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HP 40gs User's Manual

1. Z gt e hp40g book Page 27 Friday December 9 2005 1 03 AM Example If you have stored 1 2 3 4 in variable L1 entering CLVAR 11 will clear L1 Emptu List DISP Displays fextitem in a row of the display at the line number A text item consists of any number of expressions and quoted strings of text The expressions are evaluated and turned into strings Lines are numbered from the top of the screen 1 being the top and 7 being the bottom DISP line number textitem Example DISP 359A qe Result A is 4 A IS 4 displayed on line 3 DISPXY Displays object at position x_pos y_pos in size font The syntax is DISPXY x_pos y_pos font object The value of object can be a text string a variable or a combination of both x pos and y pos are relative to the current settings of Xmin Xmax Ymin and Ymax which you set in the PLOT SETUP view The value of font is either 1 small or 2 large Example DISPXY Oe OP HELLO HELLO WORLD WORLD DISPTIME Displays the current date and time DISPTIME To set the date and time simply store the correct settings in the date and time variables Use the following formats M DDYYYY for the date and H MMSS for the time Programming 21 27 d X EDITMAT FREEZE GETKEY INPUT 21 28
2. GIN e hp40g book Page 1 Friday December 9 2005 1 03 AM Solve aplet About the Solve aplet The Solve aplet solves an equation or an expression for its unknown variable You detine an equation or expression in the symbolic view then supply values for all the variables except one in the numeric view Solve works only with real numbers Note the differences between an equation and an expression An equation contains an equals sign Its solution is a value for the unknown variable that makes both sides have the same value e An expression does not contain an equals sign Its solution is a root a value for the unknown variable that makes the expression have a value of zero You can use the Solve aplet to solve an equation for any one of its variables When the Solve aplet is started it opens in the Solve Symbolic view n Symbolic view you specify the expression or equation to solve You can define up to ten equations or expressions named EO to E9 Each equation can contain up to 27 real variables named A to Z and 0 n Numeric view you specify the values of the known variables highlight the variable that you want to solve for and press You can solve the equation as many times as you want using new values for the knowns and highlighting a different unknown Note It is not possible to solve for more than one vari
3. LM 22 3 Annotating an aplet with notes pp 22 4 Annotating an aplet with 22 4 Downloading e lessons from the web 22 4 Sending and receiving aplets pp 22 4 Sorting items in the aplet library menu list 22 6 Reference information Eee R Resetting The HP 40gs i R 3 To erase all memory and reset defaults R 3 If the calculator does not turn R 4 Operaling dedil ee ne ed pn R 4 BeOS GS el ee DS R 4 R O meme dioe TIE e R 6 Function aplet variables pp R 7 Parametric aplet variables R 8 Polar aplet variables R 9 Sequence aplet R 10 viil am ad T e hp40g book Page ix Friday December 9 2005 1 03 AM NY Solve aplet variables Statistics aplet variables MATH menu categories Math furietions MR Program constants pp Constans em a a ord CR Program commands pp Status MESSAGES rere dae Limited Warranty JENE E Regulatory Notices Index
4. 20 1 ADIEU note 20 1 Aplet Sker T 20 3 Menoe POG aroaren ee nu R Li 20 6 21 Programming ON m 21 1 Program catdlgg Ote 21 2 Creating and editing programs pp 21 4 news 21 Customizing 21 9 an WY T NY 4 P hp40g book Page viii Friday December 9 2005 1 03 AM Aplet naming convention pp 21 10 e MNT UE 21 10 Programming commands pp 21 13 Aple commands i a en 21 14 BRCM 21 17 Drawing commands ea aca 21 19 CE has 21 21 LO6D command US 21 23 Mairi COMMON Stee ahs en 21 24 case D E IAM M EIE 21 25 Promp commands ee a T 21 26 Stat One and Stat Two 21 29 Sta TWO COMMANA Seso rer voe cd dut exar 21 30 Storing and retrieving variables in programs 21 31 Plotview md ed 21 31 Symbolic view variables 21 38 Numeric view variables i 21 40 Nole ee eee ee 21 43 SIEM Van DIE 21 43 22 Extending aplets Creating new aplets based on existing aplets 22 1 Using a customized 22 3 RESE MING an
5. T a e e hp40g book Page 7 Friday December 9 2005 1 03 AM NY Function aplet variables The function aplet variables are Category Available name Plot Axes Xcross Connect Yoross Coord Xtick FastRes Ytick Grid Xmin Indep Xmax Invoross Ymin Labels Ymax Hecenter Xzoom Simult Yxoom Tracing Plot FCN Area Root Extremum Slope Symbolic Angle F6 F1 F7 F2 F8 F3 F9 e F4 FO F5 Numeric Digits NumRow Format NumStart NumCol NumStep NumFont NumType NumIndep NumZoom Note NoteText Sketch Page PageNum R 7 am WY T a e hp40g book Page 8 Friday December 9 2005 1 03 AM NY Parametric aplet variables The parametric aplet variables are Category Available name Plot Axes Tracing Connect Tstep Coord ACKOSsS Grid Ycross Indep Xtick InvCross Ytick Labels Xmin Recenter Xmax Ymin Tmin Ymax Tmax Xzoom Yzoom Symbolic Angle Y5 X1 X6 Y1 Y6 X2 X Y2 3 X3 X8 I3 XO X4 9 Y4 Y9 X5 XO YO Numeric Digits NumRow Format NumStart NumCol NumStep NumFont NumType NumIndep NumZoom Note NoteText Sketch Page PageNum am 27 T a iG e hp40g book Page 9 Friday December 9 2005 Polar aple
6. To a previous line To reuse the last result To repeat a previous line Example Getting started P hp40g book Page 23 Friday December 9 2005 1 03 AM When you highlight a previous input or result by pressing 4 the and menu labels appear Highlight the line press 4 and press gass The number or expression is copied into the edit line Press ANS last answer to put the last result from the HOME display into an expression ANS is a variable that is updated each time you press ENTER To repeat the very last line just press Otherwise highlight the line press 4 first and then press ENTER The highlighted expression or number is re entered If the previous line is an expression containing the ans the calculation is repeated iteratively See how ANS retrieves and reuses the last result 50 updates ANS from 50 to 75 to 100 50 ENTER 5 25 You can use the last result as the first expression in the edit line without pressing ANS Pressing or or other operators that require a preceding argument automatically enters ans before the operator You can reuse any other expression or value in the HOME display by highlighting the expression using the arrow keys then pressing See Using previous results on page 1 22 for more details The variable A
7. Conients Preface NGnual conventions ee P 1 EA E E AAE O ee eo P 2 1 Getting started cancel operalions em ean 1 1 re dn a 1 2 Te keyboard a OTT 1 3 MENU 1 8 o M 1 9 Mode sellitigs sabe 1 10 SEN 1 11 Aplets 686 8 ebb bb 1 12 PICT a ce a dt a 1 16 ADIEU iue 1 16 Aplet view configurafion pp 1 18 Mathematical calculations pp 1 19 c USI ROC NOMS NEN a E 1 25 Complex 1 29 amp 1 30 2 and their views ADISI VOWS CH T eee 2 1 About the Symbolic view pp 2 1 Defining an expression Symbolic view 2 Evaluating expressions ie bidder sU 2 3 Abou ING Plo 2 5 Setting up the plot Plot view 2 5 Exploring Ihe tu 2 7 Other views for scaling and splitting the graph 2 13 About the numeric view pp 2 16 Setting up the table Numeric view setup 2 16 Exploring the table of numbers pp 2 17 Building your own table of numbers 2 19 Build Your Own menu keys Ne 2 20 Example plIoHingeselrlesce testari tels euet 2 20 3 Function aplet About the Function aplet
8. 4 hp40g book Page 42 Friday December 9 2005 1 03 AM TEXPAND 14 42 TCOLLECT linearizes this expression in terms of sin n x and cos n x then in Real mode reconstructs the sine and cosine of the same angle Typing TCOLLECT SIN X COS X gives e cos x 3 4 Develop transcendental expressions TEXPAND has as an argument a transcendental expression that is an expression with trigonometric exponential or logarithmic functions TEXPAND develops this expression in terms of sin x cos x exp x or In x Example 1 Typing TEXPAND EXP X Y gives Example 2 TEXPAND LN X Y gives In y In x Example 3 Typing TEXPAND COS X Y gives cos y cos x sin y sin x Example 4 Typing TEXPAND COS 3 X Computer Algebra System CAS T e NY TLIN e TRIG Computer Algebra System CAS e hp40g book Page 43 Friday December 9 2005 1 03 AM gives 4 cos x 3 cos x Linearize a trigonometric expression TLIN has as an argument a trigonometric expression TLIN linearizes this expression in terms of sin n x and cos n x Example 1 Typing THINACOS X COSY gives 1 1 p cos x y 5 cos x y Example 2 Typing TLIN COS 3 gives
9. Z e hp40g book Page 24 Friday December 9 2005 1 03 AM Matrix commands The matrix commands take variables MO M9 as arguments ADDCOL Add Column Inserts values into a column before column number in the specified matrix You enter the values as a vector The values must be separated by commas and the number of values must be the same as the number of rows in the matrix name ADDCOL name value value column number ADDROW Add Row Inserts values into a row before row number in the specified matrix You enter the values as a vector The values must be separated by commas and the number of values must be the same as the number of columns in the matrix name ADDROW name value value number DELCOL Delete Column Deletes the specified column from the e specified matrix DELCOL name column number DELROW Delete Row Deletes the specified row from the specified matrix DELROW name row number EDITMAT Starts the Matrix Editor and displays the specified matrix If used in programming returns to the program when user EDITMAT name RANDMAT Creates random matrix with a specified number of rows and columns and stores the result in name name must be MO M9 The entries will be integers ranging from 9 to 9 RANDMAT name rows columns REDIM Redimensions the specified matrix or vector to size For a matrix size is a list of
10. NY Physical Constants e hp40g book Page 16 Friday December 9 2005 1 03 AM The physical constants are Category Available Name Chemist Phyics Quantum Avogadro Avagadro s Number NA Boltz Boltmann k mol vo molar volume Vm univ gas universal gas R std temp standard temperature St dT std pres standard pressure St dP StefBolt Stefan Boltzmann o light s speed of light c permitti permittivity 20 permeab permeability uO acce gr acceleration of gravity g gravita gravitation C Plank s Plank s constant h Dirac s Dirac s hbar e charge electronic charge q e mass electron mass me q me ra g me ratio qme proton m proton mass mp mp me r mp me ratio mpme fine str fine structure a mag flux magnetic flux 4 Faraday Faraday F Rydberg Rydberg Roo Bohr rad Bohr radius aO Bohr mag Bohr magneton uB nuc mag nuclear magneton uN photon wavelength p es photon frequency Compt w Compton wavelength Ac an ad T 4 hp40g book Page 17 Friday December 9 2005 1 03 CAS functions CAS functions are Category Function Algebra COLLECT STORE DEF EXPAND SUBST FACTOR TEXPAND PARTFRAC UNASSIGN QUOTE Complex i IM A
11. GIN e hp40g book Page 1 Friday December 9 2005 1 03 AM Getting started On off cancel operations To turn on Press ON fo turn on the calculator To cancel When the calculator is on the ON key cancels the current operation To turn off Press sHiFT OFF to turn the calculator off To save power the calculator turns itself off after several minutes of inactivity All stored and displayed information is saved If you see the annunciator or the Low Bat message e then the calculator needs fresh batteries 4 HOME is calculator s home view is common to all aplets If you want to perform calculations or you want to quit the current activity such as an aplet a program or an editor press All mathematical functions are available in the HOME The name of the current aplet is displayed in the title of the home view Protective cover The calculator is provided with a slide cover to protect the display and keyboard Remove the cover by grasping both sides of it and pulling down You can reverse the slide cover and slide it onto the back of the calculator this will help prevent you losing the cover while you are using the calculator To prolong the life of the calculator always place the cover over the display and keyboard when you are not using the calculator Getting started 1 1 4
12. combined amount earns interest at a certain rate Financial calculations involving compound interest include savings accounts mortgages pension funds leases and annuities Time Value of Money TVM calculations as the name implies make use of the notion that a dollar today will be worth more than a dollar sometime in the future A dollar today can be invested at a certain interest rate and generate a return that the same dollar in the future cannot This TVM principle underlies the notion of interest rates compound interest and rates of return TVM transactions can be represented by using cash flow diagrams A cash flow diagram is a time line divided into equal segments representing the compounding periods Arrows represent the cash flows which could be positive upward arrows or negative downward arrows depending on the point of view of the lender or borrower The following cash flow diagram shows a loan from a borrower s point of view Present value PV Loan Equal periods received is number PMT Money Payment Payment Payment Payment paid out is v Future value a negative number Equal payments On the other hand the following cash flow diagram shows a load from the lender s point of view Equal payments FV PMT PMT PMT PMT 3 4 5 Loan u A A Equal periods
13. minimum data value The box marks the first quartile the median where the cursor pimen 14 MERI is and the third quartile The right whisker marks the maximum data value The numbers below the plot mean that this column has a median of 13 Box and One variable statistics Whisker Plot The left whisker marks the i 10 16 Statistics aplet e 0 Z gt e hp40g book Page 17 Friday December 9 2005 1 03 AM Scatter Plot Two variable statistics The numbers below the plot indicate that the cursor is at d the first data point for S2 at l 1 6 Press to move to the next data point and display information about it 11 1 HEHU To connect the data points as they are plotted checkmark CONNECT in the second page of the Plot Setup This is not a regression curve sar 11 1 6 EET Fitting a curve to 2VAR data In the Plot view press ali This draws a curve to fit the checked two variable data set s See To choose the fit on page 10 12 e CEAT FIT SEL 11 1 6 HEHU eo eae ee ZEE Fiti 2 121951219251 4S2 C3 C4 Fitz EMTER USER DEFIMED FIT EDIT CHE NN Eee The expression Fit2 shows 1 9888219178182 657 slope 1 98082191781 and the y SSS Sse
14. 1 Precision set to 3 SIE nu c2 co 11 47 IETHF Bl e Precision set to 4 FUNCTION co 11 47 117 588 TDk i en entering tractions Fraction When entering fract calculations You use the key to separate the numerator part and the denominator part of the fraction To enter a mixed fraction for example 1 2 you enter it in the format 1 5 For example to perform the following calculation 3 23 4 5 g 1 Set the Number format mode to Fraction or Mixed Fraction and specify a precision value of 4 In this example we ll select Fraction as our format SHIFT MODES v ROME MOLES ANGLE MEASURE Radians rf Select MUIMEER FORMAT Fr act ian DECIMAL MARK Dott 2 Fraction ima ENTER DECIMAL PLACES TO USE ENTER gt 4 EE LEDIT GET _ Getting started 1 27 4 P hp40g book Page 28 Friday December 9 2005 1 03 AM Converting decimals to fractions 2 Enter the calculation 3 x 0002603 6402009507 380 0 THREE LHS Note Ensure you are in the HOME view 3 Evaluate the calculation Note that if you had Sece oed4 5 Tz BD selected Mixed EH Fraction instead of Fraction as the Number format the answer would have been expressed as 2547 8 rs To convert a decimal va
15. 12 Using the Finance Solver The Finance Solver or Finance aplet is available by using the APLET key in your calculator Use the up and down arrow keys to select the Finance aplet Your screen should look as follows Se See PLET LIERARY ESEZEEETH Polar HKE 4 HKE Si we Finance Statistics HEB LEAVE REZET ORT START Press the key or the soft menu key to activate the aplet The resulting screen shows the different e elements involved in the solution of financial problems with your HP 40gs calculator SASS TIME VALUE DF MONEY hi E B PY PHT 12 F End ENTER WO OF PHYMENTS OF SOLVE LEhIT ART hLWE Background information on and applications of financial calculations are provided next Background The Finance Solver application provides you with the ability of solving time value of money and amortization problems These problems can be used for calculations involving compound interest applications as well as amortization tables Compound interest is the process by which earned interest on a given principal amount is added to the principal at specified compounding periods and then the 6 Using the Finance Solver 12 1 an 4 hp40g book Page 2 Friday December 9 2005 1 03 AM
16. e NZ Z e hp40g book Page 62 Friday December 9 2005 1 03 AM CAS Functions on the CMDS menu When you are in the Equation Writer and press NES CAS COMMANDS SESS MATH a menu of the full set of CAS functions available to you is displayed Many of the functions in this menu match the functions available from the soft key menus in the Equation Writer but there are other functions that are only available from this menu This section describes the additional CAS functions that are available when you press MATH in the Equation Writer See the previous section for other CAS commands CANEL OK ABCUV This command applies the B zout identity like EGCD but the arguments are three polynomials A B and C C must be a multiple of GCD A B ABCUVIAIXI BIX C X returns UIX AND V X where U and V satisfy e C X U X A X VIX Example 1 Typing ABCUV X 2 X 1 2 1 1 gives CHINREM Chinese Remainders CHINREM has two sets of two polynomials as arguments each separated by AND CHINREM A X AND R X B X AND returns an AND with two polynomials as components P X and S X The polynomials P X and S X satisfy the following relations when GCD R X Q X 1 S X R X lt Q X P X A X modR X and P X B X modQ X There is always a solution P X if R X and
17. e NZ IN a 19 hp40g book Page 4 Friday December 9 2005 NY To draw a box To draw a circle DRAW keys 20 4 1 03 AM In Sketch view press and move the cursor to where you want any corner of the box to be Press 3 Move the cursor to mark the opposite corner for the box You can adjust the size of the box by moving the cursor Press BIB to finish the box In Sketch view press BITE and move the cursor to where you want the center of the circle to be Press MAA This turns on circle drawing 3 Move the cursor the distance of the radius Press MA to draw the circle Key Meaning Dot on Turns pixels on as the cursor moves Dot off Turns pixels off as the cursor moves LIME Draws a line from the cursor s starting position to the cursor s current position Press BIB when you have finished You can draw a line at any angle DEI Draws a box from the cursor s starting position to the cursor s current position Press BIB when you have finished Draws a circle with the cursor s starting position as the center The radius is the distance between the cursor s starting and ending position Press to draw the circle Notes and sketches an SZ gt e hp40g book Page 5 Friday December 9 2005 1 03 AM To label parts of a 1 Press and
18. Edita program 1 Press SHIFT PROGRM to open the Program PROGRAM CATALOG HEHA MTPEUL H3EB Editline H3KB _ catalog 4 EDIT HEH 2 Program Editor The name of your program appears in the title bar of the display You can use the following keys to edit your program Programming 21 5 e e amp SZ e hp40g book Page 6 Friday December 9 2005 1 03 AM Editing keys The editing keys are Key Meaning STUE Inserts the 23 character at the editing point Inserts space into text 195 Displays previous page of the program FAGET Displays next page of the program 4 v Moves up or down one line gt Moves right or left one character Alpha lock for letter entry Press A Z to lock lower case ERZE Backspaces cursor and deletes character e DEL Deletes current character Starts a new line CLEAR Erases the entire program Displays menus for selecting variable MATH names contents of variables math functions and program constants Prog CMDS Displays menus for selecting program conmmands CHARS Displays all characters To type one highlight it and press Eis To enter several characters in a row CHARS menu 21 6 Programming e 0 Y e hp40g book Page 7 Friday Decembe
19. Program constants The program constants are numbers that have been assigned to various calculator settings to enable you to test for or specify such a setting in a program For example the various display formats are assigned the following numbers 1 Standard 2 Fixed 3 Scientific 4 Engineering 5 Fraction 6 Mixed fraction In a program you could store the constant number of a particular format into a variable and then subsequently test for that particular format To access the menu of program constants e 1 Press MATH 2 Press MLA 3 Use the arrow keys to navigate through the options 4 Click EEE and then to display the number assigned to the option you selected in the previous step The use of program constants is illustrated in more detail in Programming on page 21 1 Physical constants There are 29 physical constants from the fields of chemistry physics and quantum mechanics that you can use in calculations A list of all these constants can be found in Physical Constants on page R 16 To access the menu of physical constants 1 Press MATH 2 Press Bil Using mathematical functions 13 25 e NZ IN Z gt e hp40g book Page 26 Friday December 9 2005 1 03 AM 3 Use the arrow keys to navigate through the options 4 To see the symbol and value of a selected constant press 21
20. T GIN e hp40g book Page 1 Friday December 9 2005 1 03 AM 15 Equation Writer Using CAS in the Equation Writer The Equation Writer enables you to type expressions that you want to simplify factor differentiate integrate and so on and then work them through as if on paper The key on the HOME screen menu bar opens the 3 Equation Writer and the oe key closes it This chapter explains how to write an expression in the Equation Writer using the menus and the keyboard how to select a subexpression how to apply CAS functions to an expression or subexpression and how to store values in the Equation Writer variables Chapter 14 explains all the symbolic calculation functions contained in the various menus and chapter 16 provides numerous examples showing the use of the Equation Writer The Equation Writer menu bar The Equation Writer has a TOOL ALGE JEEHRI SOLV TRIG number of soft menu keys TOOL menu Unlike the other soft menu keys the menu does i EET moge not give access to CAS Edit expr commands Instead it provides access to a number of utilities to help you work with the Equation Writer The following table explains each of the utilities on the menu Change Font Cut Equation Writer 15 1 e NZ zz gt e
21. EIE VOIR 13 25 13 25 14 Computer Algebra System CAS WTA 14 Performing symbolic calculations 14 1 ADndexample 14 2 CA 14 4 The current variable pp 14 4 CN OG oe E r 14 5 Using CAS functions in HOME 14 7 Online 14 8 CAS functions in Equation 14 9 14 10 DIEI enu oov DIE ae re 14 16 sucede testate utitur tud 14 28 SOD men eo 14 33 TRIG MENU ER 14 38 CAS Functions on the MATH menu 14 45 ee 14 45 eoe AMI TU Senet al 14 45 Bro T UAR RR EE 14 46 14 46 do M UIT PM 14 46 MONU 14 46 ee 14 51 PONV NOMIC MERU 14 55 xeu Me re 14 60 REWE mm en e 14 60 NE 14 60 TOSS MENU EE 14 61 llis Rz LS 14 61 CAS Functions on the CMDS 14 62 15 Equation Writer Using CAS in the Equation Writer 15 1 The Equation Writer menu bar 15 1 Configuration MENUS pp 15 3 Entering expressions and 15 5 How to modify an
22. P hp40g book Page 19 Friday December 9 2005 1 03 AM NOTE IBP returns the AND of u x v x and of v x u x that is the terms that are calculated when performing a partial integration It remains then to calculate the integral of the second term of the AND then add it to the first term of the AND to obtain a primitive of u x Typing IBP LN X X gives X LN X AND 1 The integration is completed by calling INTVx TNTVX X LN X AND 1 which produces the result X LN X X If the first IBP or INTVX parameter is an AND of two elements IBP concerns itself only with the second element of the AND adding the integrated term to the first element of the AND so that you can perform multiple IBP in succession Primitive and defined integral INTVX has one argument an expression INTVX calculates a primitive of its argument with respect to the variable stored in VX Example Calculate a primitive of sin x x cos x Typing INTVX SIN XxX COS gives in step by step mode Int u F u with u SIN X Pressing OK then sends the result to the Equation Writer 2 14 19 T e P X iG e hp40g book Page 20 Friday December 9 2005 1 03 AM Example Given f x z LN calculate a primitive of f Type A LN J X T x NTV Y 1 X 1
23. S2 es EC hp40g book Page i Friday December 9 2005 1 03 AM 4095 graphing calculator user s guide zl Edition Part Number F2225AA 90001 am AZ e SI 2 SN en title fm Page 11 Friday February 17 2006 9 48 AM Notice REGISTER YOUR PRODUCT AT www register hp com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED AS IS AND ARE SUBJECT TO CHANGE WITHOUT NOTICE HEWLETT PACKARD COMPANY MAKES NO WAR RANTY OF ANY KIND WITH REGARD TO THIS MANUAL INCLUDING 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 EXAMPLES CONTAINED HEREIN Copyright 1994 1995 1999 2000 2003 2006 Hewlett Packard Devel opment Company L P Reproduction adaptation or translation of this manual is prohibited without prior written permission of Hewlett Packard Company except as allowed under the copyright laws Hewlett Packard Company 4995 Murphy Canyon Rd Suite 301 San Diego CA 92123 Printing History Edition 1 April 2005 ab am N X iG e hp40g book Page 111 Friday December 9 2005 1 03 AM
24. Using the logical XOR superimposes graphicname2 onto graphicname 1 The upper left corner of graphicname2 is placed at position GROBXOR graphicname position graphicname2 Creates graphic with given width height and hexadecimal data and stores it in graphicname MAKEGROB graphicname width height hexdata Stores the Plot view display as a graphic in graphicname PLOT graphicname PLOT and DISPLAY can be used to transfer a copy of the current PLOT view into the sketch view of the aplet for later use and editing Example PageNum PLOT Page DISPLAY Page FREEZE This program stores the current PLOT view to the first page in the sketch view of the current aplet and then displays the sketch as a graphic object until any key is pressed Puts graph from graphicname into the Plot view display PLOT graphicname Replaces portion of graphic in 1 with graphicname2 starting at position REPLACE also works for lists and matrices REPLACE graphicname position graphicname2 Extracts a portion of the named graphic or list or matrix and stores it in a new variable name The portion is specified by position and positions SUB name graphicname position positions Creates a blank graphic with given width and height and stores it in graphicname ZEROGROB graphicname width height Programming T
25. Y e hp40g book Page 2 Friday December 9 2005 1 03 AM The display To adjust the Simultaneously press ON and or to increase or contrast decrease the contrast To clear the display Press C4NCEL to clear the edit line Press CLEAR to clear the edit line and the display history Parts of the display n FUNCT History 19 279 Edit line 7994 Menu key labels Menu key or soft key labels The labels for the menu e keys current meanings is the label for the first menu key in this picture Press 3 means to press the first menu key that is the lettmost top row key on the calculator keyboard Edit line The line of current entry History The HOME display HOME shows up to four lines of history the most recent input and output Older lines scroll off the top of the display but are retained in memory Title The name of the current aplet is displayed at the top of the HOME view RAD GRD DEG specity whether Radians Grads or Degrees angle mode is set for HOME The v and A symbols indicate whether there is more history in the HOME display Press v and 4 to scroll in the HOME display Getting started 4 NZ DS e hp40g book Page 3 Friday December 9 2005 1 03 AM Annunciators Annunciators are symbols that appear above the title
26. an ad T iG e hp40g book Page x Friday December 9 2005 1 03 AM T an ad e GIN e hp40g book Page 1 Friday December 9 2005 1 03 AM Preface The HP 40gs is a feature rich graphing calculator It is also a powertul mathematics learning tool with a built in computer algebra system CAS The HP 40gs is designed so that you can use it to explore mathematical functions and their properties You can get more information on the HP 40gs from Hewlett Packard s Calculators web site You can download customized aplets from the web site and load them onto your calculator Customized aplets are special applications developed to perform certain functions and to demonstrate mathematical concepts Hewlett Packard s Calculators web site can be found at http www hp com calculators Manual conventions The following conventions are used in this manual to e represent the keys that you press and the menu options that you choose to perform the described operations Key presses are represented as follows SIN COS HONE Shif keys that is the key functions that you access by pressing the key first are represented as follows CLEAR SHIFT MODES SHIFT ACOS etc Numbers and letters are represente
27. Mode settings You use the Modes input form to set the modes for HOME HINT Although the numeric setting in Modes affects only HOME the angle setting controls HOME and the current aplet The angle setting selected in Modes is the angle setting used in both HOME and current aplet To further configure an aplet you use the keys SHIFT and SHIFT NUM Press MODES to access the HOME MODES input form Setting Options Angle Angle values are Measure Degrees 360 degrees in a circle Radians 27 radians in a circle Grads 400 grads in a circle The angle mode you set is the angle 4 setting used in both HOME and the 2 current aplet This is done to ensure e that trigonometric calculations done in the current aplet and HOME give the same result Number The number format mode you set is the Format number format used in both HOME and the current aplet Standard Full precision display Fixed Displays results rounded to a number of decimal places Example 123 456789 becomes 123 46 in Fixed 2 format Scientific Displays results with an exponent one digit to the left of the decimal point and the specified number of decimal places Example 123 456789 becomes 1 23E2 in Scientific 2 format _ 1 10 Getting started e 0 GIN e hp40g book Page 11 Friday December 9 2005 1 03 AM Setting Options
28. 10 1 Getting started with the Statistics 10 1 Entering and editing statistical data 10 6 Defining a regression 10 12 oie Ie en 10 14 alo ula EET 10 15 DE ee eo es AOE 10 16 Fitting a curve to 2VAR data 10 17 Setting up the plot Plot setup view 10 18 Trouble shooting a 10 19 Explorig he 10 19 Calculating predicted values 10 20 11 Inference aplet IV an ad T e hp40g book Page v Friday December 9 2005 1 03 AM e NY About the Inference aplet pp 11 1 Getting started with the Inference 11 1 Importing sample statistics from the Statistics aplet 11 4 Hypothesis tesi se dante Md D 11 8 One Sample Z Test misan n e 11 8 Iwo Sampe ipi e 11 9 One Proportion ZTesf 11 10 PWO PRODOMION Z LOSI anes a a te be deus 11 11 Sample Test E da E 11 12 TWO 11 14 C ntidence intervals ae 11 15 One Sample Z Interval 11 15
29. e NZ 2 e hp40g book Page 27 Friday December 9 2005 1 03 AM Solution 1 Start by defining the following g x 2 x2 Now type PROPFRAC G X Note that PROPFRAC can be found on the POLYNOMIAL submenu of the MATH menu Pressing yields the result shown at the right Solution 2 Enter the integral l J ges Pressing yields the result shown at the right Pressing ENTER again yields Working by hand 2x 3 2 x 2 1 so g x 2 DEF Gtx 2 d ate PROPFRAC GCH 4 fraction ato li BK z LH 2 4 LH od x42 Then integrating term by term between O and 2 produces 2 x g x dx 2x In x 2 0 X that is since In4 21n2 g x dx 4 In2 0 Step by Step Examples an 16 27 16 28 e hp40g book Page 28 Friday December 9 2005 1 03 AM Solution 3 The calculator is not needed here Simply stating that e increases for x 0 2 is sufficient to yield the inequality Solution 4 Since g x is positive over 0 2 through multiplication we get x 2 g x lt gG e lt gae and then integrating Solution 5 2 First find the limit of e when n o aal Note pressing after you have selected t
30. T Y e hp40g book Page 2 Friday December 9 2005 1 03 AM using vectors and matrices Vectors and matrices cannot be entered using the Equation Writer To open the Equation Writer press the far soft key on the menu bar of the HOME screen The illustration at the right shows an expression being written in the Equation BIN HORE Writer The soft keys on the menu bar provide access to CAS functions and commands To leave the Equation Writer press to return to the HOME screen Note that expressions written in the Equation Writer and the results of evaluating an expression are not automatically copied to the HOME history when you leave the Equation Writer You can e however manually copy them to HOME see page 14 8 e CAS functions are described in detail in CAS functions in the Equation Writer on page 14 9 Chapter 15 Equation Writer explains in detail how to enter an expression in the Equation Writer and contains numerous worked examples of CAS in operation An example To give you an idea of how CAS works let s consider a simple example Suppose you want to convert C to the form d J5 where C is 24 45 20 and d is a whole number 1 Open the Equation Writer by pressing the 88 soft key on the HOME screen 2 Enter the expression for C 245 26 Hint use the keys on the keyboard as you would if enterin
31. an zz gt e hp40g book Page 5 Friday December 9 2005 1 03 AM CAS modes The modes that determine ERR how CAS operates can be set on CAS MODES screen To display CAS MODES screen press To navigate through the options in CAS MODES screen press the arrow keys nduln 13 Approx Facter y WMerbozg wetep step _ Ince yw Figorauzy zinp 1 nter independent uaraigble To select or deselect a mode navigate to the appropriate field and press until the correct setting is displayed indicated by a check mark in the field For some settings such as mper var and you will need to press to be able to change the setting Press H3 to close CAS MODES screen NOTE You can also set CAS modes from within the Equation Writer See Configuration menus on page 15 3 for information Selecting the Many of the functions provided by CAS use a pre independent determined independent variable By default that variable variable is the letter X upper case as shown in CAS MODES screen above However you can change this variable to any other letter or combination of letters and numbers by editing the mper van field in CAS MODES screen To change the setting press El enter a new value and then press The variable VX in the calculator s HOME CASDIR direct
32. e hp40g book Page 28 Friday December 9 2005 1 03 AM Examples 5 152000 DATE sets the date to May 15 2000 10 1500 TIME sets the time to 10 15 am Matrix Editor Opens the Matrix editor for the specified EDITMAT matrixname The EDITMAT command can also be used to create matrices 2 Press ALPHA M 1 and then press ENTER The Matrix catalog opens with M1 available for editing EDITMAT matrixname is an alternative to opening the matrix editor with matrixname It be used in a program to enter a matrix This command prevents the display from being updated after the program runs This allows you to view the graphics created by the program Cancel FREEZE by pressing any key FREEZE Waits for a key then stores the keycode rc p in name where r is row number c is column number and p is key plane number The key planes numbers are 1 for unshifted 2 for shifted 4 for alpha shifted and 5 for both alpha shitted and shifted GETKEY name Creates an input form with a title bar and one field The field has a label and a default value There is text help at the bottom of the form The user enters a value and is stored in the variable name The title label and help items are text strings and need to be enclosed in double quotes Use SHIFT CHARS to type the quote marks INPUT name title label help default Programming 4
33. PN NZ e hp40g book Page 23 Friday December 9 2005 1 03 AM AG NY Loop commands Loop hp allow a program to execute a routine repeatedly The HP 40gs has three loop structures The example programs below illustrate each of these structures incrementing the variable A from 1 to 12 DO UNTIL END Until End is aloop command that executes the loop clause repeatedly until test clause returns a true nonzero result Because the test is executed after the loop clause the loop clause is always executed at least once Its syntax is DO loop clause UNTIL testclause END lb A DO A lb A DISP 3 A UNTIL A 12 END WHILE While Repeat End is a loop command that REPEAT repeatedly evaluates fest clause and executes loop clause e END sequence if the test is true Because the test clause is executed before the loop clause the loop clause is not executed if the test is initially false Its syntax is WHILE test clause REPEAT loop clause END 1 PA WHILE A lt 12 REPEAT 1 PA DISP 3 A END FOR TO STEP FOR name start expression TO end expression END STEP increment loop clause END FOR A 1 TO 12 STEP 1 DISE 3 END Note that the STEP parameter is optional If it is omitted a step value of 1 is assumed BREAK Terminates loop BREAK Programming 21 23 T a e
34. You can also directly type name of a CAS function when you are in ALPHA mode Note that in this section CAS functions available from the sot key menus in the Equation Writer are described CAS functions available from the MATH menu are described in CAS Functions on the MATH menu on page 14 45 When using CAS you should be aware that the required syntax will vary depending on whether you are applying the command to an expression or a function All CAS commands are designed to work with expressions that is they take expressions as arguments If you are going to use a Tuncfion for example F you need to specify an expression made from this function such as F x where x is the independent variable 14 9 4 NY ALGB menu COLLECT DEF _ 14 10 e hp40g book Page 10 Friday December 9 2005 1 03 AM For example suppose you have stored the expression x in and have defined the function F x as 2 Suppose now you want to calculate INTVX X You could e enter INTVX X directly or e enter INTVX or e enter INTVX F X Note that you can apply the command directly to an expression or to a variable that holds an expression the first two cases above But where you want to apply it to a defined function you need to specify the full function name F X as in the third case above Factors over the integers COLLECT combines like
