG CCOOMMMMAANNDDSS All programming commands can by typed in by hand but, as with the MATH commands, can also be obtained

234 SETVIEWS <prompt>;<program>;<view number> This absolutely critical command is covered in great detail on page 214. TThhee B

235 RUN <program name> This command runs the program named, with execution resuming in the calling program afterwards. If a particular piece of

236 ERASE This command erases the current display screen. FREEZE This command halts execution until the user presses any key. LINE <x1>;&l

237 TThhee GGrraapphhiiccss ccoommmmaannddss See the chapter “Programming the hp 39g+” on page 226 for examples illustrating some of the graphics

238 BREAK This command will exit from the current loop, resuming execution after the end of it. There is no GOTO <label> command in the langua

239 TThhee PPrriinntt ccoommmmaannddss These commands are supplied for use with the battery operated HP infra-red thermal printer that is designed

24 Once an aplet is transferred onto any one calculator, transferring it to another takes only seconds using the built in infra-red link at the top of

240 TThhee PPrroommpptt ccoommmmaannddss BEEP <frequency>;<duration> This will use the piezo crystal in the calculator to create a so

241 This value must be a valid one. Assigning an initial value outside the range of the menu may crash the program. If the user presses CANCL then a

242 INPUT <variable>;<title>;<prompt>;<message>;<default value> This command puts up an input view which can be used to

243 TTHHEE MMAATTHH MMEENNUU FFUUNNCCTTIIOONNSS The MATH menu is accessed via the key below the APLET key. Any time that you are typing a value

244 We could use the arrow keys to scroll down to the Polynomial functions but it is far faster to simply press the key labeled with the letter ‘P’ (o

245 On the pages which follow we will look at most of the functions in each group. Some of the functions are not likely to be used at school level and

246 TThhee ‘‘RReeaall’’ ggrroouupp ooff ffuunnccttiioonnss CEILING(<num>) This is a ‘rounding’ function but different in that it always

247 FNROOT(express.,guess) This function is like a mini version of the Solve aplet. If you feed it an algebraic expression and an initial guess it w

248 HMS (dd.mmss) This function works with time and angles. It converts degrees, minutes and seconds to degrees, and also hours, minutes and second

249 INT(num) This function is related to the FLOOR and CEILING functions. Unlike those two, which consistently move down or up respectively, the INT

25 TTHHEE HHOOMMEE VVIIEEWW In addition to these aplets, there is also the HOME view, which can best be thought of as a scratch pad for all the o

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

251 %CHANGE This function calculates the percentage change moving from X to Y using the formula 100(Y-X)/X. It can be used to calculate (for exampl

252 ROUND(num,dec.pts) This function rounds off a supplied number to the specified number of decimal places (d.p.). Eg. Round 66.65 to 1 d.p. Use

253 TRUNCATE(num) This function operates similarly to the ROUND function, but simply drops the extra digits instead of rounding up or down. It is so

254 TThhee ‘‘SSttaatt--TTwwoo’’ ggrroouupp ooff ffuunnccttiioonnss PREDY(x-val) This function predicts the y value for a pair of columns set

255 TThhee ‘‘SSyymmbboolliicc’’ ggrroouupp ooff ffuunnccttiioonnss The = ‘function’ Although this is listed in the MATH menu as if it were a

256 LINEAR?(expression,var.name) This is another of those functions which is probably aimed more at the programmer than at the normal user. It is de

257 46246 46 or 225 or 1x±=+−==−Eg. Solve 2450xx−−= Use QUAD(X2-4X-5,X) Answer: (4+S1*6)/2 It is now up to you to interpret this algeb

258 The | function written as: expression | (var1=value,var2=value,…) This is called the ‘where’ function. The reason for this is that it is

259 TThhee ‘‘TTeessttss’’ ggrroouupp ooff ffuunnccttiioonnss These are all functions which are of interest only to programmers, and consequentl

26 EExxpplloorriinngg tthhee kkeeyybbooaarrdd It is worth familiarizing yourself with the mathematical functions available on the keyboard. If we

260 Some further functions are available in the Hyperbolic group of functions. They are duplicates of functions available on the face of the calculat

261 LNP1(num) Since the ln( )xfunction is asymptotic to the y axis as x approaches zero, the natural logs of numbers close to zero are very large ne

262 TThhee ‘‘CCoommpplleexx’’ ggrroouupp ooff ffuunnccttiioonnss Complex numbers on the hp 39g+ can be entered in either of two ways. Firstly,

263 In addition to the trig functions, there are other functions that take complex arguments. ABS(real or complex) The absolute function, which is f

264 ARG(complex or vector) This function, also found on the keyboard, returns the size of the angle defined by regarding the complex number as a vect

265 TThhee ‘‘CCoonnssttaanntt’’ ggrroouupp ooff ffuunnccttiioonnss These ‘functions’ consist of a set of commonly occurring constants. Two

266 ∆LIST({list}) This function produces a list which contains the differences between successive values in the supplied list. The resulting list ha

267 The MAKELIST function can also be used to simulate observations on random variables. For example, suppose we wish to simulate 10 Bernoulli trial

268 SIZE({list}) and SIZE(matrix) This function returns the size of the list or matrix specified. Since normal users would probably know anyway, and

269 TThhee ‘‘LLoooopp’’ ggrroouupp ooff ffuunnccttiioonnss This is an interesting group of functions that may be of use for students studying d

27 The APLET key is used to choose between the various different aplets available. Everything in the calculator revolves around aplets, which you can

270 RECURSE This functions is provided for programmers to let them define functions in the Sequence aplet. For example, typing RECURSE(U,U(N-1)*

271 TThhee ‘‘MMaattrriixx’’ ggrroouupp ooff ffuunnccttiioonnss This very extensive group of functions is provided to deal with matrices. The s

272 DET(matrix) This function finds the determinant of a square matrix. See page 174 for an example of its use in finding an inverse matrix. Eg. I

273 INVERSE(matrix) This function produces the inverse matrix of an n x n square matrix, where possible. A fully worked example of the use of an inv

274 LSQ See User’s manual LU See User’s manual MAKEMAT See User’s manual QR See User’s manual RANK See User’s manual ROWNORM

275 5263213xyzxyyz++=−=−+=This gives the final result shown in the matrix M2 on the right, giving a solution of (1, -2, 3). The huge advantage

276 TRACE See User’s manual TRN(matrix) This function returns the transpose of an n x m matrix. For example, if 2311 204M=− then TR

277 TThhee ‘‘PPoollyynnoommiiaall’’ ggrroouupp ooff ffuunnccttiioonnss This group of functions is provided to manipulate polynomials. We will

278 POLYFORM(expression,var.name) This is a very powerful polynomial function. It allows algebraic manipulation and expansion of an expression into

279 POLYROOT([coeff1,coeff2,…]) This function returns the roots of the polynomial whose coefficients are specified. The coefficients must be input a

28 The VIEWS menu is provided for two purposes… Intro to the VIEWS menu Firstly, within the standard aplets (Function, Sequence, Solve etc.) it provid

280 TThhee ‘‘PPrroobbaabbiilliittyy’’ ggrroouupp ooff ffuunnccttiioonnss This group of functions is provided to manipulate and evaluate probabi

281 PERM(n,r) This function gives the value of nrP using the formula !()!nrnPnr=−. Eg. How many ways can 3 Math, 4 English, and 6 German books

282 UTPN(mean,variance,value) This function, the ‘Upper-Tail Probability (Normal)’, gives the probability that a normal random variable is greater th

283 Calculator Tip The normal order for the arguments in the UTPN function is UTPN(mean,variance,value), giving the upper-tailed probability. Howev

284 AAPPPPEENNDDIIXX AA:: WWOORRKKEEDD EEXXAAMMPPLLEESS The examples which follow are intended to illustrate the ways in which the calculator ca

285 Method 3 - Using the POLYROOT function The advantage of this is that it can be done in the HOME view and is quick and easy. See page 91 for a me

286 FFiinnddiinngg ccrriittiiccaall ppooiinnttss aanndd ggrraapphhiinngg aa ppoollyynnoommiiaall For the function 32() 4 6fx x x x=− ++… (