35. Histogram width HWIDTH enables you to specify the width of a histogram bar This determines how many bars will fit in the display as well as how the data is distributed how many values each bar represents Histogram range HRNG enables you to specify the range of values for a set of histogram bars The range runs from the left edge of the leftmost bar to the right edge of the rightmost bar You can limit the range to exclude any values you suspect are outliers Plotting mark S1MARK through S5MARK enables you to specify one of 2VAR five symbols to use to plot each data set Press MITA to change the highlighted setting Connected points CONNECT on the second page when checkmarked 2VAR connects the data points as they are plotted The resulting line is not the regression curve The order of plotting is according to the ascending order of independent values 10 18 Statistics aplet e 0 4 P hp40g book Page 19 Friday December 9 2005 1 03 AM For instance the data set 1 1 3 9 4 16 2 4 would be plotted and traced in the order 1 1 2 4 3 9 4 16 Trouble shooting a plot If you have problems plotting check that you have the following The correct or EIFE menu label on Numeric view The correct fit regression model if the data set is two variable Only the data sets to compute or plot are ch
36. 4 Plot the graph 7 8 Solve aplet e e 0 zz gt e hp40g book Page 9 Friday December 9 2005 1 03 AM 5 Move the cursor near the positive right side intersection This cursor value will be an initial guess for T Press gt until the cursor is at the intersection The two points of 3 9 E1 30 MENU intersection show that there are two solutions for this equation However only positive values for X make sense so we want to find the solution for the intersection on the right side of the y axis 6 Return to the Numeric view SOLVE MUMERIC VIEH NUM E 7 3 TI 4 ENTER VALUE PRESS SOLVE EDIT INFO DEFN Note the T value is filled in with the position of the cursor from the Plot view e 7 Ensure that the 7 value is highlighted and solve the equation SOLVE NUMERIC y T EF A ENTER VALUE DR PRESS SOLVE EDIT IMFO f DEFM 0LVE Use this equation to solve for another variable such as velocity How fast must a body s initial velocity be in order for it to travel 50 m within 3 seconds Assume the same acceleration 4 m s Leave the last value of V as the initial guess 3 4 A SOLVE MUMERIC VIEH 5 amp 4 ENTER VALUE PRESS SOLVE ee Solve a
37. Select the fifth branch by pressing gt At this point the desired expression is in 2 the Equation Writer as shown at the right Suppose that you want to select the second and third branches that is First press 4 4 This selects 3 the second term Now press gt This key combination enables 1 1 you to select two contiguous 2 RME 5 branches the one already selected and the one to the right of it If you want you can evaluate the selected part by 1 Ja 1 pressing ENTER The result 2 5 is shown at the right Suppose now you want to perform the partial calculation 1 1 A Because the two terms in this partial calculation are not contiguous that is side by side you must first perform a permutation so that they are side by side To do this press This exchanges the selected element with its neighbour to E ii the left The result is shown at the right Now press gt SHIFT gt to select just the branches you are interested in 15 9 Z e hp40g book Page 10 Friday December 9 2005 1 03 AM Pressing produces the result of the partial zm calculation 12 Summing up Pressing gt enables you to select the current element and its neighbour to the right 4 enables you to exchange the selected element with its neig
38. nn Fli n 1 EAT Function aplet an zz gt e hp40g book Page 3 Friday December 9 2005 1 03 AM Change the scale Trace a graph Function aplet You can change the scale to see more or less of your graphs In this example choose Auto Scale See VIEWS menu options on page 2 13 for a description of Auto Scale VIEWS Select Auto fgg me vpqPlot Detail scale Ha vFz Plot Table Overlay Plot d Fe Trace the linear function lt 6 times 7 6 FICA 1 6 HEHU Note By default the tracer is active Jump from the linear function to the quadratic function HEN Fa 3 7 MEM 3 3 4 Y e hp40g book Page 4 Friday December 9 2005 1 03 AM Analyse graph 9 Display the Plot view menu with FCN mium functions ZOOM TRACE GOTO FCM HEH From the Plot view menu you can use the functions on the FCN menu to find roots intersections slopes and areas for a function defined in the Function aplet and any Function based aplets The FCN functions act on the currently selected graph See FCN functions on page 3 10 for further information To find a root ofthe 10 Move the cursor to the graph of the quadratic quadratic function equation by pressing t
39. the CMDS menu SRIFT CMDs in the matrix category e See Matrix commands on page 21 24 for details of the matrix commands available for use in programming Functions differ from commands in that a function can be used in an expression Commands cannot be used in an expression Argument conventions For row or column supply the number of the row counting from the top starting with 1 or the number of the column counting from the left starting with 1 The argument matrix can refer to either a vector or a matrix Matrix functions COLNORM Column Norm Finds the maximum value over all columns of the sums of the absolute values of all elements in a column COLNORM matrix 18 10 Matrices e 0 NY P hp40g book Page 11 COND CROSS DET DOT EIGENVAL EIGENVV IDENMAT INVERSE LQ LSQ Matrices Friday December 9 2005 1 03 AM Condition Number Finds the 1 norm column norm of a square matrix coND matrix Cross Product of vector with vector2 CROSS vectorl vector2 Determinant of a square matrix DET matrix Dot Product of two arrays matrix matrix2 DOT matrix 1 matrix2 Displays the eigenvalues in vector form for matrix EIGENVAL matrix Eigenvectors and Eigenvalues for a square matrix Displays a list of two arrays The first contains the
40. 1 3 Sas Sor 1 cos 3 x 1 cos x Example 3 Typing THIN ACOS 1X2 gives 2 cos 2 x Simplify using sin x cos x 1 TRIG has as an argument a trigonometric expression TRIG simplifies this expression using the identity sin x cos x 1 14 43 T e P NY 4 TRIGCOS TRIGSIN TRIGTAN 14 44 hp40g book Page 44 Friday December 9 2005 1 03 AM Typing TRIG SING s COSO sd gives 2 Simplify using the cosines TRIGCOS has as an argument a trigonometric expression TRIGCOS simplifies this expression using the identity sin x cos x 1 to rewrite it in terms of cosines Typing TRIGCOS SIN X COS X 1 gives cos cos x dq 2 Simplify using the sines TRIGSIN has as an argument a trigonometric expression TRIGSIN simplifies this expression using the identity sin x cos x 1 to rewrite it in terms of sines Typing TRIGOINOSINCEe COS 20 33 gives sin x sin x 2 Simplify using the tangents TRIGTAN has as an argument a trigonometric expression TRIGTAN simplifies this expression using the identity sin x cos x 1 to rewrite it in terms of tangents Typing PRIGTAN GIN OS gives 2 tan x 3 tan x 2 tan x 2 tan x Computer Algebra System CAS am ad T ZN
41. F LEhITIHEH IEEhHDIFECV bd MTS 2 EF n CREATE Real matrix M3 1 vector M4 Complex matrix Me Complex vector EnITIIHE In this example the matrix you created is listed as M2 6 Return to HOME and enter the calculation to left multiply the constants vector by the inverse of the coefficients matrix ALPHA M2 SHIFT x ALPHA M1 The result is a vector of the M2 x1 25 31 21 solutions x 2 and z 2 An alternative method is to use the RREF function See RREF on page 18 12 an STA 18 9 GIN e hp40g book Page 10 Friday December 9 2005 1 03 AM Matrix functions and commands About functions Functions can be used in any aplet or in HOME They are listed in the MATH menu under the Matrix category They can be used in mathematical expressions primarily in HOME as well as in programs Functions always produce and display a result They do not change any stored variables such as a matrix variable Functions have arguments that are enclosed in parentheses and separated by commas for example CROSS vector 1 vector2 The matrix input can be either a matrix variable name such as M1 or the actual matrix data inside brackets For example CROSSAML Di2 Jx About commands Matrix commands are listed
42. HHGLE MEASURE F adiansz MUMEER FORMAT F t ion DECIMAL MARK Dot ENTER DECIMAL PLACES TD USE 4 Enter the precision value that you want to use and press HA to set the precision Press to return to HOME See Setting fraction precision below for 3 information Setting fraction The fraction precision setting determines the precision in precision which the HP 4095 converts a decimal value to a fraction The greater the precision value that is set the closer the fraction is to the decimal value By choosing a precision of 1 you are saying that the fraction only has to match 0 234 to at least 1 decimal place 3 13 is 0 23076 The fractions used are found using the technique of continued fractions When converting recurring decimals this can be important For example at precision 6 the decimal 0 6666 becomes 3333 5000 6666 10000 whereas at precision 3 0 6666 becomes 2 3 which is probably what you would want For example when converting 234 to a fraction the precision value has the following effect _ 1 26 Getting started e NZ 2 Z gt e hp40g book Page 27 Friday December 9 2005 1 03 AM Precision set to 1 FUNCTION 2914 3713 TOF e Precision set to 2 PT RAD FUNCTION c2 3713
43. Sets the second menu option This option 4 runs program EXP MET then returns to view 1 Plot view My ERDEVACUSUEXPIMEZ 23 Sets the third menu option This option runs the program EXP MEA then returns to view 3 the NUM view rr hrs 44 EXP SV 0 This line specifies that the program to set the View menu this program is transferred with the aplet The space character between the first set of quotes in the trio specifies that no menu option appears for the entry You do not need to transfer this program with the aplet but it allows users to modify the aplet s menu if they want to 21 12 Programming e Na Na Z gt e hp40g book Page 13 Friday December 9 2005 1 03 AM HUS EXP ANG Os The program EXP ANG is a small routine that is called by other programs that the aplet uses This entry specifies that the program EXP ANG is transferred when the aplet is transferred but the space in the first quotes ensures that no entry appears on the menu Cart 7s VEAP This specifies the Start menu option The program that is associated with this entry EXP S runs automatically when you start the aplet Because this menu option specifies view 7 the VIEWS menu opens when you start the aplet You only need to run this program once to configure your aplet s VIEWS menu Once the aplet s VIEWS menu is configured it rema
44. To invert a matrix You can invert a square matrix in HOME by typing the matrix or its variable name and pressing x ENTER Or you can use the matrix INVERSE command Enter INVERSE matrixname in HOME and press ENTER 2 To negate each You can change the sign of each element in a matrix by element pressing before the matrix name Solving systems of linear equations Example Solve the following linear system 2x 3y 4z 5 xty z 7 4x yt2z 1 1 Open the Matrix Sup sawn E d CREATE HEH ERROR catalog and create a Mz Real matrix T veclor M2 ERNST Ma Da MS Complex vector y SHIFT MATRIX REJ fO ok EA 2 Create the vector of the mr constants in the linear 3 system gt PEDIT IMS Got eG 18 8 Matrices e 0 4 P hp40g book Page 9 Friday December 9 2005 1 03 AM Matrices 3 Return to the Matrix Catalog SHIFT MATRIX In this example the vector you created is listed as M1 4 Create a new matrix v EH Select Real matrix 5 Enter the equation coefficients 2 ENTER 3 ENTER 4 ENTER v 1 ENTER 1 ENTER C3 1 ENTER 4 ENTER 1 CENTER 2 ENTER MATRIX CATALOG 1 3 REAL VECTOR Mz 151 REAL MRTRIS EE MS 151 REAL MATRIX 0 Md 1 1 REAL MATRIH EE MS REAL MRTRIS
45. e hp40g book Page 28 Friday December 9 2005 1 03 AM Typing TAYLORO 22 P xp SIN P x TAN Q X SIN Q X gives jb SS 122251823 PESO E od 4 0 th order means that the numerator and denominator are expanded to the 4th relative order here the 5th absolute order for the numerator and for the denominator which is given in the end the 2nd order 5 3 seeing that the exponent of the denominator is 3 WO Truncate at order n 1 TRUNC enables you to truncate a polynomial at a given order used to perform limited expansions TRUNC has two arguments a polynomial and X TRUNC returns the polynomial truncated at order n 1 e that is the returned polynomial has no terms with exponents 2n Typing 1 2 3 4 TRUNC 1 X gives Ax box 3x I The REWRI menu contains functions that enable you to rewrite an expression in another form Distributivity of multiplication DISTRIB enables you to apply the distributivity of multiplication in respect to addition in a single instance DISTRIB enables you when you apply it several times to carry out the distributivity step by step Computer Algebra System CAS T e e hp40g book Page 29 Friday December 9 2005 1 03 AM NY Typing DISTRIB X 1 X42 X 3 gives 2 3 1 2
46. eFl n3 H REP EDIT le CHE Aplets and their views 2 3 PN 0 NZ e hp40g book Page 4 Friday December 9 2005 In HOME SYMB view keys 2 4 1 03 AM You can also evaluate any expression in HOME by entering it into the edit line and pressing ENTER For example define F4 as below In HOME type F4 9 and press ENTER This evaluates the expression substituting 9 in place of X into F4 FIMNCTION SYMEOLIC MIEL F1CKISARKE F2CX I FSCXISASKE B 4 1 EDIT le CHE PARAD TOF FUNCTION 262 The following table details the menu keys that you use to work with the Symbolic view Key EDIT EWAL Meaning Copies the highlighted expression to the edit line for editing Press when done Checks unchecks the current expression or set of expressions Only checked expression s are evaluated in the Plot and Numeric views Enters the independent variable in the Function aplet Or you can use the key on the keyboard Enters the independent variable in the Parametric aplet Or you can use the key on the keyboard Enters the independent variable in the Polar aplet Or you can use the key on the keyboard Enters the independent variable in the Sequence aplet Or you can use the key on the keyboard D
47. hp40g book Page 49 Friday December 9 2005 1 03 AM 48 1 0 30 0 1 1 18 1 1 1 12 1 2 1 6 2 3 2 Result 6 2 3 written to the Equation Writer The intermediate steps shown are the combination of lines For example to get line 2 take L n q L n 1 where q is the Euclidean quotient of the integers at the beginning of the vector these integers being the sequence of remainders Returns the integer quotient of the Euclidean division of two integers Example Typing IQUOT 148 5 gives 29 In step by step mode the TE 148735 division is carried out as if eee f 45 29 in longhand 5 then causes 29 to be written to the Equation Writer Returns the integer remainder from the Euclidean division of two integers Example 1 Typing IREMAINDER 148 5 gives 3 14 49 an NY ISPRIME LCM MOD 14 50 e hp40g book Page 50 Friday December 9 2005 1 03 AM IREMAINDER works with integers and with Gaussian integers This is what distinguishes it from MOD Example 2 Typing IREMAINDER 2 3 1 1 i gives Returns a value indicating whether an integer is a prime number ISPRIME n returns 1 TRUE if n is a prime or pseudo prime and O FALSE if n is not prime Definition For numbers less than 10 pseudo prime and prime mean the same thing For numbe
48. 2 the H1 definition and replace the frequency s 1 EMTER AMPLE value of 1 with the ne ES ee name C2 2 6 Return to the numeric view NUM 7 Enter the frequency data shown in the above table gt 5 ENTER 3 ENTER 8 ENTER 2 ENTER 1 CENTER 8 Display the computed statistics E The mean height is l r 631578947 approximately A 167 63cm 9 Setup a histogram plot for the data DIM SHIFT SETUP PLOT SE STATISTICS PLOT SETUP STATPLOT Hist HHIDTH 5 Enter set UD information VEMG th appropriate to your 160 155 EMTER Finsirilri HIETOGRAM BLUE IEDIT PAsE 10 Plot a histogram of the data Hl 160 165 5 HEHU Save data The data that you enter is automatically saved When you are finished entering data values you can press a key for another Statistics view like or you can switch to another aplet or HOME 10 10 Statistics aplet e 0 SN e hp40g book Page 11 Friday December 9 2005 1 03 AM Edit a data set In the Numeric view of the Statistics aplet highlight the data value to change Type a new value and press Or press to copy the value to the edit line for modification Press after modifying the value on the edit line Delete data To delete a single data item highlight it
49. EXP ME2 PROGRAM 1 HumSt art S RES MSGBOR Humeric values zet FUH use to configure the angle iF ER 3 AHGLE ERHSLIEE 5 Degrees ERadianz s Gradz 34 sets up the initial function that the aplet plots In this section we will begin by configuring the VIEWS menu by using the SETVIEWS command We will then create the helper programs called by the VIEWS menu which will do the actual work an 21 11 X iG e hp40g book Page 12 Friday December 9 2005 1 03 AM 6 Open the Program catalog and create a program named EXP SV Include the following code in the program Each entry line after the command SETVIEWS is a trio that consists of a VIEWS menu text line a space indicates none a program name and a number that defines the view to go to after the program has run its course All programs listed here will transfer with an aplet when the aplet is transferred SELVIENS Sets the first menu option to be Auto scale This is the fourth standard Function aplet view menu option and the 18 Auto scale specifies that it is to be included in the new menu The empty quotes will ensure that the old name of Auto scale appears on the new menu See SETVIEWS on page 21 14 My Entryl EXP ME1 1
50. Linear Solver aplet 8 1 e 0 zz gt e hp40g book Page 2 Friday December 9 2005 1 03 AM example in the previous step To solve a three equation set press EREN Now the input form displays three equations If the three equation input form is displayed and you want to solve a two equation set press In this example we are going to solve the following equation set 6x 9y 6z 5 7x 10y 8z 10 6x 4y 6 Hence we need the three equation input form Define and 3 You define the equations you want to solve by solve the entering the co efficienfs of each variable in each equation and constant term Notice that cursor equations is immediately positioned at the co efficient of x in the first equation Enter that co efficient and press WA or O ENTER lt 4 The cursor moves to next co efficient Enter that co efficient press BIB or ENTER and continue doing likewise until you have defined all the equations Note you can enter the name of a variable for any co efficient or constant Press ALPHA and begin entering the name The menu key appears Press that key to lock alphabetic entry mode Press it again to cancel the lock Once you have entered LIMERR EQUATION enough values for the Ba 9 6 zsh solver to be able to i generate solutions V i amp amp GGE 227 323377 those so
51. Note that the INTVX command is on the IIl menu The simplified result got by pressing ENTER twice is e shown at the right Solution 4 2 To find the limit of ne when n 00 enter the expression at the right Note that the 1im command is on the IIl 5 menu The infinity sign can H m be selected from the eee character map opened by pressing VARS Pressing once after selecting the infinity sign adds a character to the infinity sign Select the entire expression ans press to get the result which is E 2 e Step by Step Examples 16 25 e NZ SZ e hp40g book Page 26 Friday December 9 2005 1 03 AM NOTE The variable vx is now set to N Reset it to X by pressing to display CAS MODES screen and change the INDEP VAR setting To check the result we can say that jug lim x0 x and that therefore or simplifying 2 lim n 2 gt o If the limit L of exists as n approaches in the inequalities in solution 2 above we get NIU IN Part 2 1 Show that for every x in 0 2 24S 1 2 x42 2 Find the value of 2 _ 2473 J xg 3 Show that for every x in 0 2 5 Show that u is convergent and find its limit L 16 26 Step by Step Examples
52. Press to get the result at the right Finally define the result as Y t in the same way that you defined X t by firstly adding Y t to the expression as shown at the me 2 2 3 IHC right and then applying the DEF command We have now found the coordinates of M in terms of t To find an axis of symmetry for calculate x t and y t by typing ALPHA X 0 ACPA f Press gt to highlight the expression Then press to produce the result at the right In other words x t x t Now type ALPHA Y 0 ALPHA t O Press gt to highlight the expression an COSCE 2 A OSIE Step by Step Examples Z gt e hp40g book Page 17 Friday December 9 2005 1 03 AM Then press to produce the result at the right SIHG zHSING In other words y t It M x t y 2 is part of T then M_ x t y 2 is also part of Since M are symmetrical with respect to the x axis we can deduce that the x axis is an axis of symmetry for Part 3 Calculate x t by typing ALPHA X 0 ALPHA f Press gt gt to highlight the expression Pressing returns the e result at the right SIH t 2 8IH t Press to simplify the result
53. e In HOME or in the program editor use to store 4 an object a variable In CAS use the STORE command on the menu to store a value in a variable The key displays a menu that contains all the available variables Pressing while you are in HOME displays the names of the variables defined in HOME and in the Aplets Pressing while you are in the Equation Writer displays the names of the variables defined in CAS as explained on page 15 18 Predefined CAS variables e VX contains the name of the current symbolic variable Generally this is X so you should not use X as the name of a numeric variable Nor should you erase the contents of X with the UNASSIGN command on the menu after having done a symbolic calculation EPS contains the value of epsilon used in the EPSXO command 15 16 Equation Writer e 0 Z gt e hp40g book Page 17 Friday December 9 2005 1 03 AM MODULO contains the value of p for performing symbolic calculations in Z pZ or in Z pZ X You can change the value of p either with the MODSTO command on the MODULAR menu by typing for example MODSTO n to give p a value of n or from CAS MODES screen see page 14 5 PERIOD must contain the period of a function before you can find its Fourier coefficients PRIMIT contains the primitive of the last integrated function REA
54. gt 9 4 hp40g book Page 6 Friday December 9 2005 1 03 AM To import a graphics variable 1 2 3 4 5 The notepad You can copy the contents of a graphics variable into the Sketch view of an aplet Open the Sketch view of the aplet SHiFT SKETCH The graphic will be copied here Press UIS Highlight Graphic then press gt and highlight the name of the variable G1 etc Press DB to recall the contents of the graphics variable Move the box to where you would like to copy the graphic then press MA Subject to available memory you can store as many notes as you want in the Notepad sHiFT NOTEPAD These notes are independent of any aplet The Notepad catalog lists the existing entries by name lt does not include notes that were created in aplets Note views but these can be imported See To import a note on page 20 8 To create a note in 1 the Notepad 3 20 6 Display the Notepad catalog NOTEPAD Create a new note Enter a name for your note EB MYNOTE DIS an MOTE CATALOG 5 ITrHOTEs EMTER FOR MOTE p Gea LPS Z PIER NEL 1 LIRE CANEL O WOTE Notes and sketches Notepad Catalog keys Notes and sket
55. lt ho Hiu gt m Inputs The inputs are Field name Definition x Sample mean n Sample size LO Hypothetical population mean G Population standard deviation Signiticance level Inference aplet T a e Na e hp40g book Page 9 Friday December 9 2005 1 03 AM NY Results The results are Result Description Test Z Z test statistic Prob Probability associated with the Z Test statistic Critical Z Boundary values of Z associated with the level that you supplied Critical x Boundary values of x required by the a value that you supplied Two Sample Z Test Menu name Z Test ul u2 On the basis of two samples each from a separate population this test measures the strength of the evidence 4 tor a selected hypothesis against null hypothesis The null hypothesis is that the mean of the two populations are equal Ho ul u2 You select one of the following alternative hypotheses against which to test the null hypothesis HiH I Hiu gt ho H u 6 Inputs The inputs are Field name Definition zd Sample 1 mean x2 Sample 2 mean ni Sample 1 size n2 Sample 2 size o1 Population 1 standard deviation Inference aplet 11 9 E a PN NZ e hp40g book Page 10 Friday Dec
56. 13 13 T PN NZ e PN NY UTPT hp40g book Page 14 Friday December 9 2005 1 03 AM Upper Tail Student s t Probability given degrees of freedom evaluated at value Returns the probability that the Student s t random variable is greater than value UTPT degrees value Real number functions CEILING DEG RAD FLOOR FNROOT FRAC 13 14 Some real number functions can also take complex argumenis Smallest integer greater than or equal to value CEILING value Examples CEILING 3 2 returns 4 CEILING 3 2 returns 3 Degrees to radians Converts value from Degrees angle format to Radians angle format DEG gt RAD value Example DEG RAD 180 returns 3 14159265359 the value of Greatest integer less than or equal to value FLOOR value Example FLOOR 3 2 returns 4 Function rootfinder like the Solve aplet Finds the value for the given variable at which expression most nearly evaluates to zero Uses guess as initial estimate FNROOT expression variable guess Example FNROOT M 9 8 600 1 M 1 returns 61 2244897959 Fractional part FRAC value Example FRAC 23 2 returns 2 Using mathematical functions am ad T NY P hp40g book Page 15 Friday December 9 2005 1 03 AM HMS HMS INT MAN
57. NY e hp40g book Page 45 Friday December 9 2005 1 03 AM CAS Functions on the MATH menu Algebra menu Complex menu i ABS ARG CONJ DROITE Computer Algebra System CAS When you are in the Equation Writer and press CAS FUNCTIONS q P Algebra COLLECT a menu of Complex Sp Constant ERSPHHD additional CAS tunctions Pu Si available to you is displayed Many of the functions in this menu match the functions available from the softkey menus in the Equation Writer but there are other functions that are only available from this menu This section describes CAS functions that are available when you press MATH in the Equation Writer grouped by main menu name All the functions on this menu are also available on the menu in the Equation Writer See ALGB menu on page 14 10 for a description of these functions Inserts i 1 Determines the absolute value of the argument Example Typing ABS 7 4i yields 65 as does ABS 7 4i See ARG on page 13 7 See CONJ on page 13 7 DROITE returns the equation of the line through the Cartesian points 21 22 It takes two complex numbers 2 and z as arguments Example Typing DROITE 1 2 0 1 or DROITE 1 2 1 i 14 45 4 GIN e hp40g book Page 46 Friday December 9 2005 1 03 AM returns
58. To create additional aplets of the same type you must give the current aplet a new name The advantage of storing an aplet is to allow you to keep a copy of a working environment for later use The aplet library is where you go to manage your aplets Press APLET Highlight using the arrow keys the name of the aplet you want to act on In the aplet library press Select the sorting scheme and press ENTER Chronologically produces a chronological order based on the date an aplet was last used The last used aplet appears first and so on Alphabetically produces an alphabetical order by aplet name You cannot delete a built in aplet You can only clear its data and reset its default settings To delete a customized aplet open the aplet library highlight the aplet to be deleted and press DEL To delete all custom aplets press CLEAR Extending aplets an iG e hp40g book Page 1 Friday December 9 2005 1 03 AM Reference information Glossary aplet A small application limited to one topic The built in aplet types are Function Parametric Polar Sequence Solve Statistics Inference Finance Trig Explorer Quad Explorer Linear Explorer and Triangle Solve An aplet can be filled with the data and solutions for a specitic problem It is reusable like a program but easier to use and it records all your settings and
59. XS 5 gives 3 5 1 x NOTE the calculator displays a request to change to increasing powers mode respond yes FOURIER Fourier coefficients FOURIER has two parameters an expression f x and a whole number N FOURIER returns the Fourier coefficient cy of f x considered to be a function defined over interval O T e Computer Algebra System CAS 14 17 T p am ad X iG e hp40g book Page 18 Friday December 9 2005 1 03 AM IBP 14 18 and with period T T being equal to the contents of the variable PERIOD It f x is a discrete series then ius 2iNxt Y ce N Example Determine the Fourier coefficients of a periodic function f with period 2x and defined over interval 0 27 by 2 Typing STORE 27 PERIOD FOURIER X N The calculator does not know that N is a whole number so you have to replace EXP 2 i N n with 1 and then simplify the expression We get 2 i N t2 2 So if N 0 then CN c c N Typing FOURIER X 0 gives 2 4 3 so if N 0 then 4 3 Co Partial integration IBP has two parameters an expression of the form u x and v x Computer Algebra System CAS am ad T 4 INTVX Computer Algebra System CAS
60. 0 2 3 7 lt 2 Show that for every real x 0 2 x lt g x e lt x lt ears 3 After integration show that 2 2 3 7 7 ne 4 Using X lim 1 4 x0 x show that if has a limit L as n approaches infinity then lA lA NIN am ad T SZ gt e hp40g book Page 23 Friday December 9 2005 1 03 AM Solution 1 Start by defining G X DEF ALPHA ALPHA X gt DE 2 ALPHA X s X 2 Now press ENTER Press and gt to select the numerator and denominator and then EK press DEL This leaves G X displayed Finally apply the TABVAR function EIE TABVAR HE and press a number of times until the variation table appears shown above ariation table 2 tm eTtTeT2F The first line of the variation table gives the sign of g x according to x and the second line the variations of g x Note that for TABVAR the function is always called F We can deduce then that g x increases over O 2 IF you had been in step by step mode you would have obtained _ 2 X 3 F AFD Press to get the result at the right Fis Eit
61. 2 cascc 1TS8IB E 3 You can now define the x i function x t by invoking DEF Note You will first need to type X1 t then exchange X1 t with the previous expression To do this highlight X1 t and type TET 2 cos Cto 1 isnt Now select the entire expression and apply the DEF command to it DEF x1Ce3z C2 casco 1 Finally press to finish the definition e Step by Step Examples 16 17 4 4 Part 4 Part 5 16 18 P hp40g book Page 18 Friday December 9 2005 1 03 AM To calculate y t begin by typing DERVX Y Pressing ENTER returns Press again to simplify the result aC COSTE ost 1 Select FACTOR and press EnSrt 11TEE STt 1 You can now define the function y t in the same way that you defined x t To show the variations of x t and y t we will trace x t and y t on the same graph The independent variable must be t which it should be as a result of the previous calculations You can check this by pressing Type X t in the Equation Writer and press ENTER The corresponding expression is displayed Now press select Function press Bid select F1 as the destination and press Bis Now do the same thing with Y t making F2 the destination To graph the functions qui
62. 2 s1 2 N7 2 Encloses an expression that should not be evaluated numerically QUOTE expression Examples QUOTE SIN 45 F1 stores the expression SIN 45 rather than the value of SIN 45 Another method is to enclose the expression in single quotes For example 3 2 F1 X puts the expression X 3 2 X into F1 X in the Function aplet Evaluates expression where each given variable is set to the given value Defines numeric evaluation of a symbolic expression expression variable 1 value1 variable2 value2 Example 3 X 1 X 3 returns 12 Using mathematical functions 4 e hp40g book Page 19 Friday December 9 2005 1 03 AM NY Test functions The test functions are logical operators that always return either a 1 true or a false Less than Returns 1 if true O if false value 1 value2 Less than or equal to Returns 1 if true O if false value 1x value2 Equals logical test Returns 1 if true O if false value 1 value2 Not equal to Returns 1 if true O if false value 1z value2 gt Greater than Returns 1 if true O if false value 1 gt value2 e gt Greater than or equal to Returns 1 if true O if false 4 value 1 gt value2 AND Compares value and value2 Returns 1 if they are both non zero otherwise returns 0 value AND value2 IFTE IF expression is true do the t
63. 2005 1 03 AM COSH SINH TANH ALOG EXP EXPM1 LNP 1 List functions Loop functions ITERATE 13 10 Hyperbolic cosine COSH value Hyperbolic sine SINH value Hyperbolic tangent TANH value Antilogarithm exponential This is more accurate than 10 x due to limitations of the power function ALOG value Natural exponential This is more accurate than e due to limitations of the power function EX P value Exponent minus 1 e 1 This is more accurate than EXP when x is close to zero EXPM1 value Natural log plus 1 In x This is more accurate than the natural logarithm function when x is close to zero LNP1 value These functions work on list data See List functions on page 19 6 The loop functions display a result after evaluating an expression a given number of times Repeatedly for times evaluates an expression in terms of variable The value for variable is updated each time starting with initialvalue ITERATE expression variable initialvalue times Example ITERATE X X 2 3 returns 256 Using mathematical functions am a T a 4 P hp40g book Page 11 Friday December 9 2005 1 03 AM RECURSE Matrix functions Provides a method of defining a sequence without using the Symbolic view of the Sequence aplet If used with where RECURSE will step
64. 2005 1 26 AM The cursor highlight is MODES in the first field Angle lmmsLE mensure ETE HERE MUMEER FORMAT Fraction 4 Measure DECIMAL MARK Dott 3 CHOOSE ANGLE MEASURE 2 Press HEZE to display a HOME MODES O list of choices aa Dea rees 4 a Grads CHOOSE AMGLE MEASURE CAMEL 3 Press A to select HOME MODES AMGLE MEASURE K jegr Degrees and press MUMEER FORMAT Fr DECIMAL MARK Dot gt The angle measure changes to degrees CHOOSE ANGLE MEASURE ee 1 4 Press to return to HOME HINT Whenever an input form has a list of choices for a field you can press to cycle through them instead of using Aplets E lessons Aplets are the application environments where you explore different classes of mathematical operations You select the aplet that you want to work with Aplets come from a variety of sources Built in the HP 4095 initial purchase Aplefs created by saving existing aplets which have been modified with specific configurations See Creating new aplets based on existing aplets on page 22 1 e Downloaded from HP s Calculators web site Copied from another calculator Aplets are stored in the Aplet library See Aplet SE library on page 1 16 for Inference further inf Parametric Big urther information Polar AKE Sequenc
65. A and B When B has an inverse in Z pZ the result is A B simplified as Z pZ Typing DIVMOD 5 3 gives 6 Example 2 In Z pZ X the arguments are two polynomials A X and B X The result is a rational fraction A X B X simplified as Z pZ X Typing DIVMOD 2xX 5 5X 2X 3 gives E 4x 3 3x T3 EXPANDMOD Expand and simplify expressions in Z pZ or Z pZ X Example 1 In Z pZ the argument is an integer expression Typing EXPANDMOD 2 3 5 4 gives 0 Example 2 In Z pZ X the argument is a polynomial Typing EXPANDMOD 2X 12 5X 4 gives 3 x 5 x 5 x 4 14 52 Computer Algebra System CAS T a e e hp40g book Page 53 Friday December 9 2005 1 03 AM NY FACTORMOD Factors a polynomial in Z pZ X providing that p lt 97 p is prime and the order of the multiple factors is less than the modulo Example Typing FACTORMOD 3X 5X 5X 4 gives 3x 5 Q 6 GCDMOD Calculates the GCD of the two polynomials in Z pZ X Example Typing GCDMOD 2X 5 5X 2X 3 gives 1 a INVMOD Calculates the inverse of an integer in Z pZ Example Typing INVMOD 5 gives 5 since 5 5 25 1 mod 13 MODSTO Sets the value of the MODULO variable p Example Typing MODSTO 1 1 sets the value of p to 11 e Computer Algebra System CAS 14 5
66. Continued Engineering Displays result with an exponent that is a multiple of 3 and the specified number of significant digits beyond the first one Example 123 456E7 becomes 1 23E9 in Engineering 2 format Fraction Displays results as fractions based on the specified number of decimal places Examples 123 456789 becomes 123 in Fraction 2 format and 333 becomes 1 3 and 0 142857 becomes 1 7 See Using fractions on page 1 25 Mixed Fraction Displays results as mixed fractions based on the specified number of decimal places A mixed fraction has an integer part and a fractional part Examples 123 456789 becomes 123416 35 e in Fraction 2 format and 7 3 returns 4 2 1 3 See Using fractions page 1 25 Decimal Dot or Comma Displays a number Mark as 12456 98 Dot mode or as 12456 98 Comma mode Dot mode uses commas to separate elements in lists and matrices and to separate function arguments Comma mode uses periods dot as separators in these contexts Setting a mode This example demonstrates how to change the angle measure from the default mode radians to degrees for the current aplet The procedure is the same for changing number format and decimal mark modes 1 Press MODES to open the HOME MODES input form _ Getting started 1 11 e NZ zz B gt e chapter l fm Page 12 Friday December 9
67. December 9 2005 1 03 AM 13 Using mathematical functions Math functions The MATH menu Using mathematical functions The HP 40gs contains many math functions The functions are grouped in categories For example the Matrix category contains functions for manipulating matrices The Probability category shown as Prob on the MATH menu contains functions for working with probability To use a math function in HOME view you enter the function onto the command line and include the arguments in parentheses after the function You can also select a math function from the MATH menu Note that this chapter covers only the use of mathematical functions in HOME view The use of mathematical functions in CAS is described in Chapter14 Computer Algebra System CAS The MATH menu provides access to math functions physical constants and programming constants You can also access CAS commands The MATH menu is organized by category For each category of functions on the left there is a list of function names on the right The highlighted category is the See FUNCTIONS SERES 4 CEILING Stat Twao IDE ERHLI Symbolic FLOOR r Testz yi When you press MATH you see the menu list of Math categories in the left column and the corresponding functions of the highlighted category in the right column The menu key indicates that the MATH FUNCTIONS menu list
68. Function Parametric Polar Sequence NumType Function Parametric Polar Sequence NumZoom Function Parametric Polar Sequence StatMode Statistics 21 42 P hp40g book Page 42 Friday December 9 2005 1 03 AM Sets the starting value for a table in Numeric view From Num Setup enter a value for NUMSTART or In a program type n gt NumStart Sets the step size increment value for an independent variable in Numeric view From Num Setup enter a value for NUMSTEP or In a program type n gt NumStep where n gt 0 Sets the table format From Num Setup choose Automatic or Build Your Own or In a program type 0 NumType for Build Your Own 1 gt NumType for Automatic default Sets the zoom factor in the Numeric view From Num Setup type in a value for NUMZOOM or In a program type NumZoom where n gt 0 Enables you to choose between 1 variable and 2 variable statistics in the Statistics aplet Does not appear in the Plot Setup input form Corresponds to the ERES and FETTE menu keys in Numeric View In a program store the constant name or its number into the variable StatMode 1VAR 1 2VAR 2 Programming an 4 P hp40g book Page 43 Friday December 9 2005 1 03 AM Example IVAR b StatMode or 1 gt StatMode Note variables The following aplet variable is available i