287 Step4. Because I know that part (iv) of the question requires me to re-use these extremum values in an integration (which I would like to be as a

288 SSoollvviinngg ssiimmuullttaanneeoouuss eeqquuaattiioonnss.. Solve the systems of equations below: (i) 23 742xyxy−=−+= (ii) 243 2 1

289 Step 3. Change into the HOME view and enter the calculation M1-1*M2. The result is the (x,y) coordinate of the solution. A similar method ca

29 The MATH key next to VARS provides access to a library of mathematical functions. The more common functions have keys of their own, but there is

290 EExxppaannddiinngg ppoollyynnoommiiaallss Expand the expressions below. (i) ()423x + (ii) ()532ab− (i) Use POLYFORM((2X+3)^4,X)

291 EExxppoonneennttiiaall ggrroowwtthh A population of bacteria is known to follow a growth pattern governed by the equation 0;0ktNNe t=≥. It is

292 (ii) Predict N for t = 15 hours. Change to the HOME view and use the PREDY function. Result: 268 269 colonies. (iii) Find t so that 012NN

293 SSoolluuttiioonn ooff mmaattrriixx eeqquuaattiioonnss Solve for the value of X in (2)AIXB−= where 23 3 2,15 1 4AB−==−

294 IInnccoonnssiisstteenntt ssyysstteemmss ooff eeqquuaattiioonnss Solve each of the systems of equations below, where possible, indicating in e

295 FFiinnddiinngg ccoommpplleexx rroooottss (i) Find all roots of the complex polynomial 32() 4 4fzziz zi=+−−. (ii) Find the complex roots of

296 AAnnaallyyzziinngg vveeccttoorr mmoottiioonn aanndd ccoolllliissiioonnss Ship A is currently at position vector 21i + 21j km and is currentl

297 I want to graph this function for the first six seconds but I am not sure what y scale to use so I will set XRng to be 0 to 6 in the PLOT SETUP vi

298 The simplest way to show that the motion is circular is to show that the dot product of the velocity and acceleration vectors is constantly zero f

299 IInnffeerreennccee tteessttiinngg uussiinngg tthhee CChhii22 tteesstt A teacher wishes to decide, at the 5% level of significance, whether

3 The Function Aplet...51 Choose the aplet ...

30 The SETUP views The SETUP views, above PLOT, SYMB and NUM, are used to customize their respective views. For example, the PLOT SETUP screen contro

300 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.

301 AAPPPPEENNDDIIXX BB:: TTEEAACCHHIINNGG CCAALLCCUULLUUSS WWIITTHH AANN HHPP 3399GG++ There are many ways that the teaching of functions a

302 DDoommaaiinnss aanndd CCoommppoossiittee FFuunnccttiioonnss There are a number of ways that the calculator can help with this. Examples are

303 (iii) Composite functions can be introduced directly in the SYMB view. For example, enter F1(X)=X2-X and F2(X)=F1(X+3). Move the highlight to F

304 The disadvantage of the previous method is that it is not very visual. An alternative is to use the “Chords” aplet. In this aplet, a menu is p

305 TThhee CChhaaiinn RRuullee If desirable, an aplet is available from The HP HOME View web site (at http://www.hphomeview.com), called “Chain Ru

306 AArreeaa UUnnddeerr CCuurrvveess This topic is most easily handled using an aplet from The HP HOME View web site (at http://www.hphomeview.com

307 IInneeqquuaalliittiieess The topic of inequalities is one that is sometimes included in calculus courses, particularly during the study of domai

308 PPiieecceewwiissee DDeeffiinneedd FFuunnccttiioonnss Piecewise defined functions can be graphed easily on the hp 39g+ by breaking them up into

309 Finally the calculator will give the result as shown right. The problem is that students will misinterpret it as being N=10, when in fact it is s

31 Numeric formats The choices for ‘Number format’ are shown on the right. Standard is probably the best choice in most cases, although it can be a l

310 AAPPPPEENNDDIIXX CC:: TTHHEE HHPP 4400GG && IITTSS CCAASS IInnttrroodduuccttiioonn This appendix is intended to give a useful

311 The two values at the top of the screen represent the calculator’s successive approximations to the true solution. The chances are that one will h

312 What is the difference between the hp 39g, hp 40g & hp 39g+? At the time that the hp 39g was designed, as an upgrade from the original hp 38g

313 UUssiinngg tthhee CCAASS The first step is to activate the CAS. This is done from the HOME view by pressing screen key 6 (SK6), labeled .