69. GAMMA Returns the values of the T function at a given point The function is defined as DG dt e We have 4e 1 1 x 1 x Example 1 Typing GAMMA 5 gives 24 Example 2 Typing GAMMA 1 2 gives IABCUV IABCUV A B C returns U AND V such that AU BV C where A B and C are whole numbers C must be a multiple of GCD A B to obtain a solution 14 64 Computer Algebra System CAS T a e e hp40g book Page 65 Friday December 9 2005 1 03 AM NY Example Typing IABCUV 48 30 18 gives 6 AND 9 IBERNOULLI Returns the nth Bernoulli s number B n where t JE a Ta n n 0 Example Typing IBERNOULLI 6 gives B t ICHINREM Chinese Remainders ICHINREM A AND P B AND Q returns AND R where A and are whole numbers The numbers X C k R where k is an integer are such that X A mod P and X B mod Q A solution X always exists when P and Q are mutually prime GCD P Q 1 and in this case all the solutions are congruent modulo R Q Example Typing ICHINREM 7 AND 10 12 AND 15 gives 3 AND 30 ILAP LAP is the Laplace transform of a given expression The expression is the value of a function of the variable stored in VX e Computer Algebra System CAS 14 65 m
70. Scrolls through the display history Copies the highlighted expression to the position of the cursor in the edit line Displays the current expression in standard mathematical form Deletes the highlighted expression from the display history unless there is a cursor in the edit line Clears all lines of display history and CLEAR the edit line Clearing the Is a good habit to clear the display history SHIFT e display history CLEAR whenever you have finished working in HOME It saves calculator memory to clear the display history Remember that all your previous inputs and results are saved until you clear them Using fractions To work with fractions in HOME you set the number format to Fraction or Mixed Fraction as follows Setting Fraction 1 In HOME open the HOME MODES input form mode MODES HOME MODES ANGLE MEASURE HUMEEF FORMAT Standard DECIMAL MARK Dot 6 2 CHOOSE ANGLE MEASURE _ ia _ Getting started 1 25 e 0 Z gt e hp40g book Page 26 Friday December 9 2005 1 03 AM 2 Select Number Format press pig to display the options and highlight Fraction or Mixed Fraction anaE 17 Www Engineer in Mixed Fraction CHO O m 3 Press 819 to select the Number Format option then move to the precision value field Er gt HOME MODES
71. To use variables in You can use variables in calculations The calculator calculations substitutes the variable s value in the calculation 65 ALPHA A 251941 clear a va ria ble You can use the CLRVAR FUNCTION command to clear a 1 2 2 43 specified variable For example if you have FT List stored 1 2 3 4 in variable L1 entering CLRVAR 11 will clear L1 You can find the crRvAR command by pressing MATH and choosing the prompt category of commands Variables and memory management 17 3 e NZ Y e hp40g book Page 4 Friday December 9 2005 1 03 AM The VARS menu You use the VARS menu to access all variables in the calculator The VARS menu is organised by category For each variable category in the left column there is a list of variables in the right column You select a variable category and then select a variable in the category 1 Open the VARS menu 2 Use the arrow keys or press the alpha key of the first letter in the category to select a variable category For example to select the Matrix category press D Froaram 4 Note In this instance TTT e there is no need to press the ALPHA key 3 Move the highlight to the variables column gt 4 Use the arrow keys to select the variable that you want For example to select
72. Y X 1 2 Pressing simplifies this to Y X IM See IM on page 13 7 Specifies the negation of the argument RE See RE on page 13 8 IGN Determines the quotient of the argument divided by its modulus Example 74 4i Typing SIGN 7 4i or SIGN 7 4 yields Constant menu e I See Constants on page 13 8 oo Enters the sign for infinity Diff amp Int menu All the functions on this menu are also available on the EI menu in the Equation Writer See DIFF menu page 14 16 for a description of these functions Hyperb menu All the functions on this menu are described in Hyperbolic trigonometry on page 13 9 Integer menu Note that many integer functions also work with Gaussian integers a bi where a and b are integers 1446 Computer Algebra System CAS e NZ NY DIVIS EULER FACTOR GCD e hp40g book Page 47 Friday December 9 2005 1 03 AM Gives the divisors of an integer Example Typing DIVIS 12 gives 12 OR 6 OR 3 OR 4 OR 2 OR 1 Note DIVIS O returns OR 1 Returns the Euler index of a whole number The Euler index of n is the number of whole numbers less than n that are prime with n Example Typing EULER 2 1 gives 12 Explanation 2 4 5 7 8 10 11 13 15 16 17 19 is the set of whole numbers less than 21 and prime with 21 There are
73. e definitions amp T command An operation for use in programs T Commands can store results in variables but do not display results Arguments are separated by semi colons such as DISP expression line expression A number variable or algebraic expression numbers plus functions that produces a value function An operation possibly with arguments that returns a result It does not store results in variables The arguments must be enclosed in parentheses and separated with commas or periods in Comma mode such as CROSS matrix matrix2 HOME The basic starting point of the calculator Go to HOME to do calculations Library For aplet management to start save reset send and receive aplets R T 5 Y gt e hp40g book Page 2 Friday December 9 2005 list matrix menu fey menu keys note program sketch variable vector 1 03 AM A set of values separated by commas periods if the Decimal Mark mode is set to Comma and enclosed in braces Lists are commonly used to enter statistical data and to evaluate a function with multiple values Created and manipulated by the List editor and catalog A two dimensional array of values separated by commas periods if the Decimal Mark mode is set to Comma and enclosed in nested brackets Created and manipulated by the Matrix catalog and editor Vectors are al
74. eigenvectors and the second contains the eigenvalues EIGENVV matrix S Identity matrix Creates a square matrix of dimension size x size whose diagonal elements are 1 and off diagonal elements are zero IDENMAT size Inverts a square matrix real or complex INVERSE matrix LQ Factorization Factors an m x n matrix into three matrices m x n lowertrapezoidall n x n orthogonal m x m permutation LQ matrix Least Squares Displays the minimum norm least squares matrix or vector LSQ matrix 1 matrix2 18 11 T a e P PN NY LU MAKEMAT QR RANK ROWNORM RREF SCHUR SIZE 18 12 P hp40g book Page 12 Friday December 9 2005 1 03 AM LU Decomposition Factors a square matrix into three matrices lowertriangular uppertriangular permutation The uppertriangular has ones on its diagonal LU matrix Make Matrix Creates a matrix of dimension rows x columns using expression to calculate each element If expression contains the variables and J then the calculation for each element substitutes the current row number for and the current column number for J MAKEMAT expression rows columns Example MAKEMAT 0 3 3 returns a 3x3 zero matrix LO 0 QR Factorization Factors an mxn matrix into three matrices mxm orthogonal mxn uppertrapezoidall nxn p
75. gt e hp40g book Page 12 Friday December 9 2005 1 03 AM Y Zoom In Y Zoom In Now un zoom ZOOM TRACE GOTO FCM HEHU Y Zoom Out Ele Y Zoom Out WA 200M GOTO CEFN Zoom Square Square MA ETS En 0 To box zoom The Box Zoom option lets you draw a box around the e area you want to zoom in on by selecting the endpoints amp of one diagonal of the zoom rectangle 1 If necessary press ERT to turn on the menu key labels Press and select Box Position the cursor on one corner of the rectangle Press MA 4 Use the cursor keys etc to drag to the opposite corner SELECT ECDMD CORNER CT P THE 5 Press W4 to zoom in on the boxed area 2 12 Aplets and their views e 0 Z e hp40g book Page 13 Friday December 9 2005 1 03 AM To set zoom factors In the Plot view press mam Press Select Set Factors and press BIB w qo Enter the zoom factors There is one zoom factor for the horizontal scale xzooM and one for the vertical scale Y ZOOM Zooming out multiplies the scale by the factor so that a greater scale distance appears on the screen Zooming in divides the scale by the factor so that a shorter scale distance
76. hp40g book Page 7 Friday December 9 2005 1 03 AM Calculating Amortizations Amortization calculations which also use the TVM variables determine the amounts applied towards principal and interest in a payment or series of payments To calculate amortizations 1 Start the Finance Solver as indicated at the beginning of this section 2 Set the following TVM variables a Number of payments per year P YR b Payment at beginning or end of periods 3 Store values for TVM variables I YR PV PMT and FV which define the payment schedule 4 Press the soft menu key and enter the number of payments to amortize in this batch 5 Press the soft menu key to amortize a batch of payments The calculator will provide for you the amount applied to interest to principal and the remaining balance after this set of payments have been amortized Example 3 Amortization for home mortgage For the data of Example 2 above find the amortization of the loan after the first 10 years 12x10 120 payments Pressing the soft menu key produces the screen to the left Enter 120 in the PAYMENTS field and press the soft menu key to produce the results shown to the right INTEREST INTEREZT EnLnhrE EnLhhrE 127 164 13 ENTER MD OF PHYMENTS TO AMORT a EST ee To continue amortizing the loan 1 Press the soft menu key to store the new balance after the previous amortiza
77. rather than a circle without changing the equation because the changed value of TSTEP ensures that points being plotted are 120 apart instead of nearly continuous You are able to explore the graph using trace zoom split screen and scaling functionality available in the Function aplet See Exploring the graph on page 2 7 for further information Display the table of values NUM You can highlight a tvalue type in a EE replacement value and see the table jump to that value You can also zoom in or zoom out on any volue in the table build your own table and split screen functionality available in the Function aplet See Exploring the table of numbers on page 2 17 for further information 43 e 0 X iG e hp40g book Page 4 Friday December 9 2005 1 03 AM T an ad e GIN e hp40g book Page 1 Friday December 9 2005 1 03 AM Polar aplet Getting started with the Polar aplet Open the Polar 1 Open the Polar aplet aplet elect Polar Like the Function aplet the Polar aplet opens F CH 7 in the Symbolic view IEDIT ICHEL HOH L EvAL Define the 2 Define the polar equation r 2 cos 0 2 cos 6 _ expression 2 2 D POLAR YMEOLIC WRI
78. symbolic form rather than manipulating approximations of the numerical quantities represented by those symbols In other words a CAS works in exact mode giving you intinite precision On the other hand non CAS calculations such as those performed in HOME view or by an aplet are numerical calculations and are limited by the precision of the calculator to 107 in the case of the HP 40gs For example with Standard as your numerical format 1 2 1 6 returns 0 6666666666667 if you are working in the HOME screen however 1 2 1 6 returns 2 3 if you are working with CAS HOME calculations are restricted to approximate or numeric mode while CAS calculations always work in exact mode unless you specifically change the default CAS modes Each mode has advantages and disadvantages For example in exact mode there is no rounding error but some calculations will take much longer to complete and require more memory than equivalent calculations in numeric mode Performing symbolic calculations You perform CAS calculations with a special tool known as the Equation Writer Some computer algebra operations can also be done in the HOME screen as long as you take certain precautions see Using CAS functions in HOME on page 14 7 Moreover some computer algebra operations can only be done in the HOME screen for example symbolic linear algebra Computer Algebra System CAS 14 1 am ad
79. 03 AM Example Typing SIGMA X X gives X because X 1 X2 X XI SIGMAVX Returns the discrete antiderivative of the input function that is a function G that satisfies the relation G x 1 G x f x SIGMAVX has as its argument a function f of the current variable VX Example Typing SIGMAVX X gives 2x 3x7 x e c m because 1 3 x4 1 1 2x 3x x 6 STURMAB Returns the number of zeros of P in a where Pisa polynomial and a and b are numbers Example 1 Typing STURMAB X X 2 2 0 gives Example 2 Typing STURMAB X X3 2 2 1 gives 3 0 Computer Algebra System CAS 14 69 e P a TSIMP VER 14 70 e hp40g book Page 70 Friday December 9 2005 1 03 AM Simplifies a given expression by rewriting it as a function of complex exponentials and then reducing the number of variables enabling complex mode in the process Example Typing SIN 3X SIN 7X SIMPL SIN SX gives EXP i x 1 EXP x Returns the version number of your CAS Example Typing VER might give 4 20050219 This particular result means that you have a version 4 CAS dated 19 February 2005 Note that this is not the same as VERSION which returns the version of the calculator s ROM Computer Algebra System CAS am ad
80. 1 select the entire expression and press ENTER you obtain 1 An infix function is one that is typed between its arguments For example AND and MOD are infix functions You can either type them in Alpha mode and then enter their arguments or select them from a CAS menu or by pressing an appropriate key provided that you have already written and selected the first argument You move from one argument to the other by pressing gt and 4 The comma enables you to write a complex number when you type 1 2 the parentheses are automatically placed when you type the comma If you want to type 71 2 you must select 1 before you type the comma A prefix function is one that is typed before its arguments To enter a prefix function you can the first argument select it then select the function from a menu or e you can select the function from a menu or by directly entering it in Alpha mode and then type the arguments The following example illustrates the various ways of entering a prefix function Suppose you want to factor the expression x 4 then find its value for x 4 FACTOR is the function for factoring and it is found on the menu SUBST is the function for substituting a value for a variable in an expression and it is also found in the menu 15 13 an e hp40g book Page 14 Friday December 9 20
81. 11 16 One Proportion Z Interval 11 17 Two Proportion Z lInterval pp 11 17 Sample 11 18 Two Sample T Interya 11 19 12 Using the Finance Solver fo VIRI RENE 12 1 e Performing calculations pp 12 4 e Calculating Amorllzalions s coco itt petet ete ens 12 7 13 Using mathematical functions MAR HUE OMS s 13 EN 13 1 Math functions by category 13 2 Keyboard functions ee 13 3 Te 13 6 Complex number functions pp 13 7 e oo 13 8 CONVE sod coq e en a arene tan 13 8 Hyperbolic trigonometry 13 9 List ONS 13 10 LOOP AURCHONS 13 10 Matix TUMCHONS en 13 11 13 11 Probability amp a 13 12 Real number functions pp 13 14 Two variable statistics 13 17 Svmbolie 13 17 Test Be 13 19 Trigonometry functions pp 13 20 PN NZ e NY 4 P hp40g book Page vi Friday December 9 2005 1 03 AM Symbolic calcula ONS ee 13 20 Finding derivatives pe 13 21 Program constants and physical constants 13 24 Programi
82. 12 members of the set so the Euler index 1512 Decomposes an integer into its prime factors Example Typing FACTOR 90 gives 2 355 Returns the greatest common divisor of two integers Example Typing GCD 18 15 gives 3 Computer Algebra System CAS 14 47 am ad T a Z gt e hp40g book Page 48 Friday December 9 2005 1 03 AM IDIV2 IEGCD 14 48 In step by step mode there are a number of intermediate results 18 mod 15 3 15 mod 320 Result 3 Equation Writer Note that the last non zero remainder in the sequence of remainders shown in the intermediate steps is the GCD Returns the quotient and the remainder of the Euclidean division between two integers Example Typing IDIV2 148 5 gives 29 AND 3 In step by step mode the calculator shows the ie division process in longhand Returns the value of B zout s Identity for two integers For example IEGCD A B returns U AND V D with U V D such that AU BV D and D GCD A B Example Typing IEGCD 48 30 gives 2 AND 3 6 In other words 2 48 3 30 6 and GCD 48 30 6 In step by step mode we get z u v z u 48v 30 Computer Algebra System CAS an 4 IQUOT IREMAINDER Computer Algebra System CAS P
83. 2 1 k The response is 27 1 and F is now listed amongst the variables which you can verify using the vARS key For K 5 you then type BE 14 11 T e P X iG e hp40g book Page 12 Friday December 9 2005 1 03 AM which gives 4294967297 You can factor F 5 with FACTOR which yov ll find in the ALGB menu on the menu bar Typing FACTOR F 5 gives 641 6700417 Typing F 6 gives 18446744073709551617 Using FACTOR to factor it then yields ALENT 1 67260421310 721 EXPAND Distributivity 4 EXPAND expands and simplifies an expression Example Typing XPAND Y 42 X 1 X 2 X41 gives x s FACTOR Factorization FACTOR factors an expression Example To factor 4 X 1 type FACTOR X 1 FACTOR is located in the ALGB menu m2 Computer Algebra System CAS T e a PARTFRAC QUOTE Computer Algebra System CAS 14 13 e hp40g book Page 13 Friday December 9 2005 1 03 AM In real mode the result is x 2x1 G3 2 x 1 In complex mode using CFG the result is T MOREA IS y UD eO ee 2x 1 i 42 Partial fraction expansion PARTFRAC has a rational fraction as an argument PARTFRAC returns the partial fraction decomposition of this rational fraction Example To
84. 2 NOTE To find the limit as x approaches a resp a the second argument is written X A 0 resp X A 0 For the following expression find the limit as x approaches o AL SE eee e Typing lim c JX JX o produces after a short wait 1 2 NOTE the symbol is obtained by typing SHIFT To obtain oo oo To obtain You can also find the symbol in the MATH key s Constant menu PREVAL Evaluate a primitive PREVAL has three parameters an expression F VX dependent on the variable contained in VX and two expressions A and B For example if VX contains X and if F is a function PREVAL F X A B returns F B F A e Computer Algebra System CAS 14 23 T e P NY 4 hp40g book Page 24 Friday December 9 2005 1 03 AM RISCH SERIES 14 24 NOTE PREVAL is used for calculating an integral defined from a primitive it evaluates this primitive between the two limits of the integral Typing PREVAL X X 2 3 gives 6 Primitive and defined integral RISCH has two parameters an expression and the name of a variable RISCH returns a primitive of the first parameter with respect to the variable specified in the second parameter Typing RESCH 2 X41 EXP a X gives X EXP X 41 If the RISCH parameter is the AND of two elem
85. 20 Hath ainen data more than 3 values the nter Length of side A values might not be consistent that is no triangle could possibly have all the values you specified In these cases No sol with given data appears on the screen The situation is similar if you are using the simpler input form for a right angled triangle and you enter more than two values 9 3 an e hp40g book Page 4 Friday December 9 2005 1 03 AM Not enough data If you are using the general input form you need to specity at least three values enough data for the Triangle Solver to nter Length oF be able to calculate the remaining attributes of the triangle If you specify less than three Not enough data appears on the screen If you are using the simplified input form for a right angled triangle you must specify at least two values In addition you cannot specify only angles and no lengths an ZN NY e hp40g book Page 1 Friday December 9 2005 1 03 AM 10 Statistics aplet About the Statistics aplet The Statistics aplet can store up to ten data sets at one time It can perform one variable or two variable statistical analysis of one or more sets of data The Statistics aplet starts with the Numeric view which is used to enter data The Symbolic view is used to specify wh
86. 2005 1 03 AM Example ARC 0 0 2 0 2 FREEZE Draws a circle centered at 0 0 of radius 2 The FREEZE command causes the circle to remain displayed on the screen until you press a key BOX Draws a box with diagonally opposite corners x y and x2 y2 BOX xl yl x2 y2 Example BOX 1 1 1 1 FREEZE Draws a box lower corner at 1 1 upper corner at 1 1 ERASE Clears the display e ERASE D FREEZE Halts the program freezing the current display Execution resumes when any key is pressed LINE Draws a line from x1 y1 to x2 y2 LINE xl yl x2 y2 PIXOFF Turns off the pixel at the specified coordinates x y PIXOFF PIXON Turns on the pixel at the specified coordinates x y PIXON TLINE Toggles the pixels along the line from x1 y1 to x2 y2 on and off Any pixel that was turned off is turned on any pixel that was turned on is turned off TLINE can be used to erase a line TLINE Xd x2 yz 21 20 Programming e 0 Z gt e hp40g book Page 21 Friday December 9 2005 1 03 AM Example TEINE 0707373 Erases previously drawn 45 degree line from 0 0 to 3 3 or draws that line if it doesn t already exist Graphic commands The graphic commands use the graphics variables GO through G9 or the Page variable from Sketch a
87. 2284 EENI gt 20 times Note the value of A displayed near the bottom left corner of the screen The Plot view provides a convenient way to find an approximation to a solution instead of using the Numeric view Solve option See Plotting to find guesses on page 7 7 for more information P Solve aplet s NUM view keys The Solve aplet s NUM view keys are Key Meaning EDIT Copies the highlighted value to the edit line for editing Press Ef when done ma Displays a message about the solution see Interpreting results on page 7 6 FAGE Displays other pages of variables if any Displays symbolic definition of the done SOLNE Finds a solution for the highlighted variable based on the values of the other variables Solve aplet an ZN hp40g book Page 5 Friday December 9 2005 1 03 Key Meaning Continued DEL Clears highlighted variable to zero or deletes current character in edit line if edit line is active CLEAR Resets all variable values to zero or clears the edit line if cursor is in edit line Use an initial guess HINT Number format Solve aplet You can usually obtain a faster and more accurate solution if you supply an estimated value for the unknown variable before pressing Solve starts looking for
88. 2687 S0Hple neun EDIT HELP 1 The table below lists the fields in this view for our current Z Test 1 p example Field Definition name uO Assumed population mean G Population standard deviation x Sample mean n Sample size Alpha level for the test Inference apt 1123 4 ZN NY hp40g book Page 4 Friday December 9 2005 1 03 AM Display on line help Display test results in numeric format Plot test results 6 8 9 By default each field already contains a value These values constitute the example database and are explained in the Haa feature of this aplet To display the on line Tests the null hypothesis that the population Hean is gn dzzuned Pre os Se oe ud help press alternative Fupotheses ErnH le data To close the on line help A set oF SO candon numbers Frou 0 te 1 generated J cahculater PF has 3 H an oF D H5i252 The Suet E SE Display the test results in numeric format IMF STAT NUMERIC VIEH m Test 2 9462054 The test distribution value Frab 1720213 Critical 2 1 644554 and its associated Critical zz 4520435 probability are EE EE EE displayed along with the critical value s of the test and the associated critical value s of the statistic NUM Note You ca
89. 3 EPSXO Disregard small values EPSXO has as a parameter an expression in X and returns the same expression with the values less than EPS replaced by zeroes Typing EPSXO 0 001 X gives if EPS 0 01 O x or if EPS 0 0001 001 x EXPLN Transform a trigonometric expression into complex exponentials EXPLN takes as an argument a trigonometric expression It transforms the trigonometric function into exponentials and logarithms without linearizing it EXPLN puts the calculator into complex mode Typing EXPLN SIN XX gives exp i x ao 2 1 EXP2POW Transform exp n In x as a power of x EXP2POW transforms an expression of the form exp n x In x rewriting it as a power of x e Computer Algebra System CAS 14 29 T a e P e hp40g book Page 30 Friday December 9 2005 1 03 AM NY Typing EXP2POW EXP N LN X gives n X FDISTRIB Distributivity FDISTRIB has an expression as argument FDISTRIB enables you to apply the distributivity of multiplication with respect to addition all at once Typing EDISTRIB OCG I gives Xx xx 3 xx x2x 32x xx124 3 x1 4 x2 1 3 2 Atter simplification by pressing ENTER x 6x2 411 6 LIN Linearize the exponentials LIN has as an argument an expression containing exponentials and trigonometric functions
90. 33 labels 21 34 recenter 21 34 ycross 21 37 SOLVEVX 14 38 sorting 22 6 aplets in alphabetic order 22 6 e hp40g book Page 12 Friday December 9 2005 1 03 AM aplets in chronological order 22 6 elements in a list 19 9 spectral norm 18 13 spectral radius 18 13 square root 13 5 stack history printing 21 25 stairsteps graph 6 1 standard number format 1 10 statistics analysis 10 1 analyzing plots 10 19 angle mode 10 12 calculate one variable 21 30 calculate two variable 21 30 data set variables 21 40 data structure 21 40 define one variable sample 21 30 define two variable data set s de pendent column 21 30 define two variable data set s in dependent column 21 30 a fit 10 12 efining a regression model 1012 deleting data 10 11 editing data 10 11 frequency 21 30 inserting data 10 11 plot type 10 18 plotting data 10 15 predicted values 10 20 regression curve fit models 10 12 saving data 10 10 sorting data 10 11 specitying angle setting 10 12 toggling between one variable and two variable 10 12 tracing plots 10 19 troubleshooting with plots 10 19 Zooming in plots 10 19 statistics variables Axes 21 3 Connect 21 31 Grid 21 32 Hmin Hmax 21 32 Hwidth 21 33 in menu map R 12 Indep 21 33 T am v Ny NY P hp40g book Page 13 Friday December 9 2005 1 03 AM Labels 21 34 Recenter 21 34 S1moark S5mork 2
91. 8 variables 14 4 catalogs 1 30 CFG 15 3 Chinese remainders 14 62 14 65 CHINREM 14 62 chronological sorting 22 6 circle drawing 20 4 clearing aplet 22 3 characters 1 22 display 1 22 display history 1 25 edit line 1 22 lists 19 6 plot 2 7 cobweb graph 6 1 coefficients polynomial 13 11 COLLECT 14 10 columns changing position 21 25 combinations 13 12 commands aplet 21 14 branch 21 17 definition of R 1 drawing 21 19 graphic 21 21 loop 21 23 print 21 25 program 21 4 R 19 stat one 21 29 stat two 21 30 with matrices 18 10 complex number functions 13 6 13 17 conjugate 13 7 imaginary part 13 7 real part 13 8 complex numbers 1 29 entering 1 29 math functions 13 7 storing 1 29 computer algebra system See CAS confidence intervals 11 15 CONJ 13 7 conjugate 13 7 connecting data points 10 19 variable 21 31 via serial cable 22 5 via USB cable 22 5 connectivity kit 22 4 constant error message constants e 13 8 i 13 8 maximum real number 13 8 minimum real number 13 8 physical 1 8 13 25 R 16 program R 15 R 16 contrast decreasing display 1 2 increasing display 1 2 conversions 13 8 coordinate display 2 9 copying display 1 22 graphics 20 6 notes 20 8 programs 21 8 correlation coefficient 10 17 CORR 10 17 statistical 10 15 cosecant 13 20 T an Na Ny NY 4 c
92. 9B 39 652 S92hL1 o8 33 523 rl 335 C1 You will then be able to see the list data in the Numeric view of the Statistics aplet x STATISTICS as pers Fes 29 55 7H8 937 ENTER 4 Z gt e hp40g book Page 10 Friday December 9 2005 1 03 AM 3 Start the Statistics aplet and select 1 variable mode press if necessary to display pur Select Statistics EDIT IHF 0RT Ee Note Your list values are now in column 1 C1 4 In the Symbolic view define H1 for example as C1 sample and 1 frequency SYMB H2 AERE 1 H3 1 H4 1 EHTEF SAMPLE EDIT EVAL 5 Go to the Numeric view to display calculated statistics See One variable on page 10 14 for the meaning of each computed statistic 19 10 Lists e NZ Se GIN e hp40g book Page 1 Friday December 9 2005 1 03 AM 20 Notes and sketches Introduction The HP 40gs has text and picture editors for entering notes and sketches Each aplet has its own independent Note view and Sketch view Notes and sketches that you create in these views are associated with the aplet When you save the aplet or send it to another calculator the notes and sketches are saved or sent as well The No
93. AM 4 Enter data for L2 EWT IN _ 1 5 Press to access HOME 6 Open the variable menu and select L1 w lv v gt HOM mlnFLETIHnFH a VALUE CANCL OF 7 Copy it to the command line Note Because the IE option is highlighted the variable s name rather than its contents is copied to the command line 8 Insert the operator and select the L2 variable from the List variables x VARS 9 L1 LzWL3 1435 135 175 1535 14973 Note You can also type list names directly from the keyboard D 17 6 Variables and memory management e 0 Y e hp40g book Page 7 Friday December 9 2005 1 03 AM Home variables not possible to store data of one type in a variable of another type For example you use the Matrix catalog to create matrices You can create up to ten matrices and you can store these in variables MO to M9 You cannot store matrices in variables other than MO to M9 Cate Available names gory Complex ZO to Z9 id cape 1 2 ZO or 243i Fema 71 You can enter a complex by typing i where r represents the real part and i represents the imaginary part Graphic GO to G9 See Graphic commands on page 21 21 for more information on storing graphic objects via programming commands See To store into a graphic
94. Algebra System CAS an Y e hp40g book Page 7 Friday December 9 2005 1 03 AM Using CAS functions in HOME You can use many computer algebra functions directly in the HOME screen as long as you take certain precautions CAS functions that take matrices as an argument work only from HOME CAS functions can be accessed by pressing BEI when MATH menu is displayed You can also directly type a function name when you are in alpha mode Note that certain calculations will be performed in approximate mode because numbers are interpreted as reals instead of integers in HOME To do exact calculations you should use the XQ command This command converts an approximate argument into an exact argument For example if Radians is your angle setting then ARG XQ 1 i x 4 but ARG 1 i 0 7853 Similarly FACTOR XQ 45 3 x 5 but FACTOR 45 45 Note too that the symbolic HOME variable S1 serves as the current variable for CAS functions in HOME For example DERVX S12 2 51 2 51 2 The result 2 51 2 does not depend Equation Writer variable vx Some CAS functions cannot work in HOME because they require a change to the current variable Remember that you must use 51 52 55 51 52 55 and n1 n2 n5 for symbolic variables and EO E1 E9 to store symbolic expressions For example if you type S12 4
95. Computer Algebra System CAS 14 55 T am ad NY FACTOR GCD HERMITE 14 56 e hp40g book Page 56 Friday December 9 2005 1 03 AM Factors a polynomial Example 1 Typing FACTOR X lt 2 gives x 42 x 42 Example 2 Typing FACTOR X 2 1 gives x4 1f Returns the GCD Greatest Common Divisor of two polynomials Example Typing GCD X 2 X 1 X 1 gives 1 Returns the Hermite polynomial of degree n where n is a whole number This is a polynomial of the following type Cif 22 X Example Typing HERMITE 6 gives 64x 480x 720x 120 Computer Algebra System CAS am ad T a iG e hp40g book Page 57 Friday December 9 2005 1 03 AM LCM LEGENDRE PARTFRAC e Computer Algebra System CAS 14 57 Returns the LCM Least Common Multiple of two polynomials Example Typing 2 2 X 1 X 1 gives 2 2x 1 x 1 Returns the polynomial L a non null solution of the differential equation Q 1 y 2 x y n n 1 y 0 where n is a whole number Example Typing LEGENDRE 4 gives dove 328 8 Returns the partial fraction decomposition of a rational fraction Example Typing 5 3 ARTr
96. Function define two functions and a the second function aplet derivative of the first function You then evaluate the second function See To find derivatives in the Function aplet s Symbolic view on page 13 22 for an example Finding derivatives The HP 40gs can perform symbolic differentiation on some functions There are two ways of using the HP 40gs to find derivatives You can perform differentiations in HOME by using the formal variables S1 to S5 You can perform differentiations of functions of X in the Function aplet To find derivatives To find the derivative of the function in HOME use a in HOME formal variable in place of X If you use X the Using mathematical functions 13 21 4 Z e hp40g book Page 22 Friday December 9 2005 1 03 AM To find derivatives in the Function aplet s Symbolic view 13 22 differentiation function substitutes the value that X holds and returns a numeric result For example consider the function dx sin x t 2cos x Enter the differentiation function onto the command line substituting S1 in pla a c 1 d Gm ALPHA 51 IO 2 amp COS ALPHA S1 0 D 2 Evaluate the function 3 Show the result ce of X eBslcsIHcS182c2xC0854 51 L scsle3xc2x213 2 5IH raslsi1 2 21 2 81N C81 To find the derivative of the
97. Hewlett Packard s Calculators web site can be found at http www hp com calculators Sending and receiving aplets A convenient way to distribute or share problems in class and to turn in homework is to transmit copy aplets directly from one HP 40gs to another This can take place via a suitable cable You can use a serial cable with a 4 pin mini USB connector which plugs into the RS232 port on the calculator The serial cable is available as a separate accessory You can also send aplets to and receive aplets from a PC This requires special software running on the PC such as the PC Connectivity Kit A USB cable with a 5 pin mini USB connector is provided with the hp40gs for connecting with a PC It plugs into the USB port on the calculator Extending aplets an Y e hp40g book Page 5 Friday December 9 2005 1 03 AM To transmit 1 Connect the PC or aplet disk drive to the calculator by an aplet an appropriate cable 2 Sending calculator Open the Library highlight the aplet to send and press The senp ro menu appears with the following options HP39 40 USB to send via the USB port HP39 40 SER to send via the RS232 serial port USB DISK DRIVE to send to a disk drive via the USB port SER DISK DRIVE to send to a disk drive via the RS232 serial port Note choose a disk drive option if you are using the hp
98. Largest and smallest numbers Clearing numbers Using previous results Functions within an expression are evaluated in the follewing order of precedence Functions with the same precedence are evaluated in order from left to right 1 Expressions within parentheses Nested parentheses are evaluated from inner to outer 2 Prefix functions such as SIN and LOG 3 Postfix functions such as 4 Power function NTHROCT 5 Negation multiplication and division 6 Addition and subtraction 7 AND and NOT 8 OR and XOR 9 Left argument of where O Equals The smallest number the 4095 can represent is 1 x 1074 1E 499 A smaller result is displayed as zero The largest number is 9 99999999999 x 1047 1E499 A greater result is displayed as this number e e DEL clears the character under the cursor When the cursor is positioned after the last character DEL deletes the character to the left of the cursor that is it performs the same as a backspace key e CANCEL ON clears the edit line CLEAR clears all input and output in the display including the display history The HOME display HOME shows you four lines of input output history An unlimited except by memory number of previous lines can be displayed by scrolling You can retrieve and reuse any of these values or expressions Getting started 4 SZ
99. MEMORY an R 2 1 X iG e hp40g book Page 22 Friday December 9 2005 1 03 AM T an ad e e PN hp40g book Page 1 Friday December 9 2005 1 03 AM NY Limited Warranty HP 40gs Graphing Calculator Warranty period 12 months 1 HP warrants to you the end user customer that HP hardware accessories and supplies will be free from defects in materials and workmanship after the date of purchase for the period specified above If HP receives notice of such defects during the warranty period HP will at its option either repair or replace products which prove to be detective Replacement products may be either new or like new 2 HP warrants to you that HP software will not fail to execute its programming instructions after the date of purchase for the period specified above due to defects in material and workmanship when properly e installed and used If HP receives notice of such 4 defects during the warranty period will replace sottware media which does not execute its programming instructions due to such defects 3 HP does not warrant that the operation of HP products will be uninterrupted or error free If HP is unable within a reasonable time to repair or replace any product to a condition as warranted you will be ent
100. Matrices are two dimensional arrays They are composed of more than one row and more than one column Two dimensional matrices are represented with nested brackets for example 1 2 3 4 5 6 You can create complex matrices for example 1 2 3 4 4 5 6 Matrix Variables There are ten matrix variables available named MO to M9 You can use them in calculations in HOME or in a program You can retrieve the matrix names from the VARS menu or just type their names from the keyboard Matrices 18 1 e Y e hp40g book Page 2 Friday December 9 2005 1 03 AM Creating and storing matrices You can create edit MATRIS CATALOG delete send and receive 1 111 REAL Marais EE matrices in the Matrix 2 141 REAL HATRI canals Me 1451 REAL MATRIS 9 MS 111 REAL MATRIS F EDIT EEHDIEECM To open the Matrix catalog press SHIFT MATRIX You can also create and store matrices named or unnamed in HOME For example the command POLYROOT t T 0 1 0 5M1 stores the root of the complex vector of length 3 into the MI variable M1 now contains the three roots of x x 0 Matrix Catalog The table below lists the operations of the menu keys in keys the Matrix Catalog as well as the use of Delete DEL and Clear SHIFT CLEAR 3 Key Meaning 4 ELIT
101. Opens the highlighted matrix for editing HEH Prompts for a matrix type then opens an empty matrix with the highlighted name Transmits the highlighted matrix to another HP 40gs or a disk drive See RECI Receives a matrix from another HP 40gs or a disk drive See DEL Clears the highlighted matrix CLEAR Clears all matrices v or Moves to the end or the beginning A of the catalog To create a matrix 1 Press SHIFT MATRIX to open the Matrix Catalog The in the Matrix Matrix catalog lists the 10 available matrix variables Catalog MO to M9 182 Matrices e 0 zz gt e hp40g book Page 3 Friday December 9 2005 1 03 AM 2 Highlight the matrix variable name you want to use and press HEM 3 Select the type of matrix to create For a vector one dimensional array select Real vector or Complex vector Certain operations CROSS do not recognize a one dimensional matrix as a vector so this selection is important For a matrix two dimensional array select Real matrix or Complex matrix 4 For each element in the matrix type a number or an expression and press ENTER The expression may not contain symbolic variable names For complex numbers enter each number in complex form that is a b where a is the real part and b is the imaginary part You must include the parentheses and t