314 +81*2XABECD+81*^XABECD23FG+81*^XABECD23FGQP^2 (iii) Press left arrow once then down arrow once. Press Xy 3, then press up arrow three times &

315 +81*^XABECD23FGQP5R^S2+81*^XABECD23FGQP5R^S2 (iv) Press up arrow three times and then divide by 5. This moves the highlight up to node A, high-l

316 +81*^XABECD23FGQP5R^S2In-line editing mode If you find that you are not able to access part of an expression, or if you have entered an operation

317 If you want to delete the entire expression then the simplest method is to press ON and exit the CAS and then re-enter it with a blank screen. Al

318 The PUSH and POP commands Occasionally it is desirable to transfer results from the normal HOME view to the CAS screen or vice versa. This is do

319 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. Howe

32 The setting of Fraction can be quite deceptive to use and is discussed in more detail on page 40. The next alternative in the MODES view of

320 Evaluating algebraic expressions When an expression is highlighted, pressing ENTER will cause it to be algebraically evaluated and any functions

321 UUssiinngg ffuunnccttiioonnss iinn tthhee CCAASS The behavior of the MATH menu is somewhat similar in the CAS except that it gives access to

322 E.g. 2 Factorizing expressions If you highlight an expression such as (2x+3)4 and press ENTER then the CAS will expand the bracket. Since the

323 E.g. 3 Solving equations Solve the equation 413x −= , giving i) real solutions and ii) complex solutions. From any of the screen menus, access

324 The LINSOLVE function can also be used to solve problems of the form below. Solve the system of equations: The command is LINSOLVE( 2.

325 E.g. 5 Solving a simultaneous integration A continuous random variable X, has a probability distribution function given by: ()21490abxxfor xf

326 We can now use the LINSOLVE function to find A and B. While the second linear equation is still highlighted, fetch the LINSOLVE command from the

327 E.g. 6 Defining a user function The DEF function allows you to define your own functions, which are then available for use. In the example belo

328 OOnn--lliinnee hheellpp One of the most helpful features of the hp 40g CAS is the on-line help provided by the SYNTAX button (SHIFT 2). Pressi

329 CCoonnffiigguurriinngg tthhee CCAASS This can be done in a number of ways and only an overview will be given here. One method is via the conf

33 An alternative to using the ANS key is to use the History facility and the function. This is discussed on page 43. The negative key Another impo

330 Pressing takes you out of the CFG menu (as does choosing QUIT from the menu and confirming it with ) but does not discard any changes you have

331 4) Don’t use a summation variable of lower-case i. This is assumed by the CAS to be the unit imaginary value - the root of x2+1=0. 5) Althou

34 The DEL and CLEAR keys The next important key is the DEL key at the top right of the keyboard. This serves as a backspace key when typing in formu

35 AAnnggllee aanndd NNuummeerriicc sseettttiinnggss It is critical to your efficient use of the hp 39g+ that you understand how the angle and

36 Suppose we define a trig function in the Function aplet as shown. The default setting for the Function aplet is radians, so if we set the axe

37 This setting also applies to the appearance of equations and results displayed using the SHOW command. Calculator Tip Under the system used on t

38 As you can see in the screen snapshot on the previous page, my calculator has a number of extra aplets. Two of them, Statistics2 and Statistics3 a

39 The History entry will take you to the HOME view, where pressing SHIFT CLEAR will clear the History. The GRAPHICS MANAGER There are two views, show

4 Problems when evaluating limits... 88 Gradient at a point...

40 FFrraaccttiioonnss oonn tthhee hhpp 3399gg++ Earlier we examined the use of the MODES view, and the meaning of Number Format. We discussed t

41 Some examples are… (using Fraction 4 or higher) 1. 14173515+= 2. 11 134 132 6−=− The second point to remember involves the method the hp

42 The Fraction setting is thus far more powerful than most calculators but can require that you understand what is happening. It should also be clea

43 If you use a setting of only Fraction 2 to perform this, you will find to your amazement that 1/3 + 4/5 = 8/7 , whereas using Fraction 6 gives th

44 At this point you can use the left and right arrows and the DEL key to edit the calculation by removing some of the characters and/or adding to it.