102. PV In addition cash flow diagrams specify when payments occur relative to the compounding periods at the beginning of each period or at the end The Finance Solver application provides both of these payment modes Begin mode and End mode The following cash Using the Finance Solver T am S SZ SZ gt e hp40g book Page 3 Friday December 9 2005 1 03 AM flow diagram shows lease payments at the beginning of each period PV Copitalized value of lease PMT PMT PMT FV The following cash flow diagram shows deposits into an account at the end of each period PV e As these cash flow diagrams imply there are five TVM variables G N The total number of compounding periods or payments I YR The nominal annual interest rate or investment rate This rate is divided by the number of payments per year P YR to compute the nominal interest rate per compounding period which is the interest rate actually used in TVM calculations The present value of the initial cash flow To a lender or borrower PV is the amount PV of the loan to an investor PV is the initial investment PV always occurs at the beginning of the first period Using the Finance Solver 12 3 e NZ zz gt e hp40g book Page 4 Friday December 9 2005 1 03 AM The pe
103. Spain 34 915 642095 lt Sweden 46 85 1992065 Switzerland 41 1 4395358 41 22 8278780 French 39 02 75419782 Italian Turkey 420 5 41422523 UK 44 207 4580161 Czech Republic 420 5 41422523 South Africa 27 1 1 2376200 Luxembourg 32 2 7 126219 Other European 420 5 41422523 countries Australia 6 1 3 9841 5211 Singapore 61 3 9841 5211 W 3 am ad L America hp40g book Page 4 Friday December 9 2005 1 03 AM Country Argentina Brazil Telephone numbers 0 810 555 5520 Sao Paulo 3747 7799 ROTC 0 800 1 57751 Mx City 5258 9922 ROTC 01 800 472 6684 Venezuela 0800 4746 8368 Chile 800 360999 Columbia 9 800 114726 Peru 0 800 10111 Central 1 800 711 2884 America amp Caribbean Guatemala 1 800 999 5105 Puerto Rico 1 877 232 0589 Costa Rica 0 800 011 0524 N America Country Telephone numbers 1800 HP INVENT 905 206 4663 or 800 HP INVENT ROTC Rest of the country Please logon to http www hp com for the latest service and support information h S NY e hp40g book Page 5 Friday December 9 2005 1 03 AM Regulatory Notices Federal Commu nications Commission Notice Modifications Cables Declaration of Conformity for Products Marked with FCC Logo United States Only This equipme
104. TRIGCOS 14 44 trigonometric fit 10 13 functions 13 20 scaling 2 10 2 14 2 15 trigonometry functions ACOS2S 14 38 ACOT 13 20 ACSC 13 20 ASEC 13 20 ASIN2C 14 39 ASIN2S 14 39 ASIN2T 14 39 I 13 T an ad NY 4 COT 13 20 CSC 13 20 HALFTAN 14 40 SEC 13 20 SINCOS 14 40 TAN2CS2 14 40 TAN2SC 14 41 TAN2SC2 14 41 TRIGCOS 14 44 TRIGSIN 14 44 TRIGTAN 14 44 TRIGSIN 14 44 TRIGTAN 14 44 TRUNC 14 28 truncating values to decimal places 13 17 TSIMP 14 70 tstep 21 36 Two Proportion Z Interval 11 17 Two Proportion Z Test 11 11 Two Sample T Interval 11 19 Two Sample T test 11 14 Two Sample Z Interval 11 16 typing letters 1 6 U UNASSIGN 14 15 UNASSUME 14 61 undefined name K 2 1 result R 2 1 un zoom 2 11 upper tail chi squared probability 13 13 upper tail normal probability 13 13 upper tail Snedecor s F 13 13 upper tail student s t probability 13 14 USB connectivity 22 5 user defined regression fit 10 13 V value recall 17 3 storing 17 2 variables aplet 17 1 14 hp40g book Page 14 Friday December 9 2005 1 03 AM CAS 14 4 categories 1 clearing 17 3 definition 17 1 17 7 R 2 in equations 7 10 in Symbolic view 2 3 independent 14 6 21 36 local 17 1 previous result Ans 1 23 printing 21 26 root 21 34 root finding 3 10 step size of independent 21 36 types 17 1 17 7 use in calculations 17 3 variation ta
105. Ycross Coord Xtick FastRes YtCICK Grid Xmin Indep Xmax InvCross Ymin Labels Ymax Recenter Xzoom Tracing Yxoom Symbolic Angle E6 El E7 E2 E8 9 E4 EO E5 Numeric Digits NumCol Format NumRow Note NoteText Sketch Page PageNum X iG e hp40g book Page 12 Friday December 9 2005 1 03 AM Statistics aplet variables The statistics aplet variables are Category Available name Plot Axes S4mark Connect Sbmark StatPlot Grid Tracing Hmin Xcross Hmax Ycross Hwidth Xtick Indep InvCross Xmin Labels Xmax Recenter Ymin Slmark Ymax S2mark Xzoom S3mark Yxoom Symbolic Angle S3fit Slfit S4fit S2fit S5fit Numeric CO ty NumFont e Digits NumRow Format StatMode NumCol Stat One MaxX Q3 MeanX PSDev Median SSDev Min PVa N SVar Q1 Toto Stat Two Corr yx Cov 25562 Fit XXY LY Meany RelErr Note NoteText Sketch Page PageNum am 27 T PN hp40g book Page 13 Friday December 9 2005 1 03 AM NY MATH menu categories Math functions The math functions are am ad R 13 Category Available name Calculus TAYLOR Complex ARG IM CONS RE Constant e MAXREAL MINREAL TU Hyperb ACOSH TANH ASINH ALOG ATANH EXP COSH EXPM1 SINH LNP1 List CONC
106. Z gt e hp40g book Page 29 Friday December 9 2005 1 03 AM Example INPUT R Circular Area Radius Enter Number 1 MSGBOX Displays a message box containing textitem A text item consists of any number of expressions and quoted strings of text The expressions are evaluated and turned into strings of text For example AREA IS 2 2 becomes AREA IS 4 Use SHIET CHARS to type the quote marks MSGBOX textitem Example 1 MSGBOX AREA IS m A 2 You can also use the NoteText variable to provide text arguments This can be used to insert line breaks For example press SHIFT NOTE and type AREA IS ENTER te The position line MSGBOX NoteText m A 2 will display the same message box as the previous example PROMPT Displays an input box with name as the title and prompts for a value for name name can be a variable such as 9 bI 12 CEP or Zum PROMPT name WAIT Halts program execution for the specified number of seconds WAIT seconds Stat One and Stat Two commands The following commands are used for analyzing one variable and two variable statistical data Programming 21 29 e NZ NY 4 P hp40g book Page 30 Friday December 9 2005 1 03 AM Stat One commands DO1VSTATS SETFREQ SETSAMPLE Calculates STATS using datasetname and stores th
107. a e P iG e hp40g book Page 66 Friday December 9 2005 1 03 AM ILAP is the inverse Laplace transform of a given expression Again the expression is the value of a function of the variable stored in VX Laplace transform LAP and inverse Laplace transform ILAP are useful in solving linear differential equations with constant coefficients for example yitp y tay fix y 0 a y 0 b The following relations hold LAP y x I e y t dt ILAP f x e f z dz where c is a closed contour enclosing the poles of f The following property is used LAP y x 0 1 The solution y of fx VO y 0 b is then ILAP i 2 x tpx tq Example To solve y 6 y 9 y y 0 a y 0 b C type LAP X EXP 3 X The result is 1 14 66 Computer Algebra System CAS T a e iG e hp40g book Page 67 Friday December 9 2005 1 03 AM NY LAP PA2B2 PSI P Computer Algebra System CAS Typing X 6X49 LAP X 6X49 gives 3 Ga b xa ee See ILAP above Decomposes a prime integer p congruent to 1 modulo 4 as follows p b The calculator gives the result as a b i Example 1 Typing PA2B2 17 g
108. a program store the constant number or its name into the variable Format 21 40 Programming T a e e hp40g book Page 41 NumCol All Aplets except Statistics aplet NumFont Function Parametric Polar Sequence Statistics Numindep Function Parametric Polar Sequence NumRow All Aplets except Statistics aplet Programming Friday December 9 2005 1 03 AM 1 Standard 2 Fixed ar SCL 4 Eng 5 Fraction 6 MixFraction Note if Fraction or Mixed Fraction is chosen the setting will be disregarded when labeling axes in the Plot view A setting of Scientific will be used instead Example Scientific gt Format Or 3 b Format Sets the column to be highlighted in Numeric view In a program type n gt NumCol where n can be 0 1 2 3 4 5 6 7 8 9 Enables you to choose the font size in Numeric view Does not appear in the Num Setup input form Corresponds to the 8 key in Numeric view In a program type 0 gt NumFont for small default 1 NumFont for big Specifies the list of independent values to be used by Build Your Own Table In a program type LIST gt NumIndep Sets the row to be highlighted in Numeric view In a program type n gt NumRow where n gt 0 21 41 4 4 NumStart Function Parametric Polar Sequence NumStep
109. an Z gt e hp40g book Page 21 Friday December 9 2005 1 03 AM However for clarity it is better to include the multiplication sign where you expect multiplication in an expression It is clearest to enter AB as A B HINT Implied multiplication will not always work as expected For example entering A B 4 will not give A B4 Instead an error message is displayed Invalid User Function This is because the calculator interprets A 4 as meaning evaluate function A at the value B 4 and function A does not exist When in doubt insert the sign manually Parentheses You need to use parentheses to enclose arguments for functions such as SIN 45 You can omit the final parenthesis at the end of an edit line The calculator inserts it automatically Parentheses are also important in specifying the order of operation Without parentheses the HP 40gs calculates according to the order of algebraic precedence the next topic Following are some examples using parentheses e Entering Calculates SIN 45 sin 45 SIR 45 0 9 HIFP sin 45 SHIFT v 85 x 9 85 x9 v 9856 90 85 x 9 _ Getting started 1 21 e e e hp40g book Page 22 Friday December 9 2005 1 03 AM Algebraic precedence order of evaluation
110. and press EE to display the list HT a a es contenis New elements are inserted above the highlighted position In this example an element with the value of 9 is inserted between the first and second elements in the list 3 Press v to the insertion position then press and press i 4 Press MA To store one In HOME enter value lisiname element For element example to store 148 as the second element in L1 type e e 4 Y e hp40g book Page 6 Friday December 9 2005 1 03 AM Deleting lists To delete a list In the List catalog highlight the list name and press DEL You are prompted to confirm that you want to delete the contents of the highlighted list variable Press to delete the contents To delete all lists In the List catalog press CLEAR Transmitting lists You can send lists to calculators or PCs just as you can aplets programs matrices and notes 1 Connect the calculators using an appropriate cable 2 Open the List catalogs on both calculators 3 Highlight the list to send 4 Press Bi3zid and choose the method of sending 5 Press idis on the receiving calculator and choose the method of receiving e For more information on sending and receiving files see Sending and receiving aplets on page 22 4 List functions List functions are found in the MATH menu You can use them in HOME as w
111. aplet Note Quotes are needed if the name contains spaces or other special characters SELECT apletname SETVIEWS The SETVIEWS command is used to define entries in the VIEWS menu for aplets that you customize See Customizing an aplet on page 21 9 for an example of using the SETVIEWS command When you use the SETVIEWS command the aplet s standard VIEWS menu is deleted and the customized menu is used in its place You only need to apply the e command to an aplet once The VIEWS menu changes remain unless you apply the command again Typically you develop a program that uses the SETVIEWS command only The command contains a trio of arguments for each menu option to create or program to attach Keep the following points in mind when using this command The SETVIEWS command deletes an aplet s standard Views menu options If you want to use any of the standard options on your reconfigured VIEWS menu you must include them in the configuration When you invoke the SETVIEWS command the changes to an aplet s VIEWS menu remain with the aplet You need to invoke the command on the aplet again to change the VIEWS menu All the programs that are called from the VIEWS menu are transferred when the aplet is transferred for example to another calculator or to a PC As part of the VIEWS menu configuration you can specify programs that you want transferred with the aplet but are not called as menu optio
112. appears on the screen Other views for scaling and splitting the graph The preset viewing options menu VIEWS contains options for drawing the plot using certain pre defined contigurations This is a shortcut for changing Plot view settings For instance if you have defined a trigonometric function then you could select Trig to plot your function on a trigonometric scale It also contains split screen e options In certain aplets for example those that you download from the world wide web the preset viewing options menu can also contain options that relate to the aplet VIEWS menu Press VIEWS select an option and press options Option Meaning Plot Splits the screen into the plot and a Detail close up Plot Table Splits the screen into the plot and the data table Overlay Plots the current expression s Plot without erasing any pre existing plot s Aplets and their views 2 13 e 0 Z gt e hp40g book Page 14 Friday December 9 2005 1 03 AM Option Meaning Continued Auto Scale Rescales the vertical axis so that the display shows a representative piece of the plot for the supplied x axis settings For Sequence and Statistics aplets autoscaling rescales both axes The autoscale process uses the first selected function only to determine the best scale to use Decimal Rescales both axes so ea
113. are sometimes called soft keys bottom line of the display shows the labels for the menu keys current meanings Aplet control keys The aplet control keys are Key Meaning Displays the Symbolic view for the SYMB EE current aplet See Symbolic view on page 1 16 Displays the Plot view for the current aplet See Plot view on page 1 16 NUM Displays the Numeric view for the current aplet See Numeric view on e page 1 17 HOME Displays the HOME view See HOME on page 1 1 Displays the Aplet Library menu See Aplet library on page 1 16 VIEWS Displays the VIEWS menu See Aplet views on page 1 16 Getting started an STA SZ gt e hp40g book Page 5 Friday December 9 2005 1 03 AM Entry Edit keys The entry and edit keys are Key Meaning ON CANCEL Cancels the current operation if the calculator is on by pressing ON Pressing SHIFT then OFF turns the calculator off Accesses the function printed in blue above a key Returns to the HOME view for performing calculations Accesses the alphabetical ALPHA ALPHA characters printed in orange below a key Hold down to enter a string of characters Enters an input or executes an operation In calculations is present as a menu key acts the same as pressing pig Or Enters
114. blinking cursor is An expression can contain numbers functions and variables 1 19 an 4 Example Long results Negative numbers Scientific notation powers of 10 Example Explicit and implicit multiplication 1 20 P hp40g book Page 20 Friday December 9 2005 1 03 AM 2 Calculate 23 MS as 023 14 Vv 8D E 3 n 45 D 232 1448537 34L LHi 457 620 996164365 STOR If the result is too long to fit on the display line or if you want to see an expression in textbook format press 4 to highlight it and then press gm Type to start a negative number or to insert a negative sign To raise a negative number to a power enclose it in parentheses For example 5 25 whereas 5 25 A number like 5x 10 or 3 21 x 10 is written in scientific notation that is in terms of powers of ten This is simpler to work with than 50000 or 0 000000321 To enter numbers like these use EEX This is easier than using x 4x10 6 x 10 3x 10 0 4 SHIFT ZEX 23 13 DJ x 0 6 SHIFT pg 230 3 3 SHIFT zex Gi Calculate E 136 E237 HERES Implied multiplication takes place when two operands appear with no operator in between If you enter AB for example the result is A B Getting started
115. by typing in the independent variable values you want The dependent values are then calculated and displayed Build a table 1 Start with an expression defined in Symbolic view in the aplet of your choice Note Function Polar Parametric and Sequence aplets only 2 In the Numeric Setup suirr NUM choose NUMTYPE Build Your Own 3 Open the Numeric view NUM e 4 Clear existing data in the table SHIFT CLEAR 5 Enter independent values in the left hand column Type in a number and press ENTER You do not have to enter them in order because the function can rearrange them To insert a number between two others use EB and F2 entries are generated automatically You enter numbers into the X column B EDIT IN 5URET Ela DEFM Clear data Press SHIFT CLEAR to erase the data from a table Aplets and their views 2 19 e 0 Z e hp40g book Page 20 Friday December 9 2005 1 03 AM Build Your Own menu keys Key Meaning EDIT Puts the highlighted independent value X T 0 or N into the edit line Pressing replaces this variable with its current value TH Inserts a zero value at the position of the highlight Replace a zero by typing the number you want and pressing ENTER Sorts the independent variable values into ascending or descending order Press and s
116. contents of Editline Before starting to work with programs you should take a few minutes to become familiar with the Program catalog menu keys You can use any of the following keys both menu and keyboard to perform tasks in the Program catalog 21 2 Programming e 0 Y e hp40g book Page 3 Friday December 9 2005 1 03 AM Program catalog keys The program catalog keys are Key Meaning ERT Opens the highlighted program for editing Prompts for new program name then opens an empty program SEHI Transmits the highlighted program to another HP 40gs or to a disk drive ECU Receives the highlighted program from another HP 40gs or from a disk drive EUM Runs the highlighted program a or Moves to the beginning or end of e the Program catalog DEL Deletes the highlighted program CLEAR Deletes all programs in the program catalog Programming 21 3 PN 0 Y e hp40g book Page 4 Friday December 9 2005 1 03 AM Creating and editing programs Create a new 1 Press SHIFT PROGRM to open the Program catalog program 2 Press ETHER The HP 40gs prompts PROGRAM Je wc ENTER FOR MEH PROGRAM ok A program name can contain special characters such as a space H
117. each two variable data set There are three ways to select a regression model Accept the default option to fit the data to a straight line Select one of the available fit options in Symbolic Setup view Enter your own mathematical expression in Symbolic view This expression will be plotted but it will not be fitted to the data points You can ignore the angle measurement mode unless your Fit definition in Symbolic view involves a trigonometric function In this case you should specify in the mode screen whether the trigonometric units are to be interpreted in degrees radians or grads 1 In Numeric view make sure EE is set 2 Press SHIFT SETUP SYMB to display the Symbolic Setup view Highlight the Fit number S1FIT to S5FIT you want to define 3 Press GER and select from the list Press ma when done The regression formula for the fit is displayed in Symbolic view Ten fit models are available Fit model Meaning Default Fits the data to a straight line y mx b Uses a least squares fit Logarithmic Fits to a logarithmic curve y mlnx Exponential Fits to an exponential curve be Fits to a power curve bx Statistics aplet an Z gt e hp40g book Page 13 Friday December 9 2005 1 03 AM Fmodel Meaning Continued Quadratic Fits to a quadratic curve y Needs at le
118. expression 15 11 am ad T 4 hp40g book Page vii Friday December 9 2005 1 03 AM Accessing CAS funcfions pp 15 12 Equation Writer variables i 15 16 Predefined CAS variables 15 16 The keyboard in the Equation Writer 15 17 16 Step by Step Examples Turre ira 16 1 17 Variables and memory management 17 1 Storing and recalling variables 17 2 Tne VAR ed 17 4 eiat a 17 9 18 Matrices OCW ne a ei ea Ripe unused 18 1 Creating and storing mafrices 16 2 Working with matrices pp 18 4 cipit ias 18 6 Solving systems of linear 18 8 Matrix functions and 18 10 AOIUIOGGOTVeIIOSEKM teet mia ead 18 10 Me 18 10 EXampl8S a 18 13 19 Lists Displaying and editing isfs pp 19 4 ene T 19 6 isis RETO o S ie 19 6 Hist TNC UNS ee a E EE TT 19 6 Finding statistical values for list 19 9 20 Notes and sketches el
119. function in the Function aplet s Symbolic view you define two functions and define the second function as a derivative of the first function For example to differentiate sin x 2cosx 1 Access the Function aplet s Symbolic view and define Fl EV w D 2 D BIB EDIT CHE HOH EVAL FUNCTION SWFHHEHLIE VIEH SESESSE eFICHOSSIMCEBOEZEC Farxoc FC v 2 Define F2 x as the derivative of F 1 an EnITleCHEI EVAL FUNCTION SYMEODLIC VIEH SERERE WF ICH ISSINC AE 2400 WF et Sant P lox FOCIS Using mathematical functions SZ gt e hp40g book Page 23 Friday December 9 2005 1 03 AM d dx LU ALPHA 1 0 0 DJ DT 3 Select F2 X and FUNCTION SYMEOLIC VIEH evaluate it ad sh Pest ee 2 EMT w CHE HHHIEVHLI 4 Press BREE to display the result Note Use the arrow keys fo view Fatgecasi sx 2 AR 2 SINCE the entire function You could also just define F1 x dx sin x 2cos x To find the For example to find the indefinite integral of indefinite integral ES gcc e using formal variables 0 51 3 2 5 1 Enter the function 00 Stee fee Se ALPHA 51 C 3 x puo e X CJ 5 ALPHA X D 2 Show the result form
120. hp40g book Page 2 Friday December 9 2005 1 03 AM Cursor mode Enables you to go into cursor mode for quicker selection of expressions and subexpressions see page 15 10 Edit expr Enables you to edit the highlighted expression on the edit line just as you do in the HOME screen see page 15 11 Change font Enables you to choose to type using large or small characters see page 15 10 Cut Copies the selection to the clipboard and erases the selection from Equation Writer Copy Copies the selection to the clipboard Paste Copies the contents of the e clipboard to the location of e the cursor The clipboard contents will be either whatever Copy or Cut selected the last time you used these commands or the highlighted level when you selected COPY in CAS history ALGB menu The menu contains CFG R x 5 functions that enable you to COLLECT perform algebra such as Sap factoring expansion simplification substitution and so on DIFF menu The menu contains functions that enable you to perform differential calculus such as differentiation integration series expansion limits and so on 15 2 Equation Writer e NZ GIN e hp40g book Page 3 Friday December 9 2005 1 03 AM REWRI menu The 312 menu contains functions that enable you to rewrite an expression in another f
121. if you want to make a copy of your work before editing or if you want to use one program as a template for another 1 Press suirr PROGRM to open the Program catalog 2 Press 3 Type a new file name then choose 3 The Program Editor opens with a new program 4 Press to open the variables menu 5 Press 7 to quickly scroll to Program 6 Press gt then highlight the program you want to copy 7 Press GETS then press Bis The contents of the highlighted program are copied into the current program at the cursor location If you use a programming routine often save the routine under a different program name then use the above method to copy it into your programs You can send programs to and receive programs from other calculators just as you can send and receive aplets matrices lists and notes After connecting the calculators with an appropriate cable open the Program catalogs on both calculators Highlight the program to send then press Hazm on the sending calculator and 39 on the receiving calculator You can also send programs to and receive programs from a remote storage device aplet disk drive or computer This takes place via a cable connection and requires an aplet disk drive or specialized software running on a PC such as a connectivity kit Programming e 0 4 P hp40g book Page 9 Friday December 9 2005 1 0
122. intercept 2 2657 Correlation The correlation coefficient is stored in the CORR variable coefficient It is a measure of fit to a linear curve only Regardless of the Fit model you have chosen CORR relates to the linear model Statistics aplet 10 17 e NZ Z e hp40g book Page 18 Friday December 9 2005 1 03 AM Relative Error The relative error is a measure of the error between predicted values and actual values based on the specified Fit A smaller number means a better fit The relative error is stored in a variable named RELERR The relative error provides a measure of fit accuracy for all fits and it does depend on the Fit model you have chosen HINT In order to access the CORR and RELERR variables after you plot a set of statistics you must press NUM to access the numeric view and then to display the correlation values The values are stored in the variables when you access the Symbolic view Setting up the plot Plot setup view The Plot Setup view SHiFT SETUP PLOT sets most of the same plotting parameters as it does for the other built in aplets See Setting up the plot Plot view setup on page 2 5 Settings unique to the Statistics aplet are as follows Plot type 1VAR STATPLOT enables you to specify either a histogram or a box and whisker plot for one variable statistics when is set Press MIA to change the highlighted setting
123. is active an 4 hp40g book Page 2 Friday December 9 2005 1 03 AM To select a function NOTE 1 Press MATH to display the MATH menu The categories appear in alphabetical order 2 Press Y or 4 to scroll through the categories To jump directly to a category press the first letter of the category s name Note You do not need to press ALPHA first 3 The list of functions on the right applies to the currently highlighted category on the left Use gt and lt to switch between the category list and the function list 4 Highlight the name of the function you want and press WA This copies the function name and an initial parenthesis if appropriate to the edit line If you press EEE while the MATH menu is open CAS functions and commands are displayed You can select a CAS function or command in the same way that you select a function from the MATH menu by pressing the arrow keys and then Big The function or command selected appears on the edit line in HOME and with an initial parenthesis if appropriate e Function categories MATH menu Calculus loop Symbolic Complex Matrix Tests numbers Polynomial Trigonometry Constant probability Trig Convert Real numbers Hyperbolic Real trigonometry Twovariable Hyperb statistics fists Sta
124. it LUE 2 H 2 4 SZ gt e hp40g book Page 24 Friday December 9 2005 1 03 AM Now press and scroll down the screen to 1 x 4 2 gt Now press to obtain the table of variations If you are not in step by step mode you can also get the calculation of the derivative by typing DERVX G X which produces the preceding result To prove the stated inequality first calculate s 0 by typing G O and pressing ENTER The answer is Now calculate g 2 by typing G 2 and pressing The answer is The two results prove that NIU lt g x lt for x e 0 2 Solution 2 The calculator is not needed here Simply stating that x e 20 for x 0 2 is sufficient to show that for x 0 2 we have x x 2e lt g x e lt Le Solution 3 To integrate the preceding inequality type the Eu expression at the right H Br da Pressing produces the result at the right 16 24 Step by Step Examples e NZ Z gt e hp40g book Page 25 Friday December 9 2005 1 03 AM We can now see that 2 2 3 7 n le To justify the preceding calculation we must assume that X X s n NS n n e isa primitive of e If you are not sure you can use the INTVX function as illustrated at the right
125. limits LIMIT or lim has two arguments an expression dependent on a variable and an equality a variable the value to which you want to calculate the limit You can omit the name of the variable and the sign when this name is in VX It is often preferable to use a quoted expression 14 21 T a e P 14 22 e hp40g book Page 22 Friday December 9 2005 1 03 AM QUOTE expression to avoid rewriting the expression in normal form i e not to have a rational simplification of the arguments during the execution of the LIMIT command Example Typing 1 lim QUOTE 2X 1 EXP x o gives 00 To find a right limit for example type 1 gives if X is the current variable 00 To find a left limit for example type 1 gives it X is the current variable oo It is not necessary to quote the second argument when it is written with for example lim 1 0 p de gives 00 Example For n gt 2 in the following expression find the limit as x approaches tan x tan n x sin z x n sin x You can use the LIMIT command to do this Computer Algebra System CAS am ad T X iG e hp40g book Page 23 Friday December 9 2005 1 03 AM Typing TAN X TAN N X SIN N X N SIN X gives
126. on the menu in the Equation Writer See SOLV menu on page 14 33 for a description of these functions e 14 60 Computer Algebra System CAS m 5 Z e hp40g book Page 61 Friday December 9 2005 1 03 AM Tests menu ASSUME Use this function to make a hypothesis about a specified argument or variable Example Typing ASSUME X gt Y sets an assumption that X is greater than Y In fact the calculator works only with large not strict relations and thus ASSUME X gt Y will actually set the assumption that X gt Y A message will indicate this when you enter an ASSUME function Note that X gt Y will be stored in the REALASSUME variable To see the variable press UNASSUME Use this function to cancel all previously specified assumptions about a particular argument or variable Example Typing UNASSUME X cancels any assumptions made about X It returns X in the Equation Writer To see the assumptions press select REALASSUME and press 39 gt lt See Test functions on page 13 19 AND See AND on page 13 19 OR See OR on page 13 19 NOT See NOT on page 13 19 IFTE See IFTE on page 13 19 Trig menu All the functions on this menu are also available on the menu in the Equation Writer See TRIG menu on page 14 38 for a description of these functions e Computer Algebra System CAS 14 61
127. perform a partial fraction decomposition of a rational function such as x uu 1 x cs vi 1 you use the PARTFRAC command In real and direct mode this produces X 3 gt xcr2 Doc quo 2 x 2 In complex mode this produces 1 3i 1 1 3i 4 4 xti x 1l1 x i x 2 Quoted expression QUOTE expression is used to prevent an expression from being evaluated or simplified Example 1 Typing m QUOTE 2X 1 1 to gives 00 T e P STORE _ 14 14 iG e hp40g book Page 14 Friday December 9 2005 1 03 AM Example 2 Typing SUBST QUOTE CONJ 2 Z 1 1 gives CONJ 1 1 Store an object in a variable STORE stores an object in a variable STORE is found in the ALGB menu or the Equation Writer menu bar Example Type STORE X 4 ABC or type 4 then select it and call STORE then type ABC then press ENTER to confirm the definition of the variable ABC To clear the variable press VARS in the Equation Writer then choose PURGE on the menu bar or select UNASSIGN on the ALGB menu by typing for example UNASSIGN ABC Substitute a value for a variable is an infix operator used to substitute a value for a variable in an expression similar to the function SUBST has two parameters an expression dependent on a parameter and an equality paramete
128. powers with matrix arguments Division lett multiplies by the inverse of the divisor You can enter the matrices themselves or enter the names of stored matrix variables The matrices can be real or complex e For the next examples store 1 2 3 4 into M1 and e 5 6 7 8 into M2 Example 1 Create the first matrix 5 SHIFT MATRIX EE Em 1 2 ENTER v 3 4 Emr INs EE 2 Create the second matrix SHIFT MATRIX IHE DIN 5 6 ETE so es v 7 ENTER 8 ENTER 3 Add the matrices that you created Mitte C l6 3 C1b 12 18 6 Matrices e 0 Y e hp40g book Page 7 Friday December 9 2005 1 03 AM To multiply and divide by a scalar To multiply two matrices To raise a matrix to a power Matrices ALPHA M1 ALPHA M2 For division by a scalar enter the matrix first then the operator then the scalar For multiplication the order of the operands does not matter The matrix and the scalar can be real or complex For example to divide the result of the previous example by 2 press the following keys Ey SE FUNC TION SS LL6 8 E18 1211 CCS 4 954611 To multiply the two matrices M1 and M2 that you created for the previous example press the following keys ALPHA 1 x ALPHA M ET 2 E3 4
129. program commands CHARS Displays special characters To type one highlight it and press Ta copy a character without closing the CHARS screen press 20 2 Notes and sketches e v SZ e hp40g book Page 3 Friday December 9 2005 1 03 AM Aplet sketch view You can attach pictures to an aplet in its Sketch view SKETCH Your work is automatically saved with the aplet Press any other view key or to exit the Sketch view Sketch keys Key Meaning Stores the specified portion of the current sketch to a graphics variable G1 through GO Adds new blank page to current sketch set FAGET Displays next sketch in the sketch set Animates if held down TENT Opens the edit line to type a text label e DRAH Displays the menu key labels for 4 drawing DEL Deletes the current sketch CLEAR Erases the entire sketch set E Toggles menu key labels on and off If menu key labels are hidden or any menu key redisplays the menu key labels To draw a line 1 In an aplet press SHIFT SKETCH for the Sketch view 2 In Sketch view press BITE and move the cursor to where you want to start the line Press MIE This turns on line drawing 4 Move the cursor in any direction to the end point of the line by pressing the 4 v keys 5 Press W3 to finish the line Notes and sketches 20 3
130. range is from 0 to 180 to or to 200 grads Inputs and outputs depend on the current angle format Also accepts complex numbers Output will be complex for values outside the normal COS domain of 1 lt x lt 1 ACOS value Example ACOS 1 returns 0 Degrees mode Arc tangent tan x Output range is from 90 to 90 27 2 to 1 2 or 100 to 100 grads Inputs and outputs depend on the current angle format Also accepts complex numbers ATAN value Example ATAN 1 returns 45 Degrees mode Square Also accepts complex numbers value Example 182 returns 324 Square root Also accepts complex numbers value Example 324 returns 18 Negation Also accepts complex numbers value Example 1 2 returns 1 2 Power x raised to y Also accepts complex numbers value power 13 5 e NZ 2 Y e hp40g book Page 6 Friday December 9 2005 1 03 AM Example 2 8 returns 256 SHIFT ABS Absolute value For a complex number this is dx ABS value ABS x Example ABS 1 returns 1 ABS 1 2 returns 2 2360679775 Takes the nth root of x root NTHROOT value Example 3 NTHROOT 8 returns 2 Calculus functions The symbols for differentiation and integration are available directly form the keyboard d dx and S e respectively as well as from the MATH menu Differentiates expression with re
131. terms and factors the expression over the integers Example To factor 4 over the integers you would type COLLECT X 4 which gives in real mode x 2 x 2 Example To factor x 2 over the integers you would type COLLECT X 2 which gives Define function For its argument DEF takes an equality between 1 the name of a function with parentheses containing the variable and 2 an expression defining the function DEF defines this function and returns the equality Computer Algebra System CAS am ad T 4 Computer Algebra System CAS P hp40g book Page 11 Friday December 9 2005 1 03 AM Typing DEF U N 2N 41 produces the result U N 2N 1 Typing U 3 then returns 7 Example Calculate the first six Fermat numbers F1 F6 and determine whether they are prime So you want to calculate F k 22 41 for k 1 6 Typing the formula 2 1 gives a result of 17 You can then invoke the ISPRIME command which is found in the MATH key s Integer menu The response is 1 which means TRUE Using the history which you access by pressing the 2 SYMB key you put the expression 2 1 into the Equation Writer with ECHO and change it to 3 2 1 Or better define a function F K by selecting DEF from the ALGB menu on the menu bar and type k DEF F K
132. the current settings Select Statistics EDIT IN 0 es The Statistics aplet opens in the Numeric view In the C1 column enter the random numbers produced by the calculator J529 295 0952 259 EDIT INE EhET EIG LuwnRslsTHTz 925 592 If necessary select 1 variable statistics Do this by pressing the fifth menu key until pur is displayed as its menu label Calculate statistics The mean of 0 592 seems a little large compared to the expected value of 0 5 To see if the difference is statistically significant we will use the statistics computed here to construct a confidence interval for the true mean of the population of random numbers and see whether or not this interval contains 0 5 Press H8 to close the computed statistics window 11 5 an s Y e hp40g book Page 6 Friday December 9 2005 1 03 AM Open Inference 6 Open the Inference aplet and clear current settings aplet Select 8008 MF STAT SYMBOLIC VIEH Inference METHOD TEST TYRE Test 1 p ALT HYFOTH p lt pA Choose gn inFerentigl nethod Select inference 7 Select an inference method method and SiS Faria ROE WE STAT SYMEOLIC VIEH type Select CONF INTERVAL MT RESET TYFE THNTI 1 Choose dn inFgrentigl nethod 8 Sele
133. these EET transformations reflected in the BWS a toggle between E is chosen the point of control is at the origin 0 0 and the 4 Yjand 4 gt keys control vertical and horizontal transformations When The button labelled is XU 3 is chosen the point of control is on the first extremum of the graph i e for the sine graph at 1 2 1 The arrow keys change the amplitude and frequency of the graph This is most easily seen by experimenting Pressing displays the equation at the top of the screen The equation is controlled by the graph Pressing the and 4 keys moves from parameter to parameter Pressing the a or key changes the parameter s values RESET The default angle setting for this aplet is radians The angle setting can be changed to degrees by pressing 1 15 an Z e hp40g book Page 16 Friday December 9 2005 1 03 AM Aplet library Aplets are stored in the Aplet library To open an aplet Press to display the Aplet library menu Select the aplet and press ESTEE or ENTER From within an aplet you can return to HOME any time by pressing Aplet views When you have configured an aplet to define the relation or data that you want to explore you can display it in different views Here are illustrations of the three major aplet views Symbolic
134. to select the entire expression and then to obtain the intermediate result shown Press once more to yield the result 175 Therefore D 175 when 175 x 5 A baker produces two assortments of biscuits and macaroons A packet of the first assortment contains 17 biscuits and 20 macaroons A packet of the second assortment contains 10 biscuits and 25 macaroons Both packets cost 90 cents Calculate the price of one biscuit and the price of one macaroon Solution Let x be the price of one biscuit and y the price of one macaroon The problem is to solve 16 5 an SZ Exercise 5 16 6 hp40g book Page 6 Friday December 9 2005 1 03 17x 20 90 10x 25 90 Press select LINSOLVE and press Bia Enter 17 ALPHA X 20 nA Y 90 5 mee 3 10 ALPHA X 25 ALPHA Y 90 gt ALPHA X 00 AtpHA Y If you are working in step by step mode pressing produces the result at the right Press again to produce the next step in the solution Press again to produce the reduction result Pressing ENTER again produces the final result If you select is and press NUM you get X 2 and Y 2 8 In other words the price of one biscuit is 2 cents and the price of one macaroon is 2 8 cents Suppose that A and B are points having t
135. 0 ALPHA N 5 SHiFT 4 x 7 ALPHA gt gt LJ 1 Finally press Do likewise to define the other two expressions You can now calculate various values of A N B N and C N simply by typing the defined variable and a value for N and then pressing ENTER For example A 1 yields 39 A 2 yields 399 A 3 yields 3999 B 1 yields 19 B 2 yields 199 Em B 3 yields 1999 and so on In determining the number of digits the decimal representations of a and c can have the calculator is used only to try out different values of n 16 9 an SZ 16 10 e hp40g book Page 10 Friday December 9 2005 1 03 AM Show that the whole numbers k such that 10 lt k lt 10 have n 1 digits in decimal notation We have 10 3 10 a 4 10 10 ntl 10 b 2 10 10 7 1 10 lt 2 10 lt c lt 3 10 lt 10 so have n 1 digits in decimal notation Moreover d 10 1 is divisible by 9 since its decimal notation can only end in 9 We also have a 3 10 4 c 3 10 d so a and c are both divisible by 3 Let s consider whether B 3 is a prime number Type ISPRIME B 3 and press ENTER The result is 1 which means true In other words B 3 is a prime Note ISPRIME is not available fr
136. 03 AM Field Meaning Continued NUMTYPE Type of numeric table Automatic or Build Your Own To build your own table you must type each independent value into the table yourself NUMZOOM Allows you to zoom in or out ona selected value of the independent variable Reset numeric To reset the default values for all table settings press settings CLEAR Exploring the table of numbers NUM view The following table details the menu keys that you use to y menu keys work with the table of numbers Key Meaning EDDIE Displays ZOOM menu list HA Toggles between two character sizes CEFN Displays the defining function expression for the highlighted column To cancel this display press H Aplets and their views 2 17 e 0 Z e hp40g book Page 18 Friday December 9 2005 1 03 AM Zoom within a Zooming redraws the table of numbers in greater or table lesser detail ZOOM options The following table lists the zoom options Option Meaning In Decreases the intervals for the independent variable so a narrower range is shown Uses the NUMZOOM factor in Numeric Setup Out Increases the intervals for the independent variable so that a wider range is shown Uses the NUMZOOM factor in Numeric Setup Decimal Changes intervals for the independent variable to 0 1 units Starts at zero Sho
137. 05 1 03 AM First option function first then arguments In the Equation Writer press select FACTOR and FACTOR is displayed in the Equation Writer with the cursor between the FACTOR 4 parentheses as shown at the right Enter your expression using the rules of selection described earlier re 7 2 gt C 40 B The entire expression is now selected Press then produce the result With a blank Equation Writer screen press MEA select SUBST and then press With the cursor between the parentheses at the location of the first argument type your expression Note that SUBST has two arguments When you have finished entering the first argument the expression press gt to move to the second argument Now enter the second argument x 4 an STA SUBST 4 1 Equation Writer e hp40g book Page 15 Friday December 9 2005 1 03 AM Press to obtain the an intermediate result 4 4 and again to evaluate the intermediate result The final answer is 12 Second option arguments first then function Enter your expression using the rules of selection described earlier m xre 720 C 4 gt gt gt The entire expression is now selected Now press and select FACTOR Notice that th
138. 1 3 The answer is 2 4i With the answer still selected apply the ABS command by pressing SHIFT 0 Pressing gives 24 5 the same answer as with e method 1 above 4 You can also determine equation of the line by typing DROITE 1 3 3 1 Pressing then gives the result obtained before Y 2X 5 Exercise 6 In this exercise we consider some examples of integer arithmetic Part 1 For n a strictly positive integer we define a 4x 10 1 b 2x10 1 c 2x 10 1 1 Compute ay bi a and 2 Determine how many digits decimal representations of a and c can have Show that a and c are divisible by 3 3 Using a list of prime numbers less than 100 show that bs is a prime e NZ SZ Step by Step Examples e hp40g book Page 9 Friday December 9 2005 1 03 AM 4 Show that for every integer n gt 0 b x c Ap 5 Deduce the prime factor decomposition of ag 6 Show that GCD b c GCD c 2 Deduce that b and c are prime together Solution Begin by entering the three definitions Type DEF A N 4 10 1 DEF B N 2 10 1 DEF C N 2 10N 1 Here are the keystrokes for entering the first definition First select the DEF command by pressing HB Now press ALPHA A
139. 1 E5 511 To multiply a matrix by a veclor enter the matrix first then the vector The number of elements in the vector must equal the number of columns in the matrix L13 22 4 42 5811 You can raise a matrix to any power as long as the power is an integer The following example shows the result of raising matrix M1 created earlier to the power of 5 ALPHA 1 2775 ENTER Note You can also raise a Mies matrix to a power without 1869 15581 2337 24 first storing it as a variable Matrices can be raised to negative powers In this case the result is equivalent to 1 matrix ABS power In the following example M1 is raised to the power of 2 ALPHA M17 2 ENTER noces Coo 54 2 513 E72 ros lay 18 7 an Y e hp40g book Page 8 Friday December 9 2005 1 03 AM To divide by a For division of a matrix or a vector by a square matrix square matrix the number of rows of the dividend or the number of elements if it is a vector must equal the number of rows in the divisor This operation is not a mathematical division it is a left multiplication by the inverse of the divisor M1 M2 is equivalent to M27 M1 To divide the two matrices M1 and M2 that you created for the previous example press the following keys ALPHA M1 G ALPHA M2 Mi M2 LL95 41 L 4 31
140. 1 32 partial integration 14 18 hmin hmax 21 32 pause 21 29 hwidth 21 33 isect 21 33 a e Na NY hp40g book Page 10 Friday December 9 2005 1 03 AM labels 21 34 recenter 21 34 root 21 34 s mark sSmark 21 34 statplot 21 35 tracing 21 33 umin umax 21 35 ustep 21 35 polar variables axes 21 31 connect 21 31 grid 21 32 in menu map R 9 indep 21 33 labels 21 34 recenter 21 34 ycross 21 37 polynomial coefficients 13 11 evaluation 13 11 form 13 12 roots 13 12 Taylor 13 7 polynomial functions POLYCOEF 13 11 POLYEVAL 13 11 POLYFORM 13 12 POLYROOT 13 12 ports 22 5 position argument 21 21 power x raised to y 13 5 powers 14 6 POWEXPAND 14 31 POWMOD 14 54 precedence 1 22 predicted values statistical 10 20 PREVAL 14 23 PREVPRIME 14 51 prime factors 14 47 prime numbers 14 50 14 51 primitive 14 23 14 24 print contents of display 21 25 name and contents of variable 21 26 object in history 21 25 variables 21 26 probability functions I 10 an 13 13 COMB 13 12 RANDOM 13 13 UTPC 13 13 UTPF 13 13 UTPN 13 13 UTPT 13 14 program commands 21 4 copying 21 8 creating 21 4 debugging 21 7 deleting 21 9 delimiters 21 1 editing 21 5 naming 21 4 pausing 21 29 printing 21 26 sending and receiving 21 8 structured 21 1 prompt commands beep 21 26 create ee box 21 26 create inpu
141. 1 34 Ycross 21 37 step size of independent variable 21 36 step by step 14 6 STORE 14 14 storing list elements 19 1 19 4 19 5 19 6 matrix elements 18 3 18 5 18 6 results of calculation 17 2 value 17 2 strings literal in symbolic operations 13 18 STURMAB 14 69 SUBST 14 15 substitution 14 14 SUBTMOD 14 55 subtract 13 4 summation function 13 11 symbolic calculations in Function aplet 13 2 defining expressions 2 1 differentiation 13 21 displaying definitions 3 8 evaluating variables in view 2 3 setup view for statistics 10 12 symbolic calculations 14 1 symbolic functions where 13 18 equals 13 17 ISOLATE 13 17 LINEAR 13 18 QUAD 13 18 QUOTE 13 18 Symbolic view defining expressions 3 2 syntax 13 2 syntax errors 21 7 T table navigate around 3 8 numeric values 3 7 numeric view setup 2 16 TABVAR 14 27 TAN2CS2 14 40 TAN2SC 14 41 TAN2SC2 14 41 tangent 13 4 inverse hyperbolic 13 9 Taylor polynomial 13 7 TAYLORO 14 27 TCHEBYCHEFF 14 59 TCOLLECT 14 41 tests 14 61 TEXPAND 14 15 14 42 tickmarks for plotting 2 6 time 13 15 setting 21 27 time converting 13 15 times sign 1 20 TLIN 14 43 tmax 21 36 tmin 21 36 too few arguments R 21 TOOL menu 15 1 tracing functions 2 8 more than one curve 2 8 not matching plot 2 8 plots 2 8 transcendental expressions 14 42 transmitting lists 19 6 matrices 18 4 programs 21 8 transposing a matrix 18 13 Triangle Solver aplet 9 1 TRIG 14 43
142. 14 To find the area between the two functions in the area of the two range 2 lt x lt 1 first move the cursor to functions F1 x 1 and select the signed area option 15 Move the cursor to x 2 by pressing or 4 key Function aplet 3 5 4 e hp40g book Page 6 Friday December 9 2005 1 03 AM 4 f IM nhl 16 Press BIB to accept using F2 x x 3 2 as the other boundary for the integral 17 Choose the end value for x The cursor jumps to x 1 on the linear function Dares 1 O e 18 Display the numerical e value of the integral Note See Shading area on page 3 11 for another method of eres 216666666667 calculating area To find the 19 Move the cursor to the quadratic equation and find extremum of the the extremum of the quadratic quadratic a HEC un The coordinates of the extremum are EMTRM 3 2 ET displayed at the bottom of the screen Function aplet 4 HINT Display the numeric view Set up the table Explore the table Function aplet hp40g book Page 7 Friday December 9 2005 1 03 AM The Root and Extremum functions return one value only even if the function has more than one root or extremum The function finds the val
143. 2005 1 03 AM ASIN2C ASIN2T ATAN2S Computer Algebra System CAS Typing ACOS2S ACOS X ASIN X gives when simplitied 2 Transform the arcsin into arccos ASIN2C has as a trigonometric expression as an argument ASIN2C transforms the expression by replacing arcsin x with 2 arccos x Typing ASIN2C ACOS X ASIN X gives when simplitied Nola Transform the arccos into arctan ASIN2T has a trigonometric expression as an argument ASIN2T transforms the expression by replacing arcsin x with 1 Typing ASIN2T ASIN X gives wl 5 Transform the arctan into arcsin ATAN2S has a trigonometric expression os an argument ATAN2S transforms the expression by replacing arctan x with ores 2 EX 14 39 T e P NY HALFTAN SINCOS TAN2CS2 14 40 e hp40g book Page 40 Friday December 9 2005 1 03 AM Typing ATAN2S ATAN X gives isi 1 Transform in terms of tan x 2 HALFTAN has a trigonometric expression as an argument HALFTAN transforms sin x cos x and tan x in the expression rewriting them in terms of tan x 2 Typing HALFTAN SIN X COS X 2 gives SQ X X rm Y mw so tan 3 so tan 3 1 or after simplification Transform the complex exponentials into sin a
144. 3 T e P NY MULTMOD POWMOD 14 54 e hp40g book Page 54 Friday December 9 2005 1 03 AM Performs a multiplication in Z pZ or in Z pZ X Example 1 Typing MULTMOD 11 8 gives 3 Example 2 Typing MULTMOD 11X 5 8X 6 gives 3x 2x 4 Calculates A to the power of N in Z pZ X and A X to the power of N in Z pZ X Example 1 If p 13 typing POWMOD 11 195 gives 5 In effect 11 2 1 mod 13 so 11 1111253 2 5 mod 13 Example 2 Typing POWMOD 2X 1 5 gives 6x t2x 42x jx 1 since 32 6 mod 13 80 2 mod 13 40 1 mod 13 10 3 mod 13 Computer Algebra System CAS T e e hp40g book Page 55 Friday December 9 2005 1 03 AM e NY SUBTMOD Performs a subtraction in Z pZ or Z pZ X Example 1 Typing SUBTMOD 29 8 gives 5 Example 2 Typing SUBTMOD 11X 5 8X 6 gives 3x 1 Polynomial menu EGCD Returns Bezouf s Identity the Extended Greatest Common Divisor EGCD ee EGCD A X B X returns U X AND V X 2 D X with D U V such that D X U X A X V X B X Example 1 Typing EGCD X 2 X 1 X 1 gives AND 1 2x 2 Example 2 Typing EGCD C 2 X 1 X3 1 gives x 2 AND 1 3x 3
145. 3 AM Delete a program Delete all programs Delete the contents of a program To delete a program 1 Press SHIFT PROGRM to open the Program catalog 2 Highlight a program to delete then press DEL You can delete all programs at once 1 In the Program catalog press CLEAR You can clear the contents of a program without deleting the program name 1 Press SHIFT PROGRM to open the Program catalog Highlight a program then press misi 2 3 Press SHIFT CLEAR then press gizi 4 The contents of the program are deleted but the program name remains Customizing an aplet amp Programming You can customize an aplet and develop a set of programs to work with the aplet Use the SETVIEWS command to create a custom VIEWS menu which links specially written programs to the new aplet A useful method for customizing an aplet is illustrated below 1 Decide on the built in aplet that you want to customize For example you could customize the Function aplet or the Statistics aplet The customized aplet inherits all the properties of the built in aplet Save the customized aplet with a unique name 2 Customize the new aplet if you need to for example by presetting axes or angle measures 3 Develop the programs to work with your customized aplet When you develop the aplet s programs use the standard aplet naming convention This allows you to keep track of the prog
146. 34 12 and combine it with 6 3 Follow the same procedure as undertaken a number of Faas ERES times above You will find that 3 12 is equal to 6 3 and so the final two terms cancel each other out Hence the result is 4 5 3 Given the expression D 3x 1y 81 expand and reduce D e factor D solve the equation 3x 10 3x 8 0 and e evaluate D for x 5 Solution First enter D using the Equation Writer 3 ALPHA X 1 gt x 2 ej L 81 Press gt lt to select 3X 1 and to expand the expression This gives 9x 6x 1 81 16 4 an 2 244 1 814 Step by Step Examples e hp40g book Page 5 Friday December 9 2005 1 03 AM Example 4 Step by Step Examples Press A to select the entire equation then press ENTER to reduce it to 2 Ox 6x 80 Press select FACTOR press and then ENTER The result is as shown at the right Now press select SOLVEVX press and press ENTER The result is shown at the right Press to display CAS history select D or a version of it and press ENTER Press MEA select SUBST press Bii and then complete the second argument x 5 SUBSTI axe 88 x 5 Press gt gt
147. 4 the circle C M will move on a curve In this exercise we will study and plot 1 Let and m be the point on C of affix z e Find the coordinates of M in terms of Compare x t with x t and y 1 with y t Compute x and find the variations of x over O Repeat step 3 for y Show the variations of x and y in the same table e or de e Put the points of corresponding to t O 2 3 27 3 and n and draw the tangent to T at these points First go lo CAS MODES RE RT screen and make t the VX variable To do this press Indep war t nduln Approx _ Dun Factor Conplesx WMerbozg witepe Incr yw Figorouzy zinp Don Egtiongl nter Hodulo ag he BEES to open the Equation Writer and then press This opens CAS MODES screen Press H and delete the current Now enter the expression 1 22 and press gt 5 to select it Now invoke the SUBST command from the 2 menu Because the sues Z z expression was highlighted the SUBST command is automatically applied to it Note that the cursor is positioned in the second parameter Since we know 2 t that z we can enter this as the second parameter Step by Step Examples an Z gt e hp40g book Page 15 Friday December 9 2005 1 03 AM Sel
148. 40gs connectivity kit to transfer the aplet Highlight your selection and press If transmitting to a disk drive you have the options of sending to the current default e directory or to another directory 3 Receiving calculator Open the aplet library and press pmi rEcEIvE rrom menu appears with the following options HP39 40 USB to receive via the USB port HP39 40 SER fo receive via the RS232 serial port USB DISK DRIVE to receive from a disk drive via the USB port SER DISK DRIVE to receive from a disk drive via the RS232 serial port Note choose a disk drive option if you are using the hp40gs connectivity kit to transfer the aplet Highlight your selection and press pr The Transmit annunciator is displayed until transmission is complete 6 Extending aplets 22 5 4 ZN NY 4 hp40g book Page 6 Friday December 9 2005 1 03 AM If you are using the PC Connectivity Kit to download aplets from a PC you will see a list of aplets in the PC s current directory Check as many items as you would like to receive Sorting items in the aplet library menu list To sort the aplet list To delete an aplet Once you have entered information into an aplet you have defined a new version of an aplet The information is automatically saved under the current aplet name such as Function
149. 5 18 Equation Writer e NZ hp40g book Page 19 Friday December 9 2005 1 03 AM SYMB key SHIFT SYMB or SHIFT HOME keys SHIFT key PLOT key Equation Writer HA Press to clear the value of the highlighted variable XT Press to change the name of the highlighted variable Press to define a new variable which you do by specilying an object and a name for the object Pressing the key in the Equation Writer gives you access to CAS history As in the HOME screen history the calculations are written on the left and the results are written on the right Using the arrow keys you can scroll through the history ERPHNDE SEA EET AL Zu XH T BERO FACTOR SIS ARR D OE ECHO VIEH INFO COPY Press copy the highlighted entry in history to the clipboard in order to paste it in the Equation Writer Press or Gai to replace the current selection in Equation Writer with the highlighted entry in CAS history Press ON to leave CAS history without changing it in any way While you are working f x BB Equation Writer pressing SHIFT or aope hun Factor WP opens CAS MODES gf Aeros ziHp ilwh mnL nter independent varadb Le screen The various CAS t modes are described in CAS modes on page 14 5 Pressing followed by the comma key undoes that is cancels
150. 87 Click EI to close the information window that appears The following example shows the information available about the speed of light one of the physics constants SI CnMZTRHMT sed of liah alP Symbol c 299792455 mean F 5 To use the selected constant in a calculation press ma The constant appears at the position of the cursor on edit line 4 Suppose you want to know potential energy of a mass of 5 units according to the equation E mc 1 Enter 5 x 13 26 Using mathematical functions gt 9 4 P hp40g book Page 27 Friday December 9 2005 1 03 AM 3 Select light s from the Physics menu Using mathematical functions an STA light permitti 14925956228 13 27 4 X iG e hp40g book Page 28 Friday December 9 2005 1 03 AM T an ad e 4 hp40g book Page 1 Friday December 9 2005 1 03 AM 14 Computer Algebra System CAS What is a CAS A computer algebra system hereafter CAS enables you to perform symbolic calculations With a CAS you manipulate mathematical equations and expressions in
151. 9 2 Enter the measurement data 160 165 170 175 EDIT INS J SORT BIS UTC E ELE 180 ENTER Statistics aplet 10 7 e e zz gt e hp40g book Page 8 Friday December 9 2005 1 03 AM 3 Find the mean of the sample Ensure the Ea menu key label reads Press statistics calculated from the sample data in C1 Nolte that the title of the column of statistics is H1 There are 5 data set definitions available for one variable statistics H1 H5 If data is entered in C1 H1 is automatically set to use C1 for data and the frequency of each data point is set to 1 You can select other columns of data from the Statistics Symbolic setup view 4 Press BEM lo close the EE STATISTICS SYMBOLIC VIEH RE statistics window and H3 1 SYMB key t press eyfosee i Ha i 4 the data set definitions EMTER SAMPLE EDIT CHE c EYAL The first column indicates the associated column of data for each data set definition and the second column indicates the constant frequency or the column that holds the frequencies The keys you can use from this window are Copies the column variable or variable expression to the edit line for editing Press MA when done Checks unchecks the current data set Only the checkmarked data set s are computed and plotted Typi
152. AM Function aplet interactive analysis Access FCN variables Function aplet From the Plot view PLOT you can use the functions on the FCN menu to find roots intersections slopes and areas for a function defined in the Function aplet and any Function based aplets See FCN functions on page 3 10 The FCN operations act on the currently selected graph The results of the FCN functions are saved in the following variables e Area Exfremum lsect Root Slope For example if you use the Root function to find the root Root 179 366 The FCN variables are contained on the VARS menu To access FCN variables in HOME Select Plot FCN Extremum gt Izect Humer ic Foot a or v lo choosea EEESEIED EERO ea TN variable 8 To access FCN variable in the Function aplet s Symbolic view Selec Plot FCN A or v to choose a variable 3 9 an e hp40g book Page 10 Friday December 9 2005 1 03 AM FG NY FCN functions The FCN functions are Function Description Root Select Root to find the root of the current function nearest the cursor If no root is found but only an extremum then the result is labeled EXTR instead of ROOT The rooHfinder is also used in the Solve aplet See also Interpreting results on page 7 6 The cursor is moved to
153. AT REVERSE SIZE MAKELIST PAS LIST SORT POS loop ITERATE RECURSE X T a X iG e hp40g book Page 14 Friday December 9 2005 1 03 AM Category Available name Continued Matrix COLNORM QR COND RANK CROSS ROWNORM DET RREF DOT SCHUR EIGENVAL SIZE EIGENVV SPECNORM TDENMAT SPECRAD TNVERSE SVD TO SVL LSQ TRACE LU TRN MAKEMAT Polynom POLYCOEF POLYFORM POLYEVAL POLYROOT Prob COMB UTPC UTPF PERM UTPN RANDOM UTPT Real CEILING MIN DEG RAD MOD FLOOR FNROOT CHANGE FRAC TOTAL HMS gt RAD DEG gt HMS ROUND TNT STGN MANT TRUNCATE MAX XPON Stat Two PREDX PREDY Symbolic ISOLATE QUOTE LINEAR T e Na PN hp40g book Page 15 Friday December 9 2005 1 03 AM NY Category Available name Continued Tests 2 AND lt NOT XOR gt gt Trig ACOT COT ACSC CSC ASEC SEC Program constants The program constants are Category Available name Angle Degrees Grads e Radians Format Standard Sci Fixed Eng Fraction SeqPlot Cobweb Stairstep 1 5fit Linear QuadFit LogFit Cubic ExpFit Logist Power User Trigonometric Exponent StatMode StatzVar StatPlot Hist 15 a e Na
154. BS ARG RE CONJ SIGN DROITE Constant e oo TU Diff amp Int DERIV PREVAL DERVX RISCH DIVPC SERIES FOURIER TABVAR IBP TAYLORO INTVX TRUNC lim Hyperb ACOSH COSH ASINH SINH ATANH TANH Integer DIVIS TREMATNDER EULER ISPRIME FACTOR LCM GOD MOD IDIV2 NEXTPRIME IEGCD PREVPRIME IQUOT Modular ADDTMOD INVMOD DIVMOD MODSTO EXPANDMOD MULTMOD FACTORMOD POWMOD GCDMOD SUBTMOD an ad R 17 T 4 hp40g book Page 18 Friday December 9 2005 R 18 1 03 Function Continued Polynom EGCD PARTFRAC FACTOR PROPFRAC GCD PTAYL HERMITE QUOT LCM REMAINDER LEGENDRE TCHEBYCHEFF Real CEILING INT FLOOR MAX FRAC MIN Rewrite DISTRIB POWEXPAND EPSXO SINCOS EXPLN XUL SIMPLIFY FDISTRIB XNUM EIN XQ LNCOLLECT Solve DESOLVE LINSOLVE ISOLATE SOLVE LDEC SOLVEVX Tests ASSUME UNASSUME AND 4 OR NOT lt TFTE lt Trig ACOS2S TAN2SC2 ASIN2C ASIN2T TEXPAMD ATAN2S TLIN HALFTAN TRIG SINCOS TRIGCOS TAN2CS2 TRIGSIN TANZSC TRIGTAN am 27 T 4 hp40g book Page 19 Friday December 9 2005 Program commands 1 03 The program commands Category Aplet Branch Drawing Graphic Loop Matrix Print Prompt Stat One Command CHECK SELECT SE
155. CH TLUG CH R36 a 2 4 8 a ENS EMIT ee Specify plot 3 Specify the plot settings In this example we will use settings the default settings except for the ORNG fields SETUP PLOT POLAR PLOT SETUP CLEAR coe 12 5663 4 HS tne aI 82 EMTER SIEE Plot the 4 Plot the expression expression B 1082 6 283185 MAN Polar aplet 5 1 e NZ IN Y e hp40g book Page 2 Friday December 9 2005 1 03 AM Explore the 5 Display the Plot view menu key labels graph m The Plot view options available are the same as those found in the Function aplet See Exploring the graph on page 27 for further information Display the 6 Display the table of values for 0 and R1 numbers NUM The Numeric view options available are the same as those found in the Function aplet See Exploring the table of numbers on page 2 17 for further information Polar aplet 4 iG e hp40g book Page 1 Friday December 9 2005 1 03 AM Sequence aplet About the Sequence aplet The Sequence aplet allows you to explore sequences You can define a sequence named for example U1 in terms ofn in terms of U1 n 1 in terms of U1 n 2 in terms of another sequence for example U2 n in any combination of the
156. CRR 1 HE 4 1 CHARS gt 1 AND suirr cans lt 1 D 04 EJ amp 0 GJ 9 X SHIFT CHARS gt 1 D Note You can use ti menu key to assist in the entry of equations It has the same effect as pressing X18 3 12 Function aplet e e e GIN e hp40g book Page 1 Friday December 9 2005 1 03 AM Parametric aplet About the Parametric aplet The Parametric aplet allows you to explore parametric equations These are equations in which both x and y are defined as functions of t They take the forms x Kt and y g t Getting started with the Parametric aplet The following example uses the parametric equations x t 3sint y t 3cost e Note This example will produce a circle For this e example to work the angle measure must be set to degrees Open the 1 Open the Parametric aplet metric aplet Parametric apie Select APLET LIERARY Parametric Function HET EER Polar o BKE Sequence EHEM Define the 2 Define the expressions expressions 3 x SIN DJ SEES PARAMETRIC SYMEOLIC VIEH SEE WALCTI S45IHCTo YICTOSSSCOSCTS 3 xJ D YeCT CHE T EHO EVAL Parametric aplet 4 1 e NZ Y e hp40g book Page 2 Friday December 9 2005 1 03 AM S
157. Internally represented as t1017 MINREAL Internally represented as 3 14159265359 TU The conversion functions are found on the Convert menu They enable you to make the following conversions Using mathematical functions am a T a NY 4 P hp40g book Page 9 Friday December 9 2005 1 03 AM F IN lL LGAL LBS KM MILE DEG RAD Convert from Fahrenheit to Celcius Example C 212 returns 100 Convert from Celcius to Fahrenheit Example F 0 returns 32 Convert from inches to centimeters Convert from centimeters to inches Convert from US gallons to liters Convert from liters to US gallons Convert from pounds to kilograms Convert from kilograms to pounds Convert from miles to kilometers 4 Convert from kilometers to miles Convert from radians to degrees Convert from degrees to radians Hyperbolic trigonometry ACOSH ASINH ATANH Using mathematical functions The hyperbolic trigonometry functions can also take complex numbers as arguments Inverse hyperbolic cosine cosh zx ACOSH value Inverse hyperbolic sine sinh 1 ASINH value Inverse hyperbolic tangent tanh7 x ATANH value T e NY 4 hp40g book Page 10 Friday December 9
158. L x Example TOTAL 20 50 returns 250 6 RAD DEC Radians to degrees Converts value from radians to degrees RAD DEG value Example RAD DEG returns 180 ROUND Rounds value to decimal places Accepts complex numbers ROUND value places Round can also round to a number of significant digits as showed in example 2 Examples ROUND 7 8676 2 returns 7 87 ROUND 0 0036757 3 returns 0 00368 SIGN Sign of value If positive the result is 1 If negative 1 If zero result is zero For a complex number this is the unit vector in the direction of the number SIGN value SIGN x y 13 16 Using mathematical functions T a PN NZ ZN 4 P hp40g book Page 17 Friday December 9 2005 1 03 AM TRUNCATE XPON Examples SIGN 2 returns 1 SIGN 3 4 returns 6 8 Truncates value to decimal places Accepts complex numbers TRUNCATE value places Example TRUNCATE 2 3678 2 returns 2 36 Exponent of value XPON value Example XPON 123 4 returns 2 Two variable statistics Symbolic functions equals ISOLATE Using mathematical functions These are functions for use with two variable statistics See Two variable on page 10 15 The symbolic functions are used for symbolic manipulations of expressions The variables can be for
159. LASSUME contains a list of the names of the symbolic variables that are considered reals If you ve chosen the Cmp1x vars option on CFG configuration menu the defaults are X Y t S1 and 52 as well as any integration variables that are in use If you ve chosen the Real vars option on CFG configuration menu all symbolic variables are considered reals You can also use an assumption to define a variable such as X gt 1 In a case like this you use the ASSUME X gt 1 command to make REALASSUME contain X gt 1 The command UNASSUME X cancels all the assumptions you have previously made about X To see these variables as well as those that you ve defined in CAS press in the Equation Editor see CAS variables on page 14 4 The keyboard in the Equation Writer The keys mentioned in this section have different functions when pressed in the Equation Writer than when used elsewhere MATH i i MATH key The key if pressed in e the Equation Writer displays just those functions used in pees EA symbolic calculation These Diff amp Intw FHCTOUR functions are contained in the following menus The five function containing Equation Writer menus outlined in the previous section Algebra MEA Equation Writer 15 17 an Z gt e hp40g book Page 18 Friday December 9 2005 1 03 AM DiffsInt MINH R
160. LIN does not linearize trigonometric expressions as does TLIN but converts a trigonometric expression to exponentials and then linearizes the complex exponentials LIN puts the calculator into complex mode when dealing with trigonometric functions Example 1 Typing LIN EXP X 1 gives 3 exp x 1 2 exp 3 x Example 2 Typing LIN COS gives 14 30 Computer Algebra System CAS T a e NY LNCOLLECT gt POWEXPAND SINCOS Computer Algebra System CAS 2 e hp40g book Page 31 Friday December 9 2005 1 03 AM 1 1 1 E 2 1 t exp 2 i x Example 3 Typing LIN SIN X gives eXD7 5 exp i x Regroup the logarithms LNCOLLECT has as an argument an expression containing logarithms LNCOLLECT regroups the terms in the logarithms It is therefore preferable to use an expression that has already been factored using FACTOR Typing LNCOLLECT LN X 1 LN X 1 m gives In x 1 x 1 Transform a power POWEXPAND writes a power in the form of a product Typing POWEXPAND X 1 gives x 1 x 1 x 1 This allows you to do the development of x 1 3 in step 2E using DISTRIB several times on the preceding Transform the complex exponentials into sin and cos SINCOS takes as an argument an expression
161. LVE AUMERIC y l156 6r 16067 v 16 ETE VALUE OF PRES mE 100 If the Decimal Mark setting in the Modes input form SHIFT MODES is set to Comma use instead of 0 5 Solve for the unknown variable A SOLVE NUMERIC VIEH iis VALUE OF PRESS SOLVE EDIT INFO DEFN Therefore the acceleration needed to increase the speed of a car from 16 67 m sec 60 kph to 27 78 m sec 100 kph in a distance of 100 m is approximately 2 47 m s2 Because the variable A in the equation is linear we know that we need not look for any other solutions The Plot view shows one graph for each side of the selected equation You can choose any of the variables to be the independent variable The current equation is V U 240 One of these is Y V with V 27 78 that is Y 771 7284 This graph will bea horizontal line The other graph will be Y U 240 with U 16 67 and D 100 that is Y 2004 277 8889 This graph is also a line The desired solution is the value of A where these two lines intersect 7 3 e NZ zz gt e hp40g book Page 4 Friday December 9 2005 1 03 AM 6 Plot the equation for variable A Select Auto Scale A 0 El 771 7284 HAMN 7 Trace along the graph representing the lef side of the equation until the cursor nears the intersection sT EL221
162. MAS highlight your choice and press or BIB As a shortcut to MEE just highlight the field to change and press to cycle through the options If there is an option to select or deselect press to check or uncheck it 2 Press GAZ to view more settings 3 When done press to view the new plot Aplets and their views 2 5 e NZ Y e hp40g book Page 6 Friday December 9 2005 1 03 AM Plot view The plot view settings are settings Field Meaning XRNG YRNG Specifies the minimum and maximum horizontal X and vertical Y values for the plotting window RES For function plots Resolution Faster plots in alternate pixel columns Detail plots in every pixel column TRNG Parametric aplet Specifies the t values T for the graph ORNG Polar aplet Specifies the angle 0 value range for the graph NRNG Sequence aplet Specifies the index N values for the graph TSTEP For Parametric plots the increment for the independent variable OSTEP For Polar plots the increment value for the independent variable SEQPLOT For Sequence aplet Stairstep or Cobweb types XTICK Horizontal spacing for tickmarks YTICK Vertical spacing for tickmarks Those items with space for a checkmark are settings you can turn on or off Press ETHIE to display the second page Field Meaning SIMULT If more than one relation
163. MEDIES EXCEPT AS INDICATED ABOVE IN NO EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR DIRECT SPECIAL INCIDENTAL CONSEQUENTIAL INCLUDING LOST PROFIT OR DATA OR OTHER DAMAGE WHETHER BASED IN CONTRACT TORT OR OTHERWISE Some countries States or provinces do not allow the exclusion or limitation of incidental or consequential damages so the above limitation or exclusion may not apply to you The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services HP shall not be liable for technical or editorial errors or omissions contained herein FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND NEW ZEALAND THE WARRANTY TERMS CONTAINED IN THIS STATEMENT EXCEPT TO THE EXTENT LAWFULLY PERMITTED DO NOT EXCLUDE RESTRICT OR MODIFY AND ARE IN ADDITION TO THE MANDATORY STATUTORY RIGHTS APPLICABLE TO THE SALE OF THIS PRODUCT TO YOU an ad T iG e hp40g book Page 3 Friday December 9 2005 1 03 AM Service Europe Asia Pacific Country Telephone numbers Austria 43 1 3602771203 Belgium 32 2 7 126219 Denmark 45 8 2332844 Eastern Europe 420 5 41422523 countries Finland 35 89640009 France 33 1 49939006 Germany 49 69 95307 103 Greece 420 5 41422523 Holland 3 1 2 06545301 ltaly 39 02 754 19782 Norway 47 63849309 Portugal 35 1 229570200
164. NG VALUE FOR TRELE EnIT iro 5 Display the functions in numeric form NUM Aplets and their views an STA 2 21 X iG e hp40g book Page 22 Friday December 9 2005 1 03 AM T an ad e GIN e hp40g book Page 1 Friday December 9 2005 1 03 AM Function aplet About the Function aplet The Function aplet enables you to explore up to 10 real valued rectangular functions y in terms of x For example y 2x 3 Once you have defined a function you can create graphs to find roots intercepts slope signed area and extrema create tables to evaluate functions at particular values This chapter demonstrates the basic tools of the Function gt aplet by stepping you through an example See Aplet amp Y views on page 2 1 for further information about the Y functionality of the Symbolic Numeric and Plot views Getting started with the Function aplet The following example involves two functions a linear function y c 1 and a quadratic equation x 3 2 Open the 1 Open the Function aplet Function aplet Ce The Function aplet starts 5 gt in the Symbolic view LEDIT The Symbolic view is the defining view for Function Parametric Polar and Sequenc
165. NTER 3 Decide whether you want the aplet to operate Degrees Radians or Grads SHIFT MODES Degrees CHOOSE AMGLE MEASURE Ok 4 View the Aplet Library The TRIANGLES aplet is listed in the Aplet Library APLET Em z E 3 LES 51KE The Solve aplet can now be reset and used for other problems Statistics Funct 1 22 2 Extending aplets T am S m SZ Y e hp40g book Page 3 Friday December 9 2005 1 03 AM Using a customized aplet To use the Triangles aplet simply select the appropriate formula change to the Numeric view and solve for the missing variable Find the length of a ladder leaning against a vertical wall it it forms an angle of 35 with the horizontal and extends 5 metres up the wall 1 Select the aplet TRIANGLES SVMEDLIC VIEH TERES E1 SIHcB3z 0 H TRIANGLES E2 COSCA 3 R 4H ES THHCB3 0L H we EDIT lecHE EVAL 2 Choose the sine formula swremuc Ee in E JEME H zi 4 a 4 4 E4 B ES EDIT W CHE EVAL 3 Change to the Numeric a TRIANGLES MUMERIC VIEH 2555555 view and enter the amp 35 5 known values NEEEEEEEEH NUM ENTER VALUE HE PRESS SOLVE 35 5 4 Solve f
166. ONCAT Concatenates two lists into a new list CONCAT list list2 4 amp Example 1 2 3 4 returns 1 2 3 4 ALIST Creates a new list composed of the first differences that is the differences between the sequential elements in list The new list has one fewer elements than list1 The first differences for x are x5 x x x ALIST list Example In HOME store 3 5 8 12 17 23 in L5 and find the first differences for the list HOME HIFT EDIT SERES FUMCTION See 2 5 B 12 17 22285 3 5 8 12 17 23 3 5 5 124 17 232 amp LISTOLS5 SHIFT ER ALPHA 2 34 d 54 52 L 5 ENTER MATH L gt Select ALIST HZ ALPHA L5 Lists 19 7 gt 9 Y e hp40g book Page 8 Friday December 9 2005 1 03 AM MAKELIST Calculates a sequence of elements for a new list Evaluates expression with variable from begin to end values taken at increment steps MAKELIST expression variable begin end increment The MAKELIST function generates a series by automatically producing a list from the repeated evaluation of an expression Example In HOME generate a series of squares from 23 to 27 MATH L Select _ 5 23 27 12 ALPHA A 529 976 625 r 7297 C ALPHA A C 23 C 27010 IILIST Calculates the product of all eleme
167. Or if you have stored f x in F that is if you have already typed TORE LN a Ne then type INTVX F 0 Or if you have used DEF to define f x that is if you have already typed DEF F X a LN then type INTVX F X The result in all cases is equivalent to ZAD 3 3 LN gt LN IX 1 3 LN IX 1 You will obtain absolute values only in Rigorous mode See CAS modes on page 14 5 for instructions on setting and changing modes Example Calculate 2 dx 2 Fa d Typing 14 20 Computer Algebra System CAS T e a Note NOTE lim Computer Algebra System CAS e hp40g book Page 21 Friday December 9 2005 1 03 AM 3 Nrvx X 2 X x gives a primitive X 2 x 1 3 atan x Y 2 You can also type Far ax primitive which is zero for x 1 dX which gives the 3 atana a X x 4 Example Calculate 1 J Gy ene Typing KK SIN X SINQ Xy NTVX gives the result 5 LN cos X 11 3 LNeos OO 11 LN 2c0s X 1l If the argument to INTVX is the AND of two elements INTVX concerns itself only with the second element of the AND and adds the result to the first argument Calculate