45 SSttoorriinngg aanndd RReettrriieevviinngg MMeemmoorriieess Each of the alphabetic characters shown in orange below the keys can function as a

46 RReeffeerrrriinngg ttoo ootthheerr aapplleettss ffrroomm tthhee HHOOMMEE vviieeww.. Once functions or sequences have been defined in other

47 AAnn iinnttrroodduuccttiioonn ttoo tthhee MMAATTHH MMeennuu The MATH menu holds all the functions that are not used often enough to be worth

48 RReesseettttiinngg tthhee ccaallccuullaattoorr It is probably inevitable as the line between calculators and computers becomes blurred that ca

49 Just on the rare chance that you may find that the calculator locks up so completely that the keyboard will not respond a method of reset is provid

5 The Stats Aplet - Univariate Data ...122 Uni vs. Bi-variate data ...

50 SSuummmmaarryy 1. The up/down arrow key moves the history highlight through the record of previous calculations. When the highlight is visible,

51 TTHHEE FFUUNNCCTTIIOONN AAPPLLEETT The Function aplet is probably the one that you will use most of all. It allows you to: ! graph equation

52 The SYMB view Now press the key. When you do, your screen should change so that it appears like the one on the right. This is the SYMB view. No

53 Try turning the check on and off for function F1(X). Remember, the highlight has to be on the function before the check can be changed. Make sure

54 AAuuttoo SSccaallee Press the VIEWS key. Use the arrow keys to scroll down to Auto Scale and press ENTER. The calculator will adjust the y axi

55 TThhee PPLLOOTT SSEETTUUPP vviieeww If you press SHIFT then PLOT you will see something like the view on the right. The highlight should be

56 Let's have a look at the meaning of the CHKs (check marks) on the second page of PLOT SETUP. Although they are not used often they can be qui

57 TThhee ddeeffaauulltt aaxxiiss sseettttiinnggss The default scale is displayed in the PLOT SETUP view shown right. It may seem a strange cho

58 TThhee MMeennuu BBaarr ffuunnccttiioonnss In the examples and explanations which follow, the functions and settings used are: Trace is quit

59 Goto This function allows you to move directly to a point on the graph without having to trace along the graph. It is very powerful and useful. S

6 The Finance aplet ...160 Parameters...

60 The Zoom Sub-menu The next menu key we’ll examine is . Pressing the key under pops up a new menu, shown right. The menu is longer than wil

61 Box… This is the most useful of the commands. When you choose this option a message will appear at the bottom of the screen asking you to Sele

62 X-Zoom In/Out x4 and Y-Zoom In/Out x4 These two options allow you to zoom in (or out) by a factor of 4 on either axis. The factors can be set

63 TThhee FFCCNN mmeennuu Before continuing, set the axes back to the way we set them at the start of the section on the Menu bar. Looking at

64 Intersection The next function tool in the menu is Intersection. If you choose this option, then you will be presented with a choice similar to

65 Signed area… Another very useful tool provided in the menu is the Signed Area… tool. Before we begin to use it, make sure that is switched on

66 If you now press ENTER again to accept the end point, the hp 39g+ will calculate the signed area and display the result at the bottom of the screen

67 Press and again, choosing Signed Area… as before. Use the left/right arrow keys or the key to move the cursor to x = -2. Press ENTER to ac

68 Extremum The final item in the menu is the Extremum tool. This is used to find relative maxima and minima for the graphs. Ensure that is s