168. Plot and Numeric the six supporting aplet views from the VIEWS menu and the two user defined views Note and Sketch Note some aplets such as the Linear Solver aplet and the Triangle Solver aplet only have a single view the Numeric view Symbolic view Press to display the aplet s Symbolic view 1e You use this view to define ruwcrimw SyMenLic WEN ERE the function s or equation s CPI CHISCHAS E E that you want to explore See About the Symbolic un EWT Ee view on page 2 1 for further information Plot view Press to display the aplet s Plot view In this view the functions that you have defined are displayed graphically See About the Plot view on page 2 5 for further information nu Flink 7 HEHU _ 1 16 Getting started e 0 4 Numeric view Plot Table view Plot Detail view Overlay Plot view Getting started P hp40g book Page 17 Friday December 9 2005 1 03 AM Press NUM to display the aplet s Numeric view In this view the functions that you have defined are displayed in tabular format See About the numeric view on page 2 16 for further information The VIEWS menu contains the Plot Table view VIEWS Select Plot Table H amp Splits the screen into the plot and the data tabl
169. Q X are mutually primes and all solutions are congruent modulo S X R X Q X 1467 Computer Algebra System CAS e NZ e hp40g book Page 63 Friday December 9 2005 1 03 AM e NY Example Find the solutions P X of P X X mod X2 1 P X X 1 mod X2 1 Typing CHINREM X AND X 1 X 1 AND X 1 gives 2 4 Xx AND 1 That is 4 2 PLX X A mod CYCLOTOMIC Returns the cyclotomic polynomial of order n This is a polynomial having the nth primitive roots of unity as 0 Zeros CYCLOTOMIC has an integer n as its argument Example 1 When n 4 the fourth roots of unity are 1 i 1 i Among them the primitive roots are i i Therefore the cyclotomic polynomial of order 4 is X i X i X 1 Example 2 Typing CYCLOTOMIC 20 gives 8 6 4 2 X X Bue Al EXP2HYP EXP2HYP has an expression enclosing exponentials as an argument It transforms that expression with the relation exp a sinh a cosh a e Computer Algebra System CAS 14 63 T e P e hp40g book Page 64 Friday December 9 2005 1 03 AM NY Example 1 Typing EXP2HYP EXP A gives sinh a cosh a Example 2 Typing EXP2HYP EXP A EXP A gives 2 cosh a
170. RAd x 2X 2X 93 gives in real and direct mode X 3 n x 2 x7 2 2x 2 and gives in complex mode 1 3 i l 1 3 i 4 x 2 T a e P NY 4 hp40g book Page 58 Friday December 9 2005 1 03 AM PROPFRAC PTAYL QUOT 14 58 PROPFRAC rewrites a rational fraction so as to bring out its whole number part PROPFRAC A X B X writes the rational fraction A X B X in the form RW 20 60 where R X O or O lt deg R X lt deg B X Example Typing 5X 3 X 1 ROPFRA x XD gives 5x 124 2L 2 PTAYL rewrites a polynomial P X in order of its powers of X a Example Typing PTAYLOC 2 X 1 2 produces the polynomial Q X namely Note that 2 QUOT returns the quotient of two polynomials A X and B X divided in decreasing order by exponent Example Typing QUOT X 2 X 1 X gives CED Computer Algebra System CAS am ad T a REMAINDER TCHEBYCHEFF Computer Algebra System CAS e hp40g book Page 59 Friday December 9 2005 1 03 AM Note that in step by step mode synthetic division is shown with each polynomial represented as the list of its coefficients in descending order of power Returns the re
171. RDISPLAY PRHISTORY Prints all objects in the history PRHISOTORY Programming 21 25 a e PRVAR P hp40g book Page 26 Friday December 9 2005 1 03 AM Prints name and contents of variablename PRVAR variablename You can also use the PRVAR command to print the contents of a program or a note PRVAR programname PROG PRVAR notename NOTE Prompt commands BEEP CHOOSE CLRVAR 21 26 Beeps at the frequency and for the time you specity BEEP frequency seconds Creates a choose box which is a box containing a list of options from which the user chooses one Each option is numbered 1 through n The result of the choose command is to store the number of the option chosen in a variable The syntax is CHOOSE variable name title option option option where variable_name is the name of a variable for storing a default option number title is the text displayed in the title bar of the choose box and option option are the options listed in the choose box By pre storing a value into variable_name you can specity the default option number as shown in the example below Example 3 gt A CHOOSE A Y WW COMIC TRIPS DILBERT CRLVIH amp H BBES BLOHDIE CALVIN amp HOBBES BLONDIE no Clears the specified variable The syntax is CLRVAR variable Programming an
172. T MAX MIN MOD Using mathematical functions Hours minutes seconds to decimal Converts a number or expression in H MMSSs format time or angle that can include fractions of a second to x x format number of hours or degrees with a decimal fraction HMS gt H MMSSs Example HMS 8 30 returns 8 5 Decimal to hours minutes seconds Converts a number or expression in x x format number of hours or degrees with a decimal fraction to H MMSSs format time or angle up to fractions of a second HMS x x Example HMS 8 5 returns 8 3 Integer part INT value Example INT 23 2 returns 23 Mantissa significant digits of value MANT value Example MANT 21 2E34 returns 2 12 Maximum The greater of two values MAX valuel value2 Example MAX 210 25 returns 210 Minimum The lesser of two values MIN vojue7 value2 Example MIN 210 25 returns 25 Modulo The remainder of value 1 value2 value MOD valve2 13 15 T a e PN hp40g book Page 16 Friday December 9 2005 1 03 AM NY Example 9 MOD 4 returns 1 76 x percent of y that is x 100 y x y Example 20 50 returns 10 CHANGE Percent change from x to y that is 100 y x x CHANGE x y Example CHANGE 20 50 returns 150 ZTOTAL Percent total 100 y x What percentage of x is y Y TOTA
173. TRN matrix Examples Identity Matrix You can create an identity matrix with the IDENMAT function For example IDENMAT 2 creates the 2x2 identity matrix 1 0 0 1 You can also create an identity matrix using the MAKEMAT make matrix function For example entering MAKEMAT IAJ 4 4 creates a 4 x 4 matrix showing the numeral 1 for all elements except zeros on the diagonal The logical operator V4 returns when the row number and J the column number are equal and returns 1 when they are not equal Transposing a The TRN function swaps the row column and column row Matrix elements of a matrix For instance element 1 2 row 1 Matrices 18 13 a e Z e hp40g book Page 14 Friday December 9 2005 1 03 AM column 2 is swapped with element 2 1 element 2 3 is swapped with element 3 2 and so on For example TRN 1 2 3 4 creates the matrix 2 4 Reduced Row The following set of equations x 2 3z 14 Echelon Form 2x y z 3 Ay prt Does 14 can be written as the augmented matrix 1 2 3 14 2 1 1 3 4 2 2 14 which can then stored as 3 x 4 real matrix in any matrix variable M1 is used in this example You can use the RREF IE S e function to change this to reduced row echelon form RREF M1 gt M2 LLE1 5 8 114 8 1 8 7 21 storing it in any matrix variable M2 is
174. TVIEWS UNCHECK THEN ELSE END ARC BOX ERASE FREEZE DISPLAY gt DISPLAY GROB GROBNOT GROBOR GROBXOR FOR TO SIEP END DO ADDCOL ADDROW DELCOL DELROW EDITMAT RANDMAT PRDISPLAY PRHISTORY PRVAR BEEP CHOOSE CLRVAR DISP DISEXY DISPTIME EDITMAT DO1VSTATS RANDSEED an ad CASE LFERE RUN STOP LINE PIXOFF PIXON TLINE MAKEGROB PLOT gt PLOT REPLACE SUB ZEROGROB UNTIL END WHILE REPEAT END BREAK REDIM REPLACE SCALE SCALEADD SUB SWAPCOL SWAPROW FREEZE GETKEY INPUT MSGBOX PROMPT WAIT SETFREQ SETSAMPLE R 19 T GIN e hp40g book Page 20 Friday December 9 2005 1 03 AM Status messages Category Command Continued Sta Two DO2VSTATS SETDEPEND SETINDEP Message Meaning Bad Argument Type Bad Argument Value Infinite Result Insufficient Memory Insufficient Statistics Data Invalid Dimension Invalid Statistics Data Incorrect input for this operation The value is out of range for this operation Math exception such as 1 0 You must recover some memory to continue operation Delete one or more matrices lists notes or programs using catalogs or custom not built in aplets using MEMORY Not enough data points for the calculation For two variable statistics there must be two columns of data
175. The next example is for t 27 3 Selecting the entire expression and pressing displays the result 0 The final example is for the case where t Press accept YES to the message UNSIGNED INF SOLVE press Bi and press to get the result OO 5 UMEIGMED IMF SOLVE X HO CAMEL OK Here then are the variations of x t and y t an STA Step by Step Examples GIN e hp40g book Page 21 Friday December 9 2005 1 03 AM Now we will graph which is a parametric curve e In the Equation Writer type X t Xt alt i MC Select the entire expression and press ENTER Now press select Parametric and press To make the graph of quit CAS and choose the Parametric aplet Check x1 T and v1 7 Now press to see the graph T t 50 zm e Step by Step Examples 16 21 4 X iG e hp40g book Page 22 Friday December 9 2005 1 03 AM Exercise 8 For this exercise make sure that the calculator is in exact real mode with X as the current variable Part 1 For an integer n define the following Betas n 5x2 Define g over 0 2 where 2x 3 2 g x 1 Find the variations of g over 0 2 Show that for every real x in
176. Therefore the commands are described together rather than each independently IF THEN END Executes a sequence of commands in the frue clause only it the test clause evaluates to true Its syntax is IF test clause THEN true clause END Programming 21 17 T e X iG e hp40g book Page 18 Friday December 9 2005 1 03 AM Example THEN MSGBOX A EQUALS 1 END IF THEN ELSE Executes the true clause sequence of commands if the test END clause is true or the false clause sequence of commands if the test clause is false IF test clause THEN frue clause ELSE false clause END Example IF A 1 THEN MSGBOX A EQUALS 1 ELSE MSGBOX A IS NOT EQUAL TO 1 1 END CASE END Executes a series of test clause commands that execute the appropriate true clause sequence of commands Its syntax is CASE IF festclause THEN ue cjguse END IF festclause THEN frue clause END IF festclause THEN true clause END END When CASE is executed fest clause is evaluated If the lest is true frue clause is executed and execution skips to END If testclause if false execution proceeds to test clause Execution with the CASE structure continues until a true clause is executed or until all the test clauses evaluate to false IFERR Many conditions are automatically recogniz
177. a solution at the initial guess Before plotting make sure the unknown variable is highlighted in the numeric view Plot the equation to help you select an initial guess when you don t know the range in which to look for the solution See Plotting to find guesses on page 7 7 for further information An initial guess is especially important in the case of a curve that could have more than one solution In this case only the solution closest to the initial guess is returned You can change the number format for the Solve aplet in the Numeric Setup view The options are the same as in HOME MODES Standard Fixed Scientific Engineering Fraction and Mixed Fraction For all except Standard you also specify how many digits of accuracy you want See Mode settings on page 1 10 for more information You might find it handy to set a different number format for the Solve aplet if for example you define equations to solve for the value of money A number format of Fixed 2 would be appropriate in this case 7 5 an STA Y e hp40g book Page 6 Friday December 9 2005 1 03 AM Interpreting results After Solve has returned a solution press 187 in the Numeric view for more information You will see one of the following three messages Press to clear the message Message Condition Zero The Solve aplet found a point where both sides of the equation
178. able at once Simultaneous linear equations for example should be solved using the Linear Solver aplet matrices or graphs in the Function aplet Solve aplet 7 e 0 e hp40g book Page 2 Friday December 9 2005 1 03 AM Getting started with the Solve aplet Suppose you want to find the acceleration needed to increase the speed of a car from 16 67 m sec 60 kph to 27 78 m sec 100 kph in a distance of 100 m The equation to solve is U 2AD Open the Solve 1 Open the Solve aplet aplet Sequence 22 4 I 10rpi 5 The Solve aplet starts in LUPCEI Ps the symbolic view SERES Define the 2 Define the equation equation ALPHA X SOLVE SYMBOLIC wEl 2sl2 24R2D Ei ALPHA U Eos 2 x ES ALPHA D Note You can use amp menu key to assist in the entry of equations Enter known 3 Display the Solve numeric view screen variables NUM SOLVE MURMERIC VIEH y iH n d D EMTER VALUE PRES SO0LVE IDEFNEEHLWEI Solve aplet an hp40g book Page 3 Friday December 9 2005 1 03 AM HINT Solve the unknown variable Plot the equation Solve aplet 4 Enter the values for the known variables 27078 ENR uem SO
179. ables 3 10 S1mark S5mark variables 21 34 scaling automatic 2 14 decimal 2 10 2 14 integer 2 10 2 14 2 15 options 2 13 resetting 2 13 trigonometric 2 14 scatter plot 10 15 10 17 connected 10 17 10 19 SCHUR decomposition 18 12 scientific number format 1 10 1 20 scrolling in Trace mode 2 8 searching menu lists 1 9 speed searches 1 9 secant 13 20 Sending 22 5 sending aplets 22 4 lists 19 6 programs 21 8 sequence definition 2 2 sequence variables Axes 21 31 Grid 21 32 in menu map R 10 Indep 21 33 Labels 21 34 Recenter 21 34 Ycross 21 37 serial port connectivity 22 5 SERIES 14 24 setting I 11 T an ad NY date 21 27 time 21 27 SEVAL 14 68 SIGMA 14 68 SIGMAVX 14 69 SIGN 14 46 sign reversal 7 6 SIMPLIFY 14 32 simplify 14 68 14 70 SINCOS 14 31 14 40 sine 13 4 inverse hyperbolic 13 9 singular value decomposition matrix 18 13 singular values matrix 18 13 sketches creating 20 5 creating a blank graphic 21 22 creating a set of 20 5 erasing a line 21 20 labeling 20 5 opening view 20 3 sets 20 5 storing in graphics variable 20 5 slope 3 10 soft key labels 1 2 SOLVE 14 37 solve error messages initial guesses 7 5 interpreting intermediate guesses interpreting results 7 6 plotting to find guesses 7 7 setting number ien 7 5 solve variables axes 21 31 connect 21 31 fastres 21 32 grid 21 32 in menu map 1 1 indep 21
180. above The Sequence aplet allows you to create two types of e mt Stairsteps graph plots horizontal axis and U on the vertical axis A Cobweb graph plots on the horizontal axis and U on the vertical axis Getting started with the Sequence aplet The following example defines and then plots an expression in the Sequence aplet The sequence illustrated is the well known Fibonacci sequence where each term from the third term on is the sum of the preceding two terms In this example we specify three sequence fields the first term the second term and a rule for generating all subsequent terms However you can also define a sequence by specifying just the first term and the rule for generating all subsequent terms You will though have to enter the second term if the hp40gs is unable to calculate it automatically Typically if the nth term in the sequence depends on n 2 then you must enter the second term Sequence aplet 6 1 T n e SZ e hp40g book Page 2 Friday December 9 2005 1 03 AM Open the Sequence aplet Define the expression Specify plot settings 6 2 Open the Sequence oplet Select SEQUENCE SYMEULIC VIEH Sequence ES The Sequence aplet starts in the Symbolic view EDIT _ SHOH EYAL Define the Fibonacci sequence in which ea
181. aken rata time n r n r PERM n r Example PERM 5 2 returns 20 That is there are 20 different permutations of five things taken two at a time Random number between zero and 1 Produced by a pseudo random number sequence The algorithm used in the RANDOM function uses a seed number to begin its sequence To ensure that two calculators must produce different results for the RANDOM function use the RANDSEED function to seed different starting values before using RANDOM to produce the numbers RANDOM The setting of Time will be different for each calculator so using RANDSEED Time is guaranteed to produce a set of numbers which are as close to random as possible You can set the seed using the command RANDSEED Upper Tail Chi Squared Probability given degrees of freedom evaluated at value Returns the probability that a x random variable is greater than value UTPC degrees value Upper Tail Snedecor s F Probability given numerator degrees of freedom and denominator degrees of freedom of the F distribution evaluated at value Returns the probability that a Snedecor s F random variable is greater than value UTPF numerator denominator value Upper Tail Normal Probability given mean and variance evaluated at value Returns the probability that a normal random variable is greater than value for a normal distribution Note The variance is the square of the standard deviation UTPN mean variance value
182. alog keys are Key Meaning EDIT Opens the highlighted list for editing SEND Transmits the highlighted list to another HP 40gs or a PC See Sending and receiving aplets on page 22 4 for further information FECH Receives a list from another HP 40gs or a PC See Sending and receiving aplets on page 22 4 for further information DEL Clears the highlighted list CLEAR Clears all lists vy or Moves to end or the beginning A of the catalog an zz gt e hp40g book Page 3 Friday December 9 2005 1 03 AM List edit keys When you press to create or change a list the following keys are available to you Key Meaning ERF Copies the highlighted list item into the edit line IHE Inserts a new value before the highlighted item DEL Deletes the highlighted item from the list CLEAR Clears all elements from the list vy or Moves to the end or the beginning A of the list Create a list in 1 Enter the list on the edit line Start and end the list HOME with braces the shifted 8 and 9 keys and separate each element with a comma amp 2 Press to evaluate and display the list Immediately after typing in the list you can store it in a variable by pressing listname ENTER The list variable names are LO through L9 This example stores the list 25 1478 in L1 Note You c
183. amming an ad T X iG e hp40g book Page 37 Friday December 9 2005 1 03 AM Xtick Sets the distance between tick marks for the horizontal AA Aplets axis From the Plot Setup input form enter a value for Xtick or In a program type np Xtick where n gt 0 Ytick Sets the distance between tick marks for the vertical axis All Aplets From the Plot Setup input form enter a value for Ytick or In a program type nb Ytick where n gt 0 Xmin Xmax Sets the minimum and maximum horizontal values of the All Aplets plot screen Appears as the XRNG fields horizontal range in the Plot Setup input form From Plot Setup enter values for XRNG or In a program type Xmin Xmax where n n Ymin Ymax Sets the minimum and maximum vertical values of the plot All Aplets screen Appears as the YRNG fields vertical range in the Plot Setup input form From Plot Setup enter the values for YRNG or In a program type nib Ymin Ymax where n n Programming 21 37 T a PN NZ Z e hp40g book Page 38 Friday December 9 2005 1 03 AM Xzoom Sets the horizontal zoom factor All Aplets From PlotZOOM Set Factors enter the value for xzooM or In a program type nb XZOOM where n 0 The default value is 4 Yzoom Sets the vertical zoom fac
184. ams unless you use the procedure To erase all memory and reset defaults To reset using Press and hold the ON key and the third menu key the keyboard simultaneously then release them If the calculator does not respond to the above key sequence then e 1 Tum the calculator over and locate the small hole in e the back of the calculator 2 Insert the end of a straightened metal paper clip into the hole as far as it will go Hold it there for 1 second then remove it 3 Press ON If necessary press ON and the first and last menu keys simultaneously Note This will erase your calculator memory To erase all memory and reset defaults If the calculator does not respond to the above resetting procedures you might need to restart it by erasing all of memory You will lose everything you have stored All factory default settings are restored 1 Press and hold the ON key the first menu key and the last menu key simultaneously 2 Release all keys in the reverse order Note To cancel this process release only the top row keys then press the third menu key R 3 4 ZN e hp40g book Page 4 Friday December 9 2005 1 03 AM If the calculator does not turn on If the HP 40gs does not turn on follow the steps below until the calculator turns on You may find that the calculator turns on before you have completed the pr
185. an omit the final brace when f28 147 83 entering a list Lists 19 3 e 0 Y e hp40g book Page 4 Friday December 9 2005 1 03 AM Displaying and editing lists To display a list In the List catalog highlight the list name and press n HOME enter the name of the list and press ENTER To display one In HOME enter listname element For example if L2 is element 3 4 5 6 then 12 2 returns 4 To edit a list 1 Open the list catalog SHIFT LIST L2 Size 8 BKB L3 Size H L4 Size BEE L5 Size IEHDIFECV 2 Press or v to highlight the name of the list you 5 TB PETllhs 3 Press or v to highlight the element you want to edit In this example edit the third element so that it has a value of 5 v v EE DEL DEL 2 O UK 4 Press H3 TOA e 0 Y e hp40g book Page 5 Friday December 9 2005 1 03 AM insert an element 1 Open the List catalog En GNIS HER in a list SAT usr BEES HEEB L3 Size H L4 Size BEE 5 Size 2 Press a or v highlight the of the list you want to edit L1 etc
186. and each column must have at least four numbers Array argument had wrong dimensions Need two columns with equal numbers of data values an P hp40g book Page 21 Friday December 9 2005 1 03 AM Message Meaning Continued Invalid Syntax Name Conflict No Equations Checked OFF SCREEN Receive Error Too Few Arguments Undefined Name Undefined Result Out of Memory The function or command you entered does not include the proper arguments or order of arguments The delimiters parentheses commas periods and semi colons must also be correct Look up the function name in the index to find its proper syntax The where function attempted to assign a value to the variable of integration or summation index You must enter and check an equation Symbolic view before evaluating this function Function value root extremum or intersection is not visible in the current screen Problem with data reception from another calculator Re send the data The command requires more arguments than you supplied The global variable named does not exist The calculation has a mathematically undetined result such as 0 0 You must recover a lot of memory to continue operation Delete one or more matrices lists notes or programs using catalogs or custom not built in aplets using
187. and press DEL The values below the deleted cell will scroll up one row delete a column of data highlight an entry in that column and press SHIFT CLEAR Select the column name To delete all columns of data press CLEAR Select 11 columns Insert data Highlight the entry following the point of insertion Press LA then enter a number It will write over the zero that was inserted e Sort data 1 In Numeric view highlight the column you want to values sort and press 2 Specily the Sort Order You can choose either Ascending or Descending 3 Specily the INDEPENDENT and DEPENDENT data columns Sorting is by the independent column For instance if Age is C1 and Income is C2 and you want to sort by Income then you make c2 the independent column for the sorting and C1 the dependent column sort just one column choose None for the dependent column For one variable statistics with two data columns specify the frequency column as the dependent column 4 Press Statistics aplet 10 11 4 ZN NY gt 4 P hp40g book Page 12 Friday December 9 2005 1 03 AM Defining a regression model Angle Setting To choose the fit Fit models 10 12 The Symbolic view includes an expression Fit through Fit5 that defines the regression model or fit to use for the regression analysis of
188. another one like passing from one room into another in a house Data that you enter is automatically saved as you enter it You can save an aplet configuration that you have used and transfer the aplet to other HP 40gs calculators See Creating new aplets based on existing aplets on page 22 1 Mathematical calculations Where to start Entering expressions _ Getting started The most commonly used math operations are available from the keyboard Access to other math functions is via the MATH menu MATH You can also CAS for symbolic calculations See Computer Algebra System CAS on page 14 1 for further information To access programming commands press CMDS See Programming commands on page 21 13 for further information The home base for the calculator is the HOME view You can do all non symbolic calculations here and you can access all MATH operations Symbolic calculations are done using CAS n the HOME view you enter an expression in the same lett to right order that you would write the expression This is called algebraic entry In CAS you enter expressions using the Equation Writer explained in detail in Chapter 15 Equation Writer enter functions select the key or MATH menu item for that function You can also enter a function by using the Alpha keys to spell out its name e Press to evaluate the expression you have in the edit line where the
189. applications the HP 40gs is supplied with two teaching aplets Quad Explorer and Trig Explorer You cannot modify configuration settings for these aplets A great many more teaching aplets can be found at HP s web site and other web sites created by educators together with accompanying documentation often with student work sheets These can be downloaded free of _ Getting started 1 13 T am ad 4 hp40g book Page 14 Friday December 9 2005 1 03 AM Quad Explorer aplet HINT charge and transferred to the HP 40gs using the provided Connectivity Kit The Quad Explorer aplet i is used to investigate the behaviour of y a x h v as values of a hand v change both by manipulating the equation and seeing the change in the graph and by manipulating the graph and seeing the change in the equation More detailed documentation and an accompanying student work sheet can be found at HP s web site Press APLET select Quad and then press Dons in fa mode in which the arrow keys the and keys and the key are used to change the shape of the graph This changing shape is reflected in the equation displayed at the top right corner of the screen while the original graph is retained for comparison In this mode the graph controls the equation vne ETT T DTE TEST FEET It is also possi
190. ast three points Fits to a cubic curve y ax bx cx d Needs at least four points Logistic Fits to a logistic curve L Y CN ECC EN where L is the saturation value for growth You can store a positive real value in L or if L O let L be computed automatically Exponent Fits to an exponent curve y ab Trigonometric Fits to a trigonometric curve e a sin bx c d Needs at least three points User Defined Define your own expression in Symbolic view To define your 1 In Numeric view make sure EE is set own fit 2 Display the Symbolic view Highlight the Fit expression Fit1 etc for the desired data set 4 Type in an expression and press ENTER The independent variable must be X and the expression must not contain any unknown variables Example 1 5 x cosx 0 3 x sinx This automatically changes the Fit type S1FIT etc in the Symbolic Setup view to User Defined Statistics aplet 10 13 4 PN hp40g book Page 14 Friday December 9 2005 1 03 AM NY Computed statistics One variable L ML NN Number of data points Sum of data values with their frequencies Mean value of data set Population variance of data set Sample variance of data set Population standard deviation of data set Sample standard deviation of data set Minimum data value in data se
191. at 4 5 2 7 55 3 On 3 Press WA to close the 7 show window 6 Using mathematical functions 13 23 e NZ Z gt e hp40g book Page 24 Friday December 9 2005 1 03 AM 4 Copy the result and FUMCT RE evaluate re ol SWS 7 MT SMS E DET 5sS14246081 2725 Thus substituting X for S1 it can be seen that 3 X 3x 5 57 3 This result is derived from substituting X S1 and X 0 into the original expression found in step 1 However substituting X 0 will not always evaluate to zero and may result in an unwanted constant bo To see this consider e 2 dx o MS ext ie d sta hi of Em CN H ox te H 23 C4 197 ECAH substitution of x 0 into CHB C44 17 COR LYRIC 2 gt 5 and should be lt disregarded if an indefinite integral is required Program constants and physical constants When you press MATH three menus of functions and constants become available math functions menu which appears by default program constants menu and e physical constants menu The math functions menu is described extensively earlier in this chapter e 0 Z e hp40g book Page 25 Friday December 9 2005 1 03 AM
192. at least one value you specify must be a length For example you could specify the lengths of two sides and one of the angles or you could specify two angles and one length or all three lengths In each case the solver will calculate the remaining lengths or angles e The HP 40gs will alert you if no solution can be found or it you have provided insufficient data If you are determining the properties of a rightangled triangle a simpler input form is available by pressing the menu key Note that the Triangle Solver aplet only has a numeric view Getting started with the Triangle Solver aplet The following example solves for the unknown length of the side of a triangle whose two known sides of lengths 4 and 6 meet at an angle of 30 degrees Before you begin You should make sure that your angle measure mode is appropriate If the angle information you have is in degrees as in this example and your current angle measure mode is radians or grads change the mode to degrees before running the solver See Mode settings on page 1 10 for instructions Because the angle measure mode is associated with the aplet you should start the aplet first and then change the setting Triangle Solve aplet 9 E gt e e 0 am ad a ie NY hp40g book Page 2 Friday December 9 2005 1 03 AM Open the Triangle Solver aplet Choose the
193. bar and give you important status information Annunciator Description c Shift in effect for next keystroke To cancel press again Alpha in effect for next keystroke To cancel press ALPHA again e Low battery power FA Busy gt gt Data is being transferred The keyboard e HP 40gs e Graphing Calculator CA 9 Menu Key Labels Menu Keys SETUP SYMB PLOT Aplet Control 4 E Or Cursor Keys Keys CHARS CMDS CLEAR vars d dx XT6 DEL asin A acos aan Dio SIN cos TAN In log v Fas C ao Hx x x F MEMORY LIST K Lj M N 7 8 9 x alpha I RA 5 Alpha Key 4 5 6 PROGRM syntax Vy W Shift Key Ci C2 G G X Y Z OFF NOTEPAD AND Ans SPACE Enter ON 0 ENTER CANCEL 0 Key S T _ Getting started 1 3 am S SZ Y e hp40g book Page 4 Friday December 9 2005 1 03 AM Menu keys On the calculator keyboard the top row of keys are called menu keys Their meanings depend on the context that s why they are blank The menu keys
194. ble 14 27 VARS menu 17 4 17 5 vectors column 18 1 cross product 18 11 definition of R 2 VER 14 70 verbose 14 6 version 14 70 views 1 18 configuration 1 18 definition of R 3 W warning symbol 1 8 where command 13 18 X Xcross variable 21 36 XNUM 14 32 XQ 14 32 Y Ycross variable 21 37 Z Interval 11 15 zoom 2 17 axes 2 12 box 2 9 center 2 9 examples of 2 11 factors 2 13 an ad T X iG e hp40g book Page 15 Friday December 9 2005 1 03 AM in 2 9 options 2 9 3 8 options within a table 2 18 out 2 9 redrawing table of numbers op tions 2 18 an ad square 2 10 un zoom 2 11 within Numeric view 2 18 X zoom 2 9 Y zoom 2 10 I 15 T X iG e hp40g book Page 16 Friday December 9 2005 1 03 AM T an ad e
195. ble to have the equation control the graph Pressing Baa displays co T 4 TETTE sub expression of your m equation eres CHENG oS EEE Pressing the gt and 4 key moves between m expressions while pressing the 4 and v key changes their values sub expressions s will be explored at once or only one at a time A button is provided to evaluate the student s oe M knowledge Pressing HB displays a target quadratic NeT done graph The student must mpm me manipulate the equation s parameters to make the equation match the target graph When a student feels button evaluates the answer and provide feedback An button is provided for those who give up Getting started an hp40g book Page 15 Friday December 9 2005 1 03 AM Trig Explorer aplet Getting started The Trig Explorer aplet is used to investigate the behaviour of the graph of asin bx c d_ as the values of a b cand d change both by manipulating the equation and seeing the change in the graph or by manipulating the graph and seeing the change in the equation Press FRESE HELET select Trig Explorer dnd then press epe right In this mode the graph controls the equation Pressing the a and 4 keys transforms the graph with
196. can also scroll move the cursor left or right beyond the edge of the display window in trace mode giving you a view of more of the plot To move between If there is more than one relation displayed press 4 or relations v to move between relations Aplets and their views 4 SZ e hp40g book Page 9 Friday December 9 2005 1 03 AM To jump directly to To jump straight to a value rather than using the Trace a value function use the menu key Press then enter a value Press MA to jump to the value To turn trace on off If the menu labels are not displayed press MEI first Turn off trace mode by pressing HAIG Turn on trace mode by pressing HAMA To turn the coordinate display off press REI Zoom within a One of the menu key options is Zooming redraws graph the plot on a larger or smaller scale It is a shortcut for changing the Plot Setup The Set Factors option enables you to set the factors by which you zoom in or zoom out and whether the zoom is centered about the cursor ZOOM options Press select an option and press WA If is not displayed press REIM Not all options are available in all aplets Option Meaning Center Re centers the plot around the current position of the cursor without changing the scale Box Lets you draw a box to zoom in on See Other views for scali
197. ch pixel 0 1 unit Resets default values for XRNG 76 5 to 6 5 and YRNG 3 1 to 3 2 Not in Sequence or Statistics aplets Integer Rescales horizontal axis only making each pixel 1 unit Not available in Sequence or Statistics aplets Trig Rescales horizontal axis so 1 pixel 2x 24 radian 7 58 or 8 4 grads rescales vertical axis so 1 pixel 0 1 unit Not in Sequence or Statistics aplets Split the screen The Plot Detail view can give you two simultaneous views of the plot 1 Press views Select Plot Detail and press The graph is plotted twice You can now zoom in on the right side 2 Press HET select the zoom method and press or This zooms the right side Here is an example of split screen with Zoom In The Plot menu keys are available as for the full plot for tracing coordinate display equation display and so on 2 14 Aplets and their views gt 9 SZ gt e hp40g book Page 15 Friday December 9 2005 1 03 AM Overlay plots Decimal scaling Integer scaling Trigonometric scaling Aplets and their views 4 moves the leftmost cursor to the screen s left edge and moves the rightmost cursor to the screen s right edge The a menu key copies the right plot to the left plot 3 To un split the screen press PLOT The left side takes
198. ch term after the first two is the sum of the preceding two terms U 1 U 1 U _ U _ forn gt 3 n In the Symbolic view of the Sequence aplet highlight the U1 1 field and begin defining your sequence 1 1 SEQUENCE SYMEOLIC VIEH z Uuiclis 1 EE DERE 1 8 1 II1 N 1 I1CN 2 Note You can use the EEN C mr GEER Gees m and menu keys to assist in the entry of equations SEE SEQUENCE SYMEDLIC VIEH SERES e Lici 1 U1 2551 U1 CH U1CH 1 U1 CH n E In Plot Setup first set the SEQPLOT option to Stairstep Reset the default plot settings by clearing the Plot Setup view eee SEQUEMCE PLOT SETUP CLEAR alae v 8 E rmm oc gt 8 ENTER MINIMUM VERTICAL YALUE Sequence aplet an zz gt e hp40g book Page 3 Friday December 9 2005 1 03 AM Plot the 4 Plot the Fibonacci sequence sequence N 1 1rN 1 5 In Plot Setup set SEQPLOT option to Cobweb SETUP PLOT Select Cobweb RM 1 ULHI 1 HEHU Display the table 6 Display the table of values for this example NUM Sequence aplet 6 3 PN 0 X iG e hp40g book Page 4 Friday December 9 2005 1 03 AM T an ad e
199. ches e hp40g book Page 7 Friday December 9 2005 1 03 AM 4 Write your note MOTE See Note edit keys THIS IS MY TEST on page 202 for more information on the entry and editing of notes When you are finished press or an aplet key to exit Notepad Your work is automatically saved Key Meaning EDIT Opens the selected note for editing HEH Begins a new note and asks for a name Transmits the selected note to another HP 40gs or PC Goa Receives a note being transmitted from another HP 40gs or PC DEL Deletes the selected note CLEAR Deletes all notes in the catalog 20 7 4 To import a note 20 8 hp40g book Page 8 Friday December 9 2005 1 03 AM You can import a note from the Notepad into an aplet s Note view and vice versa Suppose you want to copy a note named Assignments from the Notepad into the Function Note view 1 In the Function aplet display the Note view SHIFT NOTE 2 Press fits highlight Notepad in the left column then highlight the name Assignments in the right column 3 Press DIM to copy the contents of Assignments to the Function Note view Note To recall the name instead of the contents press MZB instead of M Suppose you want to copy the Note view from the current aplet into
200. containing complex exponentials SINCOS then rewrites this expression in terms of sin x and cos x 14 31 T a e P NY SIMPLIFY XNUM XQ 14 32 e hp40g book Page 32 Friday December 9 2005 1 03 AM Typing SINCOS EXP 1 X gives after turning on complex mode if necessary cos x i gt sin x Simplify SIMPLIFY simplifies an expression automatically Typing SIN 5 X gives after simplification A cos x 2 Evaluation of reals XNUM has an expression as a parameter XNUM puts the calculator into approximate mode and returns the numeric value of the expression Typing XNUM V2 gives 1 4142135623 Rational approximation XQ has a real numeric expression as a parameter XQ puts the calculator into exact mode and gives a rational or real approximation of the expression Typing XO 1 41421 gives 66441 46981 Computer Algebra System CAS am ad T a NY SOLV menu DESOLVE e Computer Algebra System CAS e hp40g book Page 33 Friday December 9 2005 1 03 AM Typing 1 414213562 gives V2 The SOLV menu contains functions that enable you to solve equations linear systems and differential equations Solve differential equations DESOLVE enables you to solve differential equat
201. ct a distribution statistic type v Ferrites MF STAT SYMEOLIC VIEH Select T Int 1 u INTERWAL TFE Choose distribution statistic Set up the 9 Set up the interval calculation Note The default interval values are derived from sample data from the on line hel le calculation Setup NUM ME STAT NUMERIC SETUP 88 WGE She ner nb n 56 c 99 S0Hple neun EDIT HELP 11 6 Inference aplet e NZ Se zz gt e hp40g book Page 7 Friday December 9 2005 1 03 AM Import the data 10 Import the data from the Statistics aplet Note The data from C1 is displayed by default IMPORT SAMPLE Doe Note Press HIG losee gp 2978442 Ihe statistics before COLUMN imoorting them into the Stat inport data colunn Numeric Setup view Also if there is more than one aplet based on the Statistics aplet you are prompted to choose one ce INF STAT SETUP ZEE fe 207Bdd25456B2 n 99 SOHple Henhi 11 Specify a 90 EDIT HELP IMPRT confidence interval in the C field v yl to move to Se INF STHT MUMERIC SETUP the field sx 297844254603 6 0 9 c 39Hp Le neun Display Numeric 12 Disploy the confidence interval in the Numeric view view Note The
202. d is a whole number Solution In the Equation Writer enter C by typing 2 GAIT 45 5 gt 3 Sir 12 gt 0 20 gt 5 6 SHIFT p 3 Press gt gt to select 6 3 Press to select 20 and v to select 20 Now press EINE select FACTOR and an 2 J45 3 12 28 63 2j45 3 12 20 Step by Step Examples zz gt e hp40g book Page 3 Friday December 9 2005 1 03 AM Press to factor 2 lO Sh 2 Ss 12 Mis 6E Press A to select 42 5 and io 2a 2 12 Elig e 3 simplify it Press gt to select 724 5 and SH 4 72 645 to exchange 3 12 with HS Press 4 to select 2445 and v gt v 2 ER 2 5 212 2 2 lo select 45 Press select FACTOR and press mE 2 5 2 12 Press to factor 2 2 5 3 12 68 Press 4 to select 43 5 and to zEBg 2 E 2 Hz e 8 simplify the selection Press 4 to select 2 3 5 and ENSE 5 17 6 3 gt to select 2 08 15 20 15 e Step by Step Examples 16 3 e NZ e hp40g book Page 4 Friday December 9 2005 1 03 AM Press lo evaluate the selection I remains to transform
203. d normally os follows 5 Z Menu options that is the functions that you select using the menu keys at the top of the keypad are represented as follows Input form fields and choose list items are represented as follows Function Polar Parametric Your entries as they appear on the command line or within input forms are represented as follows 2 X2 3X45 P 4 4 Notice P Preface fm Page 2 Friday February 17 2006 9 47 AM This manual and any examples contained herein are provided as is and are subject to change without notice Except to the extent prohibited by law HewlettPackard Company makes no express or implied warranty of any kind with regard to this manual and specifically disclaims the implied warranties and conditions of merchantability and fitness for a particular purpose and HewlettPackard Company shall not be liable for any errors or for incidental or consequential damage in connection with the furnishing performance or use of this manual and the examples herein Copyright 1994 1995 1999 2000 2003 2006 Hewlett Packard Development Company L P The programs that control your HP 40gs are copyrighted and all rights are reserved Reproduction adaptation or translation of those programs without prior written permission from Hewlett Packard Company is also prohibited an W PS
204. d press Eli n HOME enter the name of the matrix variable and press ENTER In HOME enter matrixname row column For example if M2 is 13 4 5 6 then M2 1 2 returns 4 Enter the matrix in the edit line Start and end the matrix and each row with square brackets the shifted 5 and 6 keys 2 Separate each element and each row with a comma Example 1 2 3 41 3 Press to enter and display the matrix The left screen below shows the matrix 2 5 729 16 2 being stored into M5 The screen on the right shows the vector 66 33 11 being stored into M6 Note that you can enter an expression like 5 2 for an element of the matrix and it will be evaluated 3 5 16 211115 LEB 35 1116 LL2 254 7291 116 21 554 324 11 18 5 e 0 SZ e hp40g book Page 6 Friday December 9 2005 1 03 AM To store In HOME enter value matrixname row column element For example to change the element in the first row and second column of M5 to 728 then display the resulting matrix TTI SE F MCTIUM ee 728 ET PBRS I 2 in 5 91020 5 Clea 7261 016 211 ALPHA 5 ENTER ee An attempt to store an element to a row or column beyond the size of the matrix results in an error message Matrix arithmetic You can use the arithmetic functions x and
205. d to hold down when you press HOME This action is depicted in this manual as press MODES To cancel a shift press again The alphabetic keys are also shifted keystrokes For instance to type Z press ALPHA Z The letters are printed in orange to the lower right of each key To cancel Alpha press ALPHA again For a lower case letter press ALPHA For a string of letters hold down ALPHA while typing Getting started an STA Z gt e e chapter 1 fm Page 7 Friday December 16 2005 2 20 PM HELPWITH The HP 40gs built in help is available in HOME only It provides syntax help for builtin math functions Access the HELPWITH command by pressing SYNTAX and then the math key for which you require syntax help Example Press SHIFT SYNTAX HELPHITH 74 a Note Remove the left parenthesis from built in functions such as sine cosine and tangent before invoking the HELPWITH command Note In the CAS system pressing the SYNTAX will show the CAS help menv Math keys HOME HOME is the place to do non symbolic calculations For symbolic calculations use the computer algebra system referred throughout this manual as CAS Keyboard keys The most common operations are available from the keyboard such as the arithmetic like and trigonometric like SIN functions Press to complete the operat
206. default values for XRNG 76 5 to 6 5 and YRNG 3 1 to 3 2 Not in Sequence or Statistics aplets Integer Rescales horizontal axis only making each pixel 1 unit Not available in Sequence or Statistics aplets Trig Rescales horizontal axis so 1 pixel x 24 radians 7 58 or 8 4 grads rescales vertical axis SO 1 pixel 0 1 unit Not in Sequence or Statistics aplets 2 10 Aplets and their views E e Na Z gt e hp40g book Page 11 Friday December 9 2005 1 03 AM Option Meaning Continued Un zoom Returns the display to the previous zoom or if there has been only one zoom un zoom displays the graph with the original plot settings ZOOM examples The following screens show the effects of zooming options ona plot of 3sinx Plot of 3sinx WO Fam n Zoom In GE FI In we n n Fath n Un zoom Un zoom BI Note Press A to move to the bottom of the Zoom list Zoom Out Out DIS Now un zoom HI 0 X Zoom In EDDIE X Zoom In MA Now un zoom 200M TRACS GOTO X Zoom Out X Zoom Out Now un zoom IEHHF1ITERCE HTH Aplets and their views 9 an SZ
207. e You can modity SAYE RESET SORT SEND START contiguration settings for the graphical tabular and _ 1 12 Getting started e S e e PN hp40g book Page 13 Friday December 9 2005 1 03 AM NY symbolic views of the aplets in the following table See Aplet view contiguration on page 1 18 for further information Aplet Use this aplet to explore name Function Real valued rectangular functions y in terms of x Example y 2x 3x 5 Inference Confidence intervals and Hypothesis tests based on the Normal and Students t distributions Parametric Parametric relations x and y in terms of t Example cos f and sin Polar Polar functions rin terms of an angle Example r 2cos 40 Sequence Sequence functions U in terms of n or in terms of previous terms in the same or another sequence such as U e U 5 Example U 0 U 1 and 5 E EU RU E n n Solve Equations in one or more real valued variables Example x 1 x x 2 Finance Time Value of Money TVM calculations Linear Solutions to sets of two or three linear Solver equations Triangle Unknown values for the lengths and Solver angles of triangles Statistics One variable x or two variable x and y statistical data In addition to these aplets which can be used in a variety of
208. e FACTOR is applied to FRCTDRLX 4 whatever was selected which is automatically placed in parentheses Press to evaluate the expression The result is the factors of the expression x 2EMEFZI Because the result of an evaluation is always selected you can immediately apply another command to it To illustrate this press FIRTH select SUBST and SUBSTI MEE Note that SUBST is applied to whatever was selected which is automatically placed in parentheses Note too that the cursor is automatically placed in the position of the second argument Enter the second argument 4 SUBST X 2 8 2 2 44 15 15 4 GIN e hp40g book Page 16 Friday December 9 2005 1 03 AM Press to obtain an intermediate result 4 2 4 2 and again to e evaluate the intermediate result The final answer as before is 12 Note Ifyou call a CAS function while you re writing an expression whatever is currently selected is copied to the function s first or main argument If nothing is selected the cursor is placed at the appropriate location for completing the arguments Equation Writer variables You can store objects in variables then access an object by using the name of its variable However you should note the following Variables used in CAS cannot be used in HOME and vice versa
209. e If you were not in step by step mode this symbol would be D which stands for Direct The first line of an Equation SEE EP EE Writer menu only indicates duit config some of the mode settings l To see more settings highlight the first line and press 88 The configuration menu appears The header of the configuration menu has additional symbols In the example above the upward pointing arrow indicates that polynomials are displayed with increasing powers and the 13 indicates the modulo value You can change CAS mode settings directly from the configuration menu Just press v until the setting you want to choose is highlighted and then press His Note that the configuration menu includes only those options that are not currently selected For example if Rigorous is a current setting its opposite Sloppy will appear on the menu If you choose Sloppy then Rigorous appears in its place To return your CAS modes to their default settings select Default cfg and press To close the configuration menu select Quit config and press Bii You can also change CAS mode settings from CAS MODES screen See CAS modes on page 14 5 for information One CAS setting that only SE PE appears on the configuration Hum factor menu is the setting that CEPI E determines the language of Default cfs CANEL OK the online help Two languages are available English and French To choose French s
210. e See Other views for scaling and splitting the graph on page 2 13 for futher information The VIEWS menu contains the Plot Detail view VIEWS Splits the screen into the plot and a close up IDEFN1 See Other views for scaling and splitting the graph on page 2 13 for further information The VIEWS menu contains the Overlay Plot view VIEWS Select Overlay Plot Plots the current expression s withouterasing any pre existing plot s See Other views for scaling and splitting the graph on page 2 13 for further information 1 17 an STA 1 03 AM Y e hp40g book Page 18 Friday December 9 2005 Note view Press NOTE to display the aplet s note view This note is transferred with FUNCTION MUTE the aplet if it is sent to hee oe another calculator or to a PC A note view contains text to supplement an aplet LS faz EKSP See Notes and sketches on page 20 1 for further information Sketch view Press SKETCH to display the aplet s sketch view Displays pictures to supplement an aplet See Notes and sketches on page 20 1 for further information Aplet view configuration You use the sErUP keys SHIFT PLOT and NUM to configure aplet For example press SETUP PLOT SHIFT PLOT to dis
211. e results in the corresponding variables NZ Tot gt Mean PVarX SVarx PSDev SSDev MinX Q1 Median and MaxX Datasetname can be H1 H2 or H5 Datasetname must include at least two data points DO1VSTATS dalasetname Sets datasetname frequency according to column or value Datasetname can be H1 H2 or H5 column can be CO C and value can be any positive integer SETFREQ datasetname column or SETFREQ definition value Sets datasetname sample according to column Datasetname can be H1 H5 and column can be CO C9 SETSAMPLE datasetname column Stat Two commands DO2VSTATS SETDEPEND SETINDEP 21 30 Calculates STATS using datasetname and stores the results in corresponding variables MeanX X X2 Meany XY XY2 XXY Corr PCov SCov and RELERR Datasetname can be SI S2 or S5 Datasetname must include at least two pairs of data points DO2VSTATS dalasetname Sets datasetname dependent column Datasetname can be S1 S2 or S5 and column can be CO C9 SETDEPEND datasetname column Sets datasetname independent column Datasetname can be S1 S2 or S5 and column can be 9 SETINDEP datasetname column Programming T a e GIN e hp40g book Page 31 Friday December 9 2005 1 03 AM Storing and retrieving variables in programs The HP 40gs has both Home variables and Ap
212. e 1 10 CAS 14 5 decimal mark 1 11 number format 1 10 MODSTO 14 53 modular arithmetic 14 51 multiple solutions plotting to tind 7 7 multiplication 13 4 14 28 implied 1 20 MULTMOD 14 54 name conflict R 21 naming CROSS 18 11 programs 21 4 DET 18 11 natural exponential 13 4 13 10 E 18 1 natural log plus 1 13 10 En 18 1 natural logarithm 13 4 4 IDENMAT 18 11 t INVERSE 18 11 negative numbers 1 20 Q 181 NEXTPRIME 14 51 LSQ 18 11 no equations checked R 21 LU 18 12 non rational 14 6 MAKEMAT 18 12 Normal Z distribution confidence in SNC M tervals 11 15 note SCHUR 18 12 UL eet SIZE 18 12 importing 20 8 SPECNORM 18 13 LT SPECRAD 18 13 writing 20 1 Notepad 20 1 TRACE 1 8 13 catalog keys 20 7 TRN 18 13 creating notes 20 6 maximum real number 1 22 13 8 memory R 20 gt nth root 13 6 y clearing all R 3 organizing 17 9 out of R 21 saving 1 25 22 1 viewing 17 1 menu lists 1 8 null hypothesis 11 2 number format engineering 1 11 fixed 1 10 fraction 1 11 in Solve aplet 7 5 T an ad e hp40g book Page 9 Friday December 9 2005 1 03 AM NY mixed fraction 1 11 permutations 13 13 scientific 1 10 pictures Standard 1 10 attaching in Sketch view 20 3 numeric precision 17 9 plot Numeric view analyzing statistical data in 10 19 adding values 2 19 auto scale 2 14 automatic 2 16 box and whis
213. e aplets The other views are derived from the symbolic expression Function aplet 3 1 e NZ Y e hp40g book Page 2 Friday December 9 2005 1 03 AM Define the expressions Set up the plot Plot the functions 3 2 2 There are 10 function definition fields on the Function aplet s Symbolic view screen They are labeled F1 X to FO X Highlight the function definition field you want to use and enter an expression You can press DEL to delete an existing line or SHIFT CLEAR to clear all lines 1 ee nan EH 2 EDIT ES ee You can change the scales of the x and y axes graph resolution and the spacing of the axis ticks 3i Display plot settings SHIFT SETUP PLOT FUMCTIOM PLOT SETUP 9 3 1 Duk WTICR 1 WTICE 1 RE Detail EXTER MIRIMUR HORIZONTAL VALUE EDIT PAGE F Note For our example you can leave the plot settings at their default values since we will be using the Auto Scale feature to choose an appropriate y axis for our x axis settings If your settings do not match this example press CLEAR to restore the default values Specify a grid for the graph FUNCTION PLOT SETUP ww SIMULT IN CROSS gt v v Ease y CONNECT LABELS v AES 5610 DERE GRID mLHE PAGE Plot the functions
214. e inputs are Field Definition name x Sample success count n Sample size 8 Confidence level Results The results are te Result Description Critical Z Critical value for Z n Min Lower bound for Max Upper bound for Two Proportion Z Interval Menu name ZANT 11 x2 This option uses the Normal Z distribution to calculate a confidence interval for the difference between the proportions of successes in two populations Inputs The inputs are Field Definition name x1 Sample 1 success count x2 Sample 2 success count Inference apet e117 6 n e X iG e hp40g book Page 18 Friday December 9 2005 1 03 AM Field Definition Continued name ni Sample 1 size n2 Sample 2 size C Confidence level Results The results are Result Description Critical Z Critical value for Z An Min Lower bound for the difference between the proportions of successes Max Upper bound for the difference between the proportions of successes One Sample T Interval Menu name TNT 1 u This option uses the Student s tdistribution to calculate a confidence interval for m the true mean of a population for the case in which the true population standard deviation s is unknown Inputs The inputs are Field Definition name zu Sample mean Sx Sample standard deviat
215. e null hypothesis The null hypothesis is that the two populations means are equal You select one of the following alternative hypotheses against which to test the null hypothesis Hip lt Hy Fy Hy gt by H u zt Inputs The inputs are Field Definition name e xi Sample 1 mean 4 x2 Sample 2 mean 51 Sample 1 standard deviation S2 Sample 2 standard deviation n1 Sample 1 size n2 Sample 2 size Significance level Pooled Check this option to pool samples based on their standard deviations 11 14 Inference aplet T e Sd iG e hp40g book Page 15 Friday December 9 2005 1 03 AM Results The results are Result Description Test T T Test statistic Prob Probability associated with the T Test statistic Critical T Boundary values of T associated with the a level that you supplied Confidence intervals The confidence interval calculations that the HP 4095 can perform are based on the Normal Z distribution or Student s t distribution One Sample Z Interval Menu name ZANT 1 e This option uses the Normal Z distribution to calculate a K2 confidence interval for m the true mean of a population when the true population standard deviation s is known Inputs The inputs are Field Definition name x Sample mean o Population standard dev
216. e periods Lists represent a convenient way to group related objects There are ten list variables available named LO to L9 You can use them in calculations or expressions in HOME or in a program Retrieve the list names from the VARS menu or just type their names from the keyboard You can create edit delete send and receive named lists in the List catalog SHIFT 7757 You can also create and store lists named or unnnamed in HOME lists List variables are identical in behaviour to the columns C1 CO in the Statistics aplet You can store a statistics column to a list or vice versa and use any of the list functions on the statistics columns or the statistics functions on the list variables 1 Open the List catalog SHIFT LIST 2 Highlight the list name you want to assign to the new list L1 etc display the List editor NEN RN ERN 19 1 an List catalog keys e hp40g book Page 2 Friday December 9 2005 3 Enter the values you want in the list pressing 1 0 3 AM after each one Values can be real or complex numbers or an expression If you enter a calculation it is 5 evaluated and the result is inserted in the list 4 When done press SHIFT LIST to see the List catalog or press to return to HOME The list cat
217. eans based on the Student s distribution If you choose one of the hypothesis tests you can choose the alternative hypothesis to test against the null hypothesis For each test there are three possible choices for an alternative hypothesis based on a quantitative comparison of two quantities The null hypothesis is always that the two quantities are equal Thus the alternative hypotheses cover the various cases for the two quantities being unequal and z In this section we will use the example data for the Z Test on 1 mean to illustrate how the aplet works and what features the various views present Inference aplet am ad T a Y e hp40g book Page 3 Friday December 9 2005 1 03 AM Select the 2 Select the Hypothesis Test inferential method inferential DITE SENSE INF STAT STHEDLIC VIEH method Select HYPOTH TEST AETHps _ mm IHTE m gn nethed ok Choo m aL ok 4 Select an alternative hypothesis T IMF STAT SYMEOLIC VEH ESSE HETHOD HYPOTH TEST was WE Z Testi 1 p u lt LO HYPOTH Chasse alternative hypothesis e Enter data 5 Enter the sample statistics and population parameters setup NUM MERIC SETUP SERERE 58
218. eckmarked Symbolic view The correct plotting range Try using Auto Scale instead of PLOT or adjust the plotting parameters in Plot Setup for the ranges of the axes and the width of histogram bars HWIDTH In ED mode ensure that both paired columns contain ICE data and that they are the same length In mode ensure that a paired column of frequency values is the same length as the data column that it refers to Exploring the graph The Plot view has menu keys for zooming tracing and coordinate display There are also scaling options under views These options are described in Exploring the graph on page 2 7 Statistics aplet s PLOT view keys Statistics aplet CLEAR Erases the plot VIEWS Offers additional pre defined views for splitting the screen overlaying plots and autoscaling the axes Moves cursor to far left or far right 10 19 4 Z gt e hp40g book Page 20 Friday December 9 2005 1 03 AM Meaning Continued Displays ZOOM menu TRACE Turns trace mode on off The white box appears next to the option when Trace mode is active Turns fit mode on or off Turning on draws a curve to fit the data points according to the current regression model 2var Enables you to specify a value on the statistics only line of best fit to jump to or a data point number to jump to EFM Displays the equation of the
219. ected expression by applying a CAS function to it which you can invoke from one of CAS menus along the bottom of the screen Delete the selected expression by pressing ALPHA DEL Delete a selected unary operator at the top of the expression tree by pressing SHIFT For example to replace SIN expr with COS expr e select SIN expr press DEL and then press COS Delete a binary infix operator and one of its arguments by selecting the argument you want delete and pressing SHIFT For example if you have the expression 1 2 and select 1 pressing DEL deletes 1 and leaves only 2 Similarly to delete F x in the expression F x x x 1 you select F x and then press DEL This produces x x x 1 Delete a binary operator by selecting Edit expr from the menu and then making the correction Copy an element from CAS history You access CAS history by pressing See page 15 19 for details Equation Writer 15 1 e NZ P hp40g book Page 12 Friday December 9 2005 1 03 AM Accessing CAS functions 15 12 NOTE While you are in the Equation Writer you can access all CAS functions and you can access them in various ways General principle When you have written an expression in the Equation Writer all you have to do is press to evaluate whatever you have se
220. ecting the entire expression and pressing gives the result at the right Now linearize the result by applying the LIN command which can be found on the AMA menu The result after accepting the switch to complex mode is shown at the right LESPLi t Je ESP 1 Now store the result in variable M Note that STORE is on the menu To calculate real part of EE the expression apply the RE ne a a it STORE Lupe eo enr Cnt RE command available on the COMPLEX submenu of the MATH menu Pressing yields the result at the right TOOL ALGE DIFF 0LY TEIG We are now going to define this result as x To do this enter X t highlight the X t by pressing and press 4 to swap the two parts of the expression as COstt 2 2COS t shown at the right Now select the entire expression and apply the Po Coget a a DEF aiti k e Step by Step Examples 16 15 e NZ SZ P hp40g book Page 16 Friday December 9 2005 1 03 AM Part 2 16 16 DEF command to it Press to complete the definition To calculate the real part of the expression apply the IM command available on the COMPLEX submenu of the MATH menu to the stored variable M
221. ection not just the last entered term The 4 key selects just the last entry 3 and makes the next operation _ Equation Writer 15 7 2 e 3 84 an 4 hp40g book Page 8 Friday December 9 2005 1 03 AM X apply to it As a result the entered expression is interpreted and displayed as 2 X 3 X Select the entire expression by pressing gt 5 gt and evaluate it by pressing ENTER The result is X X 6 Example2 To enter 2 3 1 press 2 gt n 3 XT6 TE If instead you had to enter x 3X 1 you would need to press Ke 0 2 gt 0 3 1 Note that you press gt twice to ensure that the exponent applies to X and not just to X Example 3 Suppose you want to enter 1 1 1 1 2 3 amp 5 Each fraction can be viewed as a separate branch on the equation tree In the H Equation Writer type the first branch and then select this branch by pressing gt Now type and enter the second branch 1 3 Select the second branch by pressing gt Now type and enter the third branch 1 4 Likewise select the third branch by pressing gt type and then the fourth branch 1 5 Equation Writer an e hp40g book Page 9 Friday December 9 2005 1 03 AM
222. ed by the HP THEN 40gs as error conditions and are automatically treated as ELSE errors in programs END 21 18 Programming 4 e NY hp40g book Page 19 Friday December 9 2005 1 03 AM RUN STOP IFERR THEN ELSE END allows a program to intercept error conditions that otherwise would cause the program to abort Its syntax is IFERR frap clause THEN clause 1 ELSE clause_2 END Example IFERR 60 X gt Y THEN MSGBOX Error X is zero ELSE MSGBOX Value is Y END Runs the named program If your program name contains special characters such as a space then you must enclose the file name in double quotes RUN program name or RUN programname Stops the current program STOP Drawing commands ARC Programming The drawing commands act on the display The scale of the display depends on the current aplet s Xmin Xmax Ymin and Ymax values The following examples assume the HP 40gs default settings with the Function aplet as the current aplet Draws a circular arc of given radius whose centre is at x y The arc is drawn from start_angle_measurement to end_angle_measurement ARC radius start angle measurement end_angle_measurement 21 19 T p am a Z gt e hp40g book Page 20 Friday December 9
223. ee Polar aplet variables on page R 9 Sequence UO to U9 Symbolic view See Sequence aplet variables on page R 10 E Solve EO to E9 Symbolic view See Solve aplet variables on page R 11 Statistics CO to C9 Numeric view See Statistics aplet variables on page R 1 2 To access an aplet 1 Open the aplet that contains the variable you want to variable recall 2 Press to display the VARS menu 3 Use the arrow keys to select a variable category in the left column then press 5 to access the variables in the right column 4 Use the arrow keys to select a variable in the right column 5 To copy the name of the variable onto the edit line 6 To copy the value of the variable into the edit line press and press Hg D 17 8 Variables and memory management e 0 Y e hp40g book Page 9 Friday December 9 2005 1 03 AM Memory Manager You can use the Memory Manager to determine the amount of available memory on the calculator You can also use Memory Manager to organize memory For example if the available memory is low you can use the Memory Manager to determine which aplets or variables consume large amounts of memory You can make deletions to free up memory Example 1 Start the Memory Manager A list of variable categories is displayed SHIFT MEMORY Free memory is displayed in the top
224. eft column then highlight an item in the right column The list in the right column changes when a different category is highlighted selection To speed search a list type the first letter of the word For example to find the Matrix category in MATH press the Alpha M key To go up a page you can press 4 To go down a page press gt e To cancel a menu Press ON for CANCEL or a5 This cancels the 4 current operation Input forms An input form shows several fields of information for you to examine and specify After highlighting the field to edit you can enter or edit a number or expression You can also select options from list Some input forms include items to check See below for examples input forms FUMCTIOM PLOT ETHP FUMCTIOM PLOT SETUP 2 52145 RIS IMULT INY CROSS 2 1 3 2 w CONNECT v LABELE ETICK 1 YTICK 1 v HE GRID RE Faster ENTER MINIMUM HORIZONTAL VALUE PLOT FUNCTIONS SIMULTANEOUSLY EDIT PHGET jl CHE Reset input form reset a field to its default values in an input form move values the cursor to that field and press DEL reset all default field values in the input form press CLEAR _ Getting started 1 9 e NZ GIN e hp40g book Page 10 Friday December 9 2005 1 03 AM
225. el you supplied Two Proportion Z Test Menu name Z Test nl 22 On the basis of statistics from two samples each from a different population the Two Proportion Z Test measures the strength of the evidence for a selected hypothesis against the null hypothesis The null hypothesis is that the proportion of successes in the two populations is equal HO 112 You select one of the following alternative hypotheses against which to test the null hypothesis lt T H n gt 77 Inference aplet 11 11 T a e NY Inputs Results e hp40g book Page 12 Friday December 9 2005 The inputs are 1 03 AM Field name Definition X2 nl n2 Ol Sample 1 mean Sample 2 mean Sample 1 size Sample 2 size Significance level The results are Result Description Test 11 2 Difference between the proportions of successes in the two samples Test Z Z Test statistic Prob Probability associated with the Z Test statistic Critical Z Boundary values of Z associated with the level that you supplied One Sample T Test Menu name 11 12 T Test 1 u The One sample T Test is used when the population standard deviation is not known On the basis of statistics from a single sample this test measures the strength of the evide
226. elect Francais and press Hi To return to English select English and press iid Equation Writer an hp40g book Page 5 Friday December 9 2005 1 03 AM Entering expressions and subexpressions How do select NOTE Equation Writer You type expressions in the Equation Writer is much the same way as you type them in the HOME screen using the keys to directly enter numbers letters and operators and menus to select various functions and commands When you type an expression in the Equation Writer the operator that you are typing always carries over to the adjacent or selected expression You don t have to worry about where the parentheses go they are automatically entered for you It will help you understand how the Equation Writer works if you view a mathematical expression as a tree with the four arrow keys enabling you to move through the tree the gt and lt keys enable you to move from one branch to another the 4 and keys enable you to move up and down a particular tree the A and key combinations 4 enable you to make multiple selections There are two ways of going into selection mode e Pressing takes you into selection mode and selects the element adjacent to the cursor For example 1 2 3 4 4 selects 4 Pressing it again selects the entire tree 1 2 3 4 Pre
227. elect the ascending or descending option from the menu and press MA Toggles between two character e sizes 4 pra Displays the defining function expression for the highlighted column DEL Deletes the highlighted row CLEAR Clears all data from the table Example plotting a circle Plot the circle 2 y 9 First rearrange it to read y x9 x To plot both the positive and negative y values you need to define two equations as follows y 49 x and y cr 1 In the Function aplet specify the functions Aplets and their views 4 4 P hp40g book Page 21 Friday December 9 2005 1 03 AM Select Function surr 09 2 DJ 09 FUNCTION SYMEOLIC VIEH SERERE 1 ame ET CTS 0 2 Reset the graph setup to default settings SHIFT SETUP PLOT SHIFT CLEAR 3 Plot the two functions and hide the menu so that you can see all the circle PLOT EEN GE FUNCTION PLOT SETUP 56 5 TRANG 3 1 Bad STICK 1 TICK 1 RES Detail ENTER MINIMUM HORIZONTAL VALUE EDIT PAGE F 4 Reset the numeric setup to the default settings SETUP NUM SHIFT CLEAR Se EUMCTIOM NUMERIC SETUP 3EERERE MUMS TART MUMSTEP 1 MUMTYPE Automatic MUMZOOM 4 ENTER STARTI
228. eleting list items 19 3 displaying 19 4 displaying list elements 19 4 editing 19 3 T an ad NY 4 hp40g book Page 7 Friday December 9 2005 1 03 finding statistical values in list ele logical operators 13 19 ments 19 9 menu 1 7 generate a series 19 8 polynomial 13 11 list function syntax 19 6 probability 13 12 list variables 19 1 real number 13 14 returning position of element in symbolic 13 17 19 8 trigonometry 13 20 reversing order in 19 8 MATH menu 13 1 sending and receiving 19 6 math operations 1 19 sorting elements 19 9 enclosing arguments 1 21 storing elements 19 1 19 4 19 5 in scientific notation 1 20 storing one element 19 6 negative numbers in 1 20 INCOLLECT 14 31 mu logarithm 13 4 adding rows 21 24 logarithmic addition and subtraction 18 6 fit 10 13 arguments 18 10 functions 13 4 arithmetic operations in 18 6 logarithms 14 31 assembly from vectors 18 1 logical operators changing row position 21 25 AND 13 19 column norm 18 10 equals logical test 13 19 comma 19 7 greater than 13 19 commands 18 10 greater than or equal to 13 19 condition number 18 11 IFTE 13 19 create identity 18 13 less than 13 19 creating 18 3 e less than or equal to 13 19 creating in Home 18 5 NOT 13 19 deleting 18 4 not equal to 13 1 9 deleting columns 21 24 OR 13 19 deleting rows 21 24 XOR 13 20 determinant 18 11
229. ell as in programs You can type in the name of the function or you can FUNCTION z copy the name of the function from the List category of the MATH menu Press MATH the alpha L character key This highlights the List category in the left column Press gt to move the cursor to the right column which contain the List functions select a function and press BIB List functions have the following syntax Functions have arguments that are enclosed in parentheses and separated by commas Example CONCAT L1 L2 An argument can be either a list 19 6 Lists e 0 SZ gt e hp40g book Page 7 Friday December 9 2005 1 03 AM variable name such as L1 or the actual list For example REVERSE 1 2 3 f Decimal Mark in Modes is set to Comma use periods to separate arguments For example CONCAT 11 12 Common operators like x and can take lists as arguments If there are two arguments and both are lists then the lists must have the same length since the calculation pairs the elements If there are two arguments and one is a real number then the calculation pairs the number with each element of the list Example 5 11 2 3 returns 5 10 15 Besides the common operators that can take numbers matrices or lists as arguments there are commands that can only operate on lists C
230. ember 9 2005 1 03 AM NY Field name Definition o2 Population 2 standard deviation Signiticance level Results The results are Result Description Test Z Z Test statistic Prob Probability associated with the Z Test statistic Critical Z Boundary value of Z associated with the a level that you supplied One Proportion Z Test Z Test 1 4 On the basis of statistics from a single sample this test measures the strength of the evidence for a selected hypothesis against the null hypothesis The null hypothesis is that the proportion of successes in the two populations is equal 1 2 You select one of the following alternative hypotheses against which to test the null hypothesis H n lt To H n gt ng H n To 11 10 Inference aplet T e Na e hp40g book Page 11 Friday December 9 2005 1 03 AM NY Inputs The inputs are Field name Definition x Number of successes in the sample n Sample size Population proportion of successes Significance level Results The results are Result Description Test P Proportion of successes in the sample Test Z Z Test statistic Prob Probability associated with the Z Test statistic e Critical Z Boundary value of Z associated with e the lev
231. ending 5 Press GE on the receiving calculator and choose the method of receiving For more information on sending and receiving files see Sending and receiving aplets on page 22 4 Working with matrices To edit a matrix In the Matrix catalog highlight the name of the matrix you want to edit and press Hail Matrix edit keys The following table lists the matrix edit key operations 9 Key Meaning ELIT Copies the highlighted element to the edit line Inserts a row of zeros above column of zeros to the left of the highlighted cell You are prompted to choose row or column A three way toggle for cursor advancement in the Matrix editor ERE advances to the right HES advances downward and does not advance at alll Switches between larger and smaller font sizes DEL Deletes the highlighted cells row or column you are prompted to make a choice CLEAR Clears all elements from the matrix 18 4 Matrices e 0 hp40g book Page 5 Friday December 9 2005 1 03 AM To display a matrix To display one element To create a matrix in HOME Matrices Ke Meaning Continued Y g A Moves to the first row last row first MEDIZ column or last column respectively n the Matrix catalog SHiFT MATRIX highlight the matrix name an
232. ents RISCH concerns itself only with the second element of the AND and adds the result to the first argument Limited mh order expansion SERIES has three arguments an expression dependent on a variable an equality the variable x the value a to which you want to calculate the expansion and a whole number the order n of the limited expansion You can omit the name of the variable and the sign when this name is in VX SERIES returns the limited nth order expansion of the expression in the vicinity of x a Example Expansion in the vicinity of x a Give a limited 4th order expansion of cos 2 in the vicinity of x e For this you use the SERIES command Computer Algebra System CAS am ad T 4 P hp40g book Page 25 Friday December 9 2005 1 03 AM Typing 2 D iERIES COS 2 D gives 1 3 89 3 8 4 e 2 pon 4s epp qs G 3 2h 3 0 h x P Example Expansion in the vicinity of x oo or X oo Example 1 Give a 5th order expansion of arctan x in the vicinity of x 00 taking as infinitely small h el Typing SERIES ATAN X X oo 5 gives GE a eo 2 2 EE Example 2 1 Give 2nd order expansion of 2x ler in the vicinity of x 00 taking as infinitely small SERIES 2X 1 EXP x oo 3 giv
233. equence aplets start in the Symbolic view If the highlight is on an existing expression scroll to an empty line unless you don t mind writing over the expression or clear one line DEL or all lines CLEAR Expressions are selected check marked on entry To deselect an expression press EMTA All selected expressions are plotted Aplets and their views 2 1 e e hp40g book Page 2 Friday December 9 2005 1 03 AM For a Function definition enter an expression to detine F X The only independent variable in the expression is X rr Nn Ht PARAMETRIC SYMEOLIC Pa ra metric definition enter vi T a pair of Y2cTa expressions fo aAscTa detine X T and emt che T SHO EVAL Y T The only independent variable in the expressions is T For a Polar definition enter POLAR 2 MEOLIC an expression to Rech define R 0 The icm only independent CH variable in the expression 15 For a Sequence definition either SEQUENCE SYMEOLIC VIEN enter the first term HEESE or the first and i second terms for U 225 EDIT ACHE 1 SHOH EVAL or U9 or UO Then define the nth term of the sequence in terms of N or of the prior terms U N 1 and or U N 2 The expressions should produce real valued se
234. ered your data NUM defined your data set and defined your Fit model for two variable statistics SHiFT SETUP SYMB you can plot your data You can plot up to five scatter or box and whisker plots at a time You can plot only one histogram at a time 10 15 Z e hp40g book Page 16 Friday December 9 2005 1 03 AM To plot statistical 1 In Symbolic view select ETA the data data sets you want to plot 2 For one variable data select the plot type in Plot Setup sHiFT SETUP PLOT Highlight STATPLOT press select either Histogram or BoxWhisker and press MA 3 For any plot but especially for a histogram adjust the plotting scale and range in the Plot Setup view If you find histogram bars too fat or too thin you can adjust them by adjusting the HWIDTH setting 4 Press PLOT If you have not adjusted the Plot Setup yourself you can try select Auto Scale DIA Auto Scale can be relied upon to give a good starting scale which can then be adjusted in the Plot Setup view Plot types Histogram One variable statistics The numbers below the plot mean that the current bar where the cursor is starts at O and ends at 2 not zi mE including 2 and the frequency for this column that is the number of data elements that fall between O and 2 is 1 You can see information about the next bar by pressing gt key