69 TTIIPPSS && TTRRIICCKKSS -- FFUUNNCCTTIIOONN Finding a suitable set of axes This is probably the most frustrating aspect of graphic

7 Using, Copying & Creating aplets...189 Creating a copy of a Standard aplet...

70 5. Another possible strategy for graphing which works quite well and, perhaps importantly, always gives ‘nice’ scales is to use ZOOM. ! Enter yo

71 Composite functions The Function aplet is capable of dealing with composite functions such as ()2fx+ or ()()fgx in its SYMB view. The and k

72 On the other hand there is a way to further simplify the expression. If you now the result and enclose it with the POLYFORM function as shown ri

73 Differentiating There are different approaches that can be taken to differentiating, most of which are best done in the SYMB view of the Function

74 The process is easiest in the SYMB view of Function. When done this way the result is algebraic rather than numeric. The best method is to define

75 The simplest way to deal with this is to use scales which are multiples of the default scales. For example by using 13 13x−≤≤ and 6.2 6.4y−≤≤ (

76 However, for the scale of -6 to 6 the pixels are no longer 'nice' values of 0.1. If you try to trace the circle you'll see that the

77 Retaining calculated values When you find an extremum or an intersection, the point is remembered until you move again even if it is not actually

78 Firstly, one can change the start value and the step size for the view. NumStart & NumStep For example, values of 10 and 2 give: Automat

79 Pressing the key pops up the menu on the right. The first option of In causes the step size to decrease from 0.1 to 0.025. This is a factor o

8 The Graphics commands ...237 The Loop commands ...

80 Integration: The definite integral using the ∫ function The situation for integration is very similar to that of differentiation. The difference

81 Integration: The algebraic indefinite integral Algebraic integration is also possible (for simple functions), in the following fashions: i. If d

82 A caveat… This substitution process has one implication which you need to be wary of and so it is worth examining the process in more detail… 1132

83 Integration: The definite integral using PLOT variables As was discussed earlier, when you find roots, intersections, extrema or signed areas in t

84 Suppose we want to find the area between 2() 2fx x=− and () 0.5 1gx x=−from x = -2 to the first positive intersection of the two graphs. From the

85 Piecewise defined functions It is possible to graph piecewise defined functions using the Function aplet, although it involves literally splitting

86 ‘Nice’ scales As discussed earlier, the reason for the seemingly strange default scale of -6.5 to 6.5 is to ensure that each dot on the screen is

87 This can be solved by changing the x axis scale to -6.4 to 6.4, which gives table values of 0.2. Using -3.2 to 3.2 is even better since it

88 Problems when evaluating limits In evaluating limits to infinity using substitution, problems can be encountered if values are used which are too

89 The problem lies in the fact that the slow convergence will mean that people will often try to graph this function for very large values of x. The

9 The ‘Tests’ group of functions...259 The ‘Trigonometric’ & ‘Hy

90 Gradient at a point This can be introduced via the Function aplet. In the Function aplet, enter the function being studied into F1(X). To exam

91 Finding and accessing polynomial roots The POLYROOT function can be used to find roots very quickly, but the results are often difficult to see in

92 TTHHEE VVIIEEWWSS MMEENNUU In addition to the views of PLOT, SYMB and NUM (together with their SETUP views), there is another key which we ha

93 Plot-Detail Choosing Plot-Detail from the menu splits the screen into two halves and re-plots the graph in each half. The right hand side can now

94 Plot-Table The next item on the VIEWS menu is Plot-Table. This option plots the graph on the right, with the Numeric view on the right half scree

95 Nice table values What makes this view even more useful is that the table keeps its ‘nice’ scale even while the usual ‘FCN’ tools are being used.

96 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

97 Decimal, Integer & Trig The next option of Decimal resets the scales so that each pixel (dot on the screen) is exactly 0.1. The result is a

98 The default axes under the Trig option is 2π− to 2π. If you are primarily interested in the first 2π of the graph then simply change Xmin to zer

99 DDoowwnnllooaaddeedd AApplleettss ffrroomm tthhee IInntteerrnneett The most powerful feature of the hp 39g+ is that you can download aplets a