235. erence 11 1 key 1 4 library 22 6 Linear Solver 8 1 opening 1 16 Parametric 4 1 Polar 5 1 receiving 22 5 resetting 22 3 sending 22 4 22 5 Sketch view 20 1 Solve 7 1 sorting 22 6 statistics 10 1 transmitting 22 5 Triangle Solver 9 1 aplet commands an ad UNCHECK 21 17 aplet variables definition 17 1 17 8 in Plot view 21 31 new 17 1 aplet views canceling operations in 1 1 changing 1 19 note 1 18 Numeric view 1 17 Plot view 1 16 sketch 1 18 splitscreen 1 17 Symbolic view 1 16 approximation 14 32 arc cosecant 13 20 arc cosine 13 5 arc cotangent 13 20 13 20 arc sine 13 4 arc tangent 13 5 area graphical 3 10 interactive 3 10 variable 21 31 ARG 13 7 arguments with matrices 18 10 ASIN2C 14 39 ASIN2T 14 39 ASSUME 14 61 ATAN2S 14 39 attaching a note to an aplet 20 1 a sketch to an aplet 20 3 auto scale 2 14 axes plotting 2 7 variable 21 31 B bad argument R 20 NY 4 hp40g book Page 2 Friday December 9 2005 1 03 AM bad guesses error message 7 7 batteries R 4 Bernoulli s number 14 65 box and whisker plot 10 16 branch commands CASE END 21 18 IF THEN ELSE END 21 18 IFERR THEN ELSE 21 18 branch structures 21 17 build your own table 2 19 C calculus operations 13 CAS 14 1 15 1 contiguration 15 3 help 15 4 history 14 8 in HOME 14 7 list of functions 14 9 R 17 modes 14 5 15 3 online help 14
236. ermutation OR matrix Rank of a rectangular matrix RANK matrix Row Norm Finds the maximum value over all rows for the sums of the absolute values of all elements in a row ROWNORM matrix Reduced Row Echelon Form Changes a rectangular matrix to its reduced row echelon form RREF matrix Schur Decomposition Factors a square matrix into two matrices If matrix is real then the result is orthogonal upper quasi triangular If matrix is complex then the result is unitary upper triangular SCHUR matrix Dimensions of matrix Returned as a list rows columns S1ZE matrix Matrices am ad T a e hp40g book Page 13 Friday December 9 2005 1 03 AM NY SPECNORM Spectral Norm of matrix SPECNORM matrix SPECRAD Spectral Radius of a square matrix S PECRAD matrix SVD Singular Value Decomposition Factors an m x n matrix into two matrices and a vector m m square orthogonal n n square orthogonal real SVD matrix SVL Singular Values Returns a vector containing the singular values of matrix SVL matrix TRACE Finds the trace of a square matrix The trace is equal to the sum of the diagonal elements It is also equal to the sum of the eigenvalues TRACE matrix TRN Transposes matrix For a complex matrix TRN finds the conjugate transpose
237. es 12 6 dod 177 3 Te 1 m 0 2 h al Unidirectional expansion To perform an expansion in the vicinity of x a where x gt use a positive real such as 4 0 for the order To perform an expansion in the vicinity of x a where x lt a use a negative real such as 4 0 for the order Computer Algebra System CAS 14 25 T e P X iG e hp40g book Page 26 Friday December 9 2005 1 03 AM You must be in Rigorous not Sloppy mode to apply SERIES with unidirectional expansion See CAS modes on page 14 5 for instructions on setting and changing modes Example 1 Give a 3rd order expansion of mE in the vicinity of xD Typing SERIES JX X X 0 3 0 gives Tg tgo ry ene OC m Example 2 3rd order expansion of 2 3 in the vicinity of 07 Typing SERIESQ X X X 0 3 0 gives e 4 3 I 2 5 3 16 h a h 5 h h 0 h h x Note that h x is positive as x gt Example 3 If you enter the order as an integer rather than a real as in SERIES 4X X X 0 3 you will get the following error SERIES Error Unable to find sign Note that if you had been in Sloppy rather than Rigorous mode all three examples above would have returned the same answer as you got when exploring in the vicinity of xc 142 Computer Algebra Sy
238. ese can be numbers you have entered or the results of calculations These variables are available e within all aplets and within any programs Aplet variables apply only to a single aplet Aplets have specific variables allocated to them which vary from aplet to aplet You use the calculator s memory to store the following objects copies of aplets with specific configurations new aplets that you download oplet variables home variables variables created through a catalog or editor for example a matrix or a text note programs that you create You can use the Memory Manager SHIFT MEMORY to view the amount of memory available The catalog views which are accessible via the Memory Manager can be used to transfer variables such as lists or matrices between calculators Variables and memory management 17 1 4 hp40g book Page 2 Friday December 9 2005 1 03 AM Storing and recalling variables Numeric Precision To store a value To store the results of a calculation 17 2 You can store numbers or expressions from a previous input or result into variables A number stored in a variable is always stored as a 12 digit mantissa with a 3 digit exponent Numeric precision in the display however depends on the display mode Standard Fixed Scientific Engineering or Fraction A displayed number
239. et angle measure Set up the plot Plot the expression 42 MODES Select Degrees MA SHIFT PLOT Set the angle measure to degrees CHOOSE AMGLE MEASURE ee l Display the graphing options PARAMETRIC PLOT SETUP TSTEP 1 5 2 6 2 YENG 5 1 3 28 ENTER MINIMUM TIME VALUE E EDIT FAGE The Plot Setup input form has two fields not included in the Function aplet TRNG and TSTEP TRNG specifies the range of t values TSTEP specifies the step value between values Set the TRNG and TSTEP so that 7 steps from O to 360 in 5 steps gt 360 ma Plot the expression PARAMETRIC PLOT SETUP TRANG ae 5 5 5 YRNG 3 1 3 2 ENTER MINIMUM HORIZONTAL VALUE EDIT PHGEW T 00 3 To see all the circle press gramm twice an Parametric aplet Overlay plot Display the numbers Parametric aplet hp40g book Page 3 Friday December 9 2005 1 03 AM 8 9 Plot a triangle graph over the existing circle graph SAFT ALOL PARAMETRIC PLOT SETUP TENG 35H 28 HENG EESHESS 5 120 BS YRNG 5 1 3 2 ENTER MINIMUM HORIZONTAL VALUE EDIT VIEWS Select Overlay Plot DT i GE A triangle is displayed
240. ets See chapter 21 e Programming for further details Creating new aplets based on existing aplets You can create a new aplet based on an existing aplet To create a new aplet save an existing aplet under a new name then modify the aplet to add the configurations and the functionality that you want Information that defines an aplet is saved automatically as it is entered into the calculator To keep as much memory available for storage as possible delete any aplets you no longer need Example This example demonstrates how to create a new aplet by saving a copy of the built in Solve aplet The new aplet is saved under the name TRIANGLES and contains the formulas commonly used in calculations involving right angled triangles Extending aplets 22 1 T 5 NZ DS e hp40g book Page 2 Friday December 9 2005 1 03 AM 1 Open the Solve aplet and save it under the new name Solve SAVE APLET ALPHA NEN TRIANGLES TRIANGLES 2 Enter the four formulas ALPHA TRIANGLES SYMEDLIC VIEH Semen D B ALPHA ES TAN 8 zH Ed He c Br Ce ALPHA ENTER FE COS ArPHA 00 B PEDT e CHEL UNI EIT EVAL PHA A E ALPHA ENTER TAN AFA 9 D B ALPHA s ALPHA ENTER ALPHA A 02 E PHA eo E ALPHA C E
241. etting default values 1 9 setting Modes 1 11 insufficient memory R 20 insufficient statistics data R 20 integer rank K ISPRIME 14 50 keyboard editing keys 1 5 entry keys 1 5 inactive keys 1 8 list keys 19 2 math functions 1 7 menu keys 1 4 Notepad keys 20 8 shifted keystrokes 1 6 labeling axes 2 7 parts of a sketch 20 5 LAP 14 67 Laplace transform 14 65 Laplace transform inverse 14 66 LCM 14 50 14 57 LDEC 14 35 least common multiple 14 50 14 57 matrix 18 12 2 integer scaling 2 14 2 15 LEGENDRE 14 57 integral letters typing 1 6 definite 13 6 library managing aplets in 22 6 indefinite 13 23 lim 14 21 integration 13 6 14 18 14 24 limits 14 21 LIN 14 30 interpreting intermediate guesses 7 7 intersection 3 11 INTVX 14 19 invalid dimension R 20 statistics data R 20 syntax R 2 1 inverse hyperbolic cosine 13 9 inverse hyperbolic functions 13 10 inverse hyperbolic sine 13 9 inverse hyperbolic tangent 13 9 inverse Laplace transform 14 66 inverting matrices 18 8 INVMOD 14 53 IQUOT 14 49 IREMAINDER 14 49 isect variable 21 33 ISOLATE 14 34 list linear fit 10 13 Linear Solver aplet 8 1 linear systems 14 35 linearize 14 30 14 43 LINSOLVE 14 35 arithmetic with 19 7 calculate sequence of elements 19 8 calculating product of 19 8 composed from differences 19 7 concatenating 19 7 counting elements in 19 9 creating 19 1 19 3 19 4 19 5 deleting 19 6 d
242. ewrite HUM solve and Trig A The Complex menu providing functions specific to manipulating with complex numbers The Constant menu containing Loo and The Hyperb menu containing hyperbolic functions The Integer menu containing functions that enable you to perform integer arithmetic The Modular menu containing functions that enable you to perform modular arithmetic using the value contained in the MODULO variable The Polynom menu containing functions that enable you to perform calculations with polynomials The Real menu containing functions specific to common real number calculations The Tests menu containing logic functions for working with hypotheses e SHIFT MATH keys The MATH key e combination opens an alphabetical menu of all iM CAS commands You can RSIH2ZC enter a command by selecting it from this menu so that you don t have to type it in ALPHA mode VARS key Pressing while you re in the Equation Writer displays the names of the variables defined in CAS Take special note of namvx which contains the name of the current variable The menu options on the variables screen are fait Press to copy the name of the highlighted variable to the position of the cursor in Equation Writer ma Press to see the contents of the highlighted variable Ws Press to change the contents of the highlighted variable e 1
243. forecasting 10 20 FOURIER 14 17 fraction number format 1 11 ful precision display 1 10 function PRSE graph with FCN tools 3 4 efinition 2 2 R 1 P entering 1 19 gamma 13 13 intersection point 3 5 math menu R 13 R 17 slope 3 5 syntax 13 2 tracing 2 8 Function aplet 2 20 3 1 tunction variables area 21 31 axes 21 31 connect 21 31 fastres 21 32 grid 21 32 in menu map R indep 21 33 isect 21 33 labels 21 34 Recenter 21 34 root 21 34 ycross 21 37 G GAMMA 14 64 GCD 14 47 14 56 GCDMOD 14 53 T am v NY P hp40g book Page 5 Friday December 9 2005 1 03 AM glossary R 1 graph analyzing statistical data in 10 19 auto scale 2 14 box and whisker 10 16 capture current display 21 21 cobweb 6 1 comparing 2 5 connected points 10 17 defining the independent variable 21 36 drawing axes 2 7 expressions 3 3 grid points 2 7 histogram 10 15 in Solve aplet 7 7 one variable statistics 10 18 overlaying 2 15 scatter 10 15 10 17 split screen view 2 14 splitting into plot and close up 2 13 splitting into plot and table 2 13 stairsteps 6 1 statistical data 10 15 t values 2 6 tickmarks 2 6 tracing 2 8 two variable statistics 10 18 Graphic commands GROB 21 21 DISPLAY 21 21 GROBNOT 21 21 GROBOR 21 2 GROBXOR 21 22 MAKEGROB 21 22 21 22 REPLACE 21 22 SUB 21 22 ZEROGROB 21 22 graphics copying 20 6 copying into Sketch v
244. function with respect to the variable given as the second parameter used for calculating partial derivatives Example Calculate O x y x y Oz Typing DERIV X Y 2 X Y Z gives DERVX Derivative DERVX has one argument an expression DERVX calculates the derivative of the expression with respect to the variable stored in VX For example given fx Eod 2 is X calculate the derivative of f Type X ERVX 3 IT rw 1 1 Or if you have stored the definition of f x in F that is if you have typed TORE a i 1 X 1 then type 14 16 Computer Algebra System CAS T a e e hp40g book Page 17 Friday December 9 2005 1 03 AM NY DERVX Or if you have defined F X using DEF that is if you have typed X 1 JEF F X va LN 3 then type DERVX F X Simplify the result to get gD Pi DIVPC Division in increasing order by exponent DIVPC has three arguments two polynomials A X and B X where B O 40 and a whole number n DIVPC returns the quotient Q X of the division of A X by B X in increasing order by exponent and with deg Q 0 lt nor 0 4 Q X is then the limited nth order expansion of ALX B X in the vicinity of X O Typing DEVEC
245. g the expression in HOME Press the key twice to select the entire first term before entering the second term e 14 2 Computer Algebra System CAS e NZ 4 Computer Algebra System CAS hp40g book Page 3 Friday December 9 2005 1 03 AM Press gt and v to select just the 20 in the 20 ferm Press the menu key and choose FACTOR Then press gra Note that the FACTOR function is added to the selected term Press to factor the selected term Press 4 to select the entire second term and then press to simplify it Press gt gt v v gt to select the 45 in the first term As you did earlier press the menu key and choose FACTOR Then press fig and to factor the selected term Press 4 to select the entire second term and then press to simplify it an 2 45 E 2 15 2E 14 3 CAS variables e hp40g book Page 4 Friday December 9 2005 1 03 AM 10 Press gt three times to select the entire on ma expression and then press to simplify it to the form required When you use the symbolic calculation functions you are working with symbolic variables variables that do not contain a permanent value In the HOME scree
246. gh an example using the example data for the Z Test on 1 mean 1 Open the Inference aplet Select Inference The Inference aplet opens in the Symbolic view an SS NF STAT SYMEOLIC VIEH METHOD EA TPE Z Tezt 1 p ALT HYPOTH pA Choose inFerentaidl Hethod NY hp40g book Page 2 Friday December 9 2005 1 03 AM Inference aplet s SYMB view keys The table below summarizes the options available in Symbolic view Hypothesis Confidence Intervals Tests Z 1 u the Z Test on mean Z u the Z Test on the difference of two means Z 1 m the Z Test on proportion Z n n2 the Z Test on the difference in two proportions T the T Test on mean T un the T Test on the difference of two means Z Int 1 u the confidence interval for 1 mean based on the Normal distribution Z Int the confidence interval for the difference of two means based on the Normal distribution Z Int 1 x the confidence interval for 1 proportion based on the Normal distribution Z nt x1 x2 the confidence interval for the difference of two proportions based on the Normal distribution Tnt 1 u the confidence interval for 1 mean based on the Student s t distribution T Int the confidence interval for the difference of two m
247. h this function uncheck all fits except the one that you want to work with or use the Plot View method Statistics aplet 10 21 PN NZ X iG e hp40g book Page 22 Friday December 9 2005 1 03 AM T an ad e e hp40g book Page 1 Friday December 9 2005 1 03 AM Inference aplet About the Inference aplet The Inference capabilities include calculation of Example data confidence intervals and hypothesis tests based on the 11 Normal Z distribution or Student s t distribution Based on the statistics from one or two samples you can test hypotheses and find confidence intervals for the following quantities mean e proportion e difference between two means e difference between two proportions When you first access an input form for an Inference test by default the input form contains example data This example data is designed to return meaningful results that relate to the test It is useful for gaining an understanding of what the test does and for demonstrating the test The calculator s on line help provides a description of what the example data represents Getting started with the Inference aplet Open the Inference aplet Inference aplet This example describes the Inference aplet s options and functionality by stepping you throu
248. has only the precision that is displayed If you copy it from the HOME view display history you obtain only the precision displayed not the full internal precision On the other hand the variable Ans always contains the most recent result to full precision 1 On the command line enter the value or the calculation for the result you wish to store Press 3 Enter a name for the variable 4 Press If the value you want to store is in the HOME view display history for example the results of a previous calculation you need to copy it to the command line then store it 1 Perform the calculation for the result you want to store 36 0 8 696 0 7 3 ENTER 1 rr 2 Press 4 to highlight to the result you wish to store 3 Press to copy the result to the command line Variables and memory management an zz gt e hp40g book Page 3 Friday December 9 2005 1 03 AM 5 Enter a name for the variable ALPHA A 6 Press ENTER to store the result The results of a calculation can also be stored directly to a variable For example 20 05030 FEES ALPHA Be 3 174230210394 To recall a value To recall a variable s value type the name of the variable and press ENTER ALPHA A 221775
249. hbour to the left The selected element remains selected after you move if Cursor mode In cursor mode you can select a large expression quickly To select cursor mode press wim Cursor mode Eis As you press the arrow key various parts of the expression are enclosed n in 0 When what you want to select is enclosed press to select it Mts Changing the If you are entering a long expression you may find it font useful to reduce the size of the font used in the Equation Writer Select Change font from the menu This enables you to view a large expression in its entirety when you need to Selecting Change font again returns the font size to its previous setting You can also see the selected expression or subexpression is a smaller or larger font size by pressing and then to use the smaller font or HATA to use the larger font 15 10 Equation Writer e 0 SZ gt e hp40g book Page 11 Friday December 9 2005 1 03 AM How to modify an expression If you re typing an expression the DEL key enables you to erase what you ve typed If you re selecting you can Cancel the selection without deleting the expression by pressing DEL The cursor moves to the end of the deselected portion Replace the selection with an expression just by typing the desired expression Transform the sel
250. he 4 or v key Then move the cursor so that it is near x 1 by pressing the gt or lt key Zaz SelectRoot T E 4 Intersection Slope ASigned area Extremum The root value is displayed at the bottom of the screen Note If there is more than one root as in our example the coordinates of the root closest to the current cursor position are displayed ROOT 1 585708643763 HEHU Find the intersection of the two functions To find the intersection of the iuo ances faim pum vw BH E I X Dk 6 3 4 Function aplet e 0 zz gt e hp40g book Page 5 Friday December 9 2005 1 03 AM 12 Choose the linear function whose intersection with the quadratic function you wish to find The coordinates of the intersection point are displayed at the bottom of the screen I SECT 1 87 MEM Note If there is more than one intersection as in our example the coordinates of the intersection point closest to the current cursor position are displayed To find the slope of 13 Find the slope of the quadratic function at the the quadratic intersection point gt function PETITUM sa 4 MD The slope value is SLOPE mg displayed at the bottom of the screen To find the signed
251. he infinity sign from the character map places a character in front of the infinity sign e emm Selecting the entire expression and pressing yields i In effect tends to Oas n 0 tends to so o tends to e las n tends to As n tends to is the portion between 7 and a quantity that tends to 7 Hence u converges and its limit is 7 We have therefore shown that L J 4 1n2 Step by Step Examples an 4 P hp40g book Page 29 Friday December 9 2005 1 03 AM Step by Step Examples am ad 16 29 X iG e hp40g book Page 30 Friday December 9 2005 1 03 AM T an ad e GIN e hp40g book Page 1 Friday December 9 2005 1 03 AM 17 Variables and memory management Introduction The HP 40gs has approximately 200K of user memory The calculator uses this memory to store variables perform computations and store history A variable is an object that you create in memory to hold data The HP 40gs has two types of variables home variables and aplet variables Home variables are available in all aplets For example you can store real numbers in variables A to Z and complex numbers in variables ZO to Z9 Th
252. he comma 5 Use the cursor keys to move to a different row or column You can change the direction of the highlight bar by pressing The Ef menu key toggles e between the following three options specifies that the cursor moves to the cell below the current cell when you press ENTER specifies that the cursor moves to the cell to the right of the current cell when you press CENTER Ef specifies that the cursor stays in the current cell when you press ENTER 6 When done press SHIFT MATRIX to see the Matrix catalog or press to return to HOME The matrix entries are automatically stored MATRIS CATALOG ZEE GEERT 11 151 REAL MATRIK KE fit 243 REAL MATRIS M3 151 REAL MATRIK 4 191 REAL MATRIS M5 151 REAL MATRIK WKE EDIT IMS 0 Ea L EDITIHEM sEHDIFECV A matrix is listed with two dimensions even if itis 3x1 A vector is listed with the number of elements such as 3 Matrices 18 3 e NZ Y e hp40g book Page 4 Friday December 9 2005 1 03 AM To transmit a You can send matrices between calculators just as you matrix can send aplets programs lists and notes 1 Connect the calculators using an appropriate cable 2 Open the Matrix catalogs on both calculators 3 Highlight the matrix to send 4 Press and choose the method of s
253. he coordinates LIMSOLVE 1 45 L1 4L2 iv 2a 90 B 225 638 eduction result roo H 1530 225 63H H 2 HHD y 1 3 and 3 1 respectively and where the unit of measure is the centimetre an Step by Step Examples zz gt e hp40g book Page 7 Friday December 9 2005 1 03 AM 1 Find the exact length of AB in centimetres 2 Determine the equation of the line AB First method Type STORE 1 3 A and press Accept the change to Complex mode if necessary Note that pressing returns the coordinates in complex form 1 3i SEHH Now type STORE and press The coordinates this time are represented as 34 1 e The vector AB has coordinates A Type oO XT Press ENTER The result is 245 Now apply the DROITE command to determine the equation of the line AB MATH Complex DROITE ALPHA A gt J DROITELR B ALPHA B Pressing ENTER gives an intermediate result e Step by Step Examples 16 7 e NZ zz gt e hp40g book Page 8 Friday December 9 2005 1 03 AM Press again to simplify the result to Y 2X5 his Second method Type 3
254. iation n Sample size C Confidence level D Inference aplet 11 15 m n e iG e hp40g book Page 16 Friday December 9 2005 1 03 AM Results The results are Result Description Critical Z Critical value for Z L min Lower bound for L max Upper bound for u Two Sample Z Interval Menu name Z INT ul u2 This option uses the Normal Z distribution to calculate a confidence interval for the difference between the means of two populations u when the population standard deviations and o are known Inputs The inputs are xe plete Definition D zi Sample 1 mean x2 Sample 2 mean ni Sample 1 size n2 Sample 2 size c1 Population 1 standard deviation 02 Population 2 standard deviation C Confidence level Results The results are Result Description Critical Z Critical value for Z p Min Lower bound for u u Max Upper bound for u 11 16 Inference aplet T 5 iG e hp40g book Page 17 Friday December 9 2005 1 03 AM One Proportion Z Interval Menu name Z INT 1 x This option uses the Normal Z distribution to calculate a confidence interval for the proportion of successes in a population for the case in which a sample of size n has a number of successes x Inputs Th
255. ice complies with Part 15 of the FCC Rules Operation is subject to the following two conditions 1 this device may not cause harmful interference and 2 this device must accept any interference received including interference that may cause undesired operation For questions regarding your product contact T e zz gt e hp40g book Page 6 Friday December 9 2005 1 03 AM Hewlett Packard Company Box 692000 Mail Stop 530113 Houston Texas 77269 2000 Or call 1 800 474 6836 For questions regarding this FCC declaration contact Hewlett Packard Company P O Box 692000 Mail Stop 510101 Houston Texas 77269 2000 Or call 1 281 514 3333 To identify this product refer to the part series or model number found on the product Canadian This Class B digital apparatus meets all requirements of Notice the Canadian Interference Causing Equipment Regulations Avis Canadien Cet appareil num rique de la classe B respecte toutes les exigences du R glement sur le mat riel brouilleur du Canada European Union This product complies with the following EU Directives Regulatory Low Voltage Directive 73 23 EEC Notice Directive 89 336 EEC Compliance with these directives implies conformity to applicable harmonized European standards European Norms which are listed on the EU Declaration of Conformity issued by Hewlett Packard for
256. ich columns contain data and which column contains frequencies You can also compute statistics values in HOME and recall the values of specific statistics variables The values computed in the Statistics aplet are saved in variables and many of these variables are listed by the function accessible from the Statistics aplet s Numeric view screen Getting started with the Statistics aplet The following example asks you to enter and analyze the advertising and sales data in the table below compute statistics fit a curve to the data and predict the effect of more advertising on sales Advertising minutes Resulting Sales independent x dependent y Statistics aplet 10 1 am SZ e hp40g book Page 2 Friday December 9 2005 1 03 AM the 1 Open the Statistics aplet and clear existing data by Statistics aplet pressing HES Select Statistics nies The Statistics aplet starts in the Numerical view 1VAR 2VAR menu key labe At any time the Statistics aplet is configured for only one of two types of statistical explorations one variable ER or two variable ARA The 5th menu key label in the Numeric view toggles between these two options and shows the current option 2 Select IEG You need to select HHI because in this example we are analyzi
257. iday December 9 2005 1 03 AM where X is distance Vo is initial velocity Tis time and A is acceleration This is actually two equations Y X and 2 Since this equation is quadratic for there can be both a positive and a negative solution However we are concerned only with positive solutions since only positive distance makes sense 1 Select the Solve aplet and enter the equation Select Solve ALPHA V x 4 ALPHA ES 7 LEDIT CHE ALPHA A 2 Find the solution for T time when 30 V 2 and 4 4 Enter the values for X V and then highlight the independent variable T SOLVE MUMERIC NUM 30 EMTER VALUE PRES SOLVE v 4 EDIT INFO EN Ee v v to highlight T 3 Usethe Plot view to find an initial guess for T First set appropriate X and Y ranges in the Plot Setup With equation X Vx T Ax T 2 the plot will produce two graphs one for Y X and one for X VxT Ax 2 Since we have set X 30 in this example one of the graphs will be Y 30 Therefore make the YRNG 5 to 35 Keep the XRNG default of 6 5 to 6 5 SHIFT SETUP PLOT SOLVE PLOT SETUP 6 5 5 5 ENTER 35 mns WTILE il TICK 1 RES i ENTER Detail EMTER HORIZONTAL TICK SPACING PAGEF
258. iew 20 6 storing and recalling 20 6 21 21 greatest common divisor 14 56 H HALFTAN 14 40 HERMITE 14 56 histogram 10 15 an ad adjusting 10 16 range 10 18 setting min max values for bars 21 32 width 10 18 history 1 2 14 8 21 25 Home 1 1 calculating in 1 19 display 1 2 evaluating expressions 2 4 reusing lines 1 23 variables 17 1 17 7 R 6 home 14 7 horizontal zoom 21 38 hyperbolic maths functions 13 10 hyperbolic trigonometry ACOSH 13 9 ALOG 13 10 ASINH 13 9 ATANH 13 9 COSH 13 10 EXP 13 10 EXPM1 13 10 LNP1 13 10 SINH 13 10 TANH 13 10 hypothesis alternative 11 2 inference tests 11 8 null 11 2 tests 11 2 i 13 8 14 45 IABCUV 14 64 IBERNOULLI 14 65 IBP 14 18 ICHINREM 14 65 IDIV2 14 48 IEGCD 14 48 ILAP 14 65 IM 13 7 implied multiplication 1 20 importing graphics 20 6 notes 20 8 increasing display contrast 1 2 indefinite integral NY e hp40g book Page 6 Friday December 9 2005 1 03 AM using symbolic variables 13 23 independent values adding to table 2 19 independent variable defined for Tracing mode 21 33 inference confidence intervals 11 15 hypothesis tests 11 8 One Proportion Z Interval 11 17 One Sample Z Interval 11 15 One Sample Z Test 11 8 Two Proportion Z Interval 11 17 Two Proportion Z Test 11 11 Two Sample T Interval 11 19 L Two Sample Z Interval 11 16 infinite result R 20 initial guess 7 5 input forms res
259. ing check marking the expression or expressions that you want to explore in the Symbolic view press NUM to view a table of data values for the independent variable X T 0 or N and dependent variables Setting up the table Numeric view setup Press SHIFT NUM to define ES FUNCTIUM HMURERIC SETUP SE LS any of the table settings TART MUMSTEP 1 Use the Numeric Setup NUMTYPE Automatic input form to configure the _ 02207 4 EMTERE THRTIMG VALUE FOR THELE table 1 Highlight the field to edit Use the arrow keys to move from field to field If there is a number to enter type it in and press e or To modify an existing number 4 press Elli If there is an option to choose press MITA highlight your choice and press or MA Shortcut Press the key to copy values from the Plot Setup into NUMSTART and NUMSTEP Effectively the menu key allows you to make the table match the pixel columns in the graph view 2 When done press NUM to view the table of numbers Numeric view The following table details the fields on the Numeric settings Setup input form Field Meaning NUMSTART The independent variable s starting value NUMSTEP The size of the increment from one independent variable value to the next Aplets and their views 4 GIN e hp40g book Page 17 Friday December 9 2005 1
260. ins that way until you run SETVIEWS again e You do not need to include this program for your aplet to work but it is useful to specify that the program is attached to the aplet and transmitted when the aplet is transmitted 7 Return to the program 1 catalog The programs ee that you created should EXP ANG 25 EXP MEZ 21KB appear as follows EXF ME1 19 MEM 1sEND REC FUN 8 You must now fai the program EXP SV to execute the SETVIEWS command and create the modified VIEWS menu Check that the name of the new aplet is highlighted in the Aplet view 9 You can now return to the Aplet library and press to run your new aplet Programming commands This section describes the commands for programming with HP 40gs You can enter these commands in your program by typing them or by accessing them from the Commands menu Programming 21 13 e NZ e hp40g book Page 14 Friday December 9 2005 1 03 AM NY Aplet commands CHECK Checks selects the corresponding function in the current aplet For example Check 3 would check F3 if the current aplet is Function Then a checkmark would appear next to F3 in Symbolic view F3 would be plotted in Plot view and evaluated in Numeric view CHECK n SELECT Selects the named aplet and makes it the current
261. interval setting is 0 5 NUM IMF TAT n d VIEL Critical T2427 015048 H Hin 2469514 H 8978186 Display Plot 13 Display the confidence interval in the Plot view play 1 e ae cl gt BBPU1HE Es You can see from the aa m second text row that the iil HEE EN es mean is contained within the 90 confidence interval Cl of 0 34698 14 to 0 83701 86 Note The graph is a simple generic bell curve It is not meant to accurately represent the tdistribution with 5 degrees of freedom Inference aplet 11 7 4 e hp40g book Page 8 Friday December 9 2005 1 03 AM NY Hypothesis tests You use hypothesis tests to test the validity of hypotheses that relate to the statistical parameters of one or two populations The tests are based on statistics of samples of the populations The HP 4095 hypothesis tests use the Normal Z distribution or Student s tdistribution to calculate probabilities One Sample Z Test Menu name Z Test 1 u On the basis of statistics from a single sample the One Sample Z Test measures the strength of the evidence for a selected hypothesis against the null hypothesis The null hypothesis is that the population mean equals a specified value Ho u You select one of the following alternative hypotheses against which to test the null hypothesis
262. ion n Sample size C Confidence level 11 18 Inference aplet E n e X iG e hp40g book Page 19 Friday December 9 2005 1 03 AM Results The results are Result Description Critical T Critical value for T u Min Lower bound for u L Max Upper bound for u Two Sample T Interval Menu name FINT ul u2 This option uses the Student s t distribution to calculate a confidence interval for the difference between the means of two populations ul u2 when the population standard deviations sland s2 are unknown Inputs The inputs are e Definition amp zi Sample 1 meon x2 Sample 2 mean s1 Sample 1 standard deviation s2 Sample 2 standard deviation ni Sample 1 size n2 Sample 2 size Confidence level Pooled Whether or not to pool the samples based on their standard deviations Inference aplet 11 19 E e 5 e hp40g book Page 20 Friday December 9 2005 1 03 AM e NY Results The results are Result Description Critical T Critical value for T u Min Lower bound for u A u Max Upper bound for u 11 20 Inference aplet T e e SZ gt e hp40g book Page 1 Friday December 9 2005 1 03 AM
263. ion y 256 displays 16 MATH menu Press pp T EEE EE MATH to open the MATH Real CEILING menu The MATH menu isa gee comprehensive list of math Tests FHROOT functions that do not appear on the keyboard It also includes categories for all other functions and constants The functions are grouped by category ranging in alphabetical order from Calculus to Trigonometry e The arrow keys scroll through the list v 4 and move from the category list in the lett column to the item list in the right column J Press ff to insert the selected command onto the edit line e Press to dismiss the MATH menu without selecting a command Getting started 1 7 4 Program commands Inactive keys Menus HINT hp40g book Page 8 Friday December 9 2005 1 03 AM Pressing displays the list of Program Constants You can use these in programs that you develop Pressing iil displays a menu of physical constants from the fields of chemistry physics and quantum mechanics You can use these constants in calculations pSee Physical constants on page 13 25 for more information See Math functions by category on page 1 3 2 for details of the math functions When using the MATH menu or any menu on the HP 40gs pressing an alpha key takes you straight to the first men
264. ions For linear differential equations having constant coefficients it is better to use LDEC DESOLVE has two arguments 1 the differential equation where y is written as d 1Y X or the differential equation and the initial conditions separated by AND a 2 the unknown Y X w The mode must be set to real Example 1 Solve y y cos x XUi co y 0 c Typing DESOLVE d1d1Y Y X COS X Y X gives x 2 cCl Y X cC0 cos x 5 sin x cCO and cCl are integration constants y O cCO 0 EC You can then assign values to the constants using the SUBST command 14 33 T e P X iG e hp40g book Page 34 Friday December 9 2005 1 03 AM ISOLATE 14 34 To produce the solutions for y 0 1 type SUBST Y X CO COS X 2091 cCO 1 which gives sie 2 cos x x cCl1 sin x Example 2 Solve y y cos x y 0 1 y 0 1 It is possible to solve for the constants from the outset Typing DESOLVE 1 1 X Y X COS X AND Y 0 1 AND d1Y 0 1 Y X gives Y x cosx ar sin x The zeros of an expression ISOLATE returns the values that are the zeros of an expression or an equation ISOLATE has two parameters an expression or equation and the name of the variable to isolate ignoring REALASSUME Typing ISOLATE X 1 3 X gives i
265. ions are of the form expression O SOLVE has as arguments the first members of the various equations separated by AND and the names of the various variables separated by AND Typing SOLVE X Y 3 AND X Y 41 X AND Y gives x 1 AND y 42 OR x 1 AND y V2 Computer Algebra System CAS 14 37 m e P e hp40g book Page 38 Friday December 9 2005 1 03 AM NY SOLVEVX Solve equations SOLVEVX has as a parameter either 1 an equality between two expressions in the variable contained in VX or 2 a single such expression in which case is implied SOLVEVX solves the equation Example 1 Typing SOLVEVX X 1 3 gives in real mode x N2 OR x V2 or in complex mode even if you have chosen X as real x V2 OR x V2 OR x i N2 OR x iv2 Example 2 e9 Typing e SOLVEVX 2 gives in real mode x 1 2 OR x 0 TRIG menu The TRIG menu contains functions that enable you to transform trigonometric expressions ACOS2S Transform the arccos into arcsin ACOS2S has as a trigonometric expression as an argument ACOS2S transforms the expression by replacing arccos x with 2 arcsin x 1438 Algebra System CAS T a PN 0 NY 4 P hp40g book Page 39 Friday December 9
266. ire expression is selected If you now press just the numerator is selected f you now press Y again the top most branch selected that is 5x 3 Continue pressing Y to select each top most leaf in turn 5x and then 5 15 6 Equation Writer 4 zz gt e hp40g book Page 7 Friday December 9 2005 1 03 AM Press 4 again and again to progressively select more of the top most branch and then lower branches 5x 5x 3 and then the entire numerator and finally the entire expression More Examples Example If you enter 2 Xx 3 and press gt gt gt the entire expression is selected Pressing evaluates what is selected that is the entire expression and returns 2X 2 If you enter the same expression as earlier but press gt atter the first X as in 2 X 5 x3 X the 2 X is selected and the next operation multiplication is applied to to it The expression becomes e e 3 H 2 X x 3 X Pressing 5 selects the entire expression and pressing evaluates it resulting in 2X 6 Now enter the same expression but press 4 after the 3 as in 2 X gt x 3 4 X Note that selects the expression so far entered 2 X thus making the next operation apply to the entire sel
267. is being plotted plots them simultaneously otherwise sequentially INV CROSS Cursor crosshairs invert the status of the pixels they cover e 0 4 hp40g book Page 7 Friday December 9 2005 1 03 AM Field Meaning Continued CONNECT Connect the plotted points The Sequence aplet always connects them LABELS Label the axes with XRNG and YRNG values AXES Draw the axes GRID Draw grid points using XTICK and YTICK spacing Reset plot To reset the default values for all plot settings press settings SHIFT CLEAR in the Plot Setup view To reset the default value for a field highlight the field and press DEL Exploring the graph Plot view gives you a selection of keys and menu keys to explore a graph further The options vary from aplet to aplet PLOT view keys The following table details the keys that you use to work with the graph ey Meaning CLEAR Erases the plot and axes lt Offers additional pre defined views for splitting the screen and for scaling Zooming the axes Moves cursor to far left or far right vJl Moves cursor between relations O Interrupts plotting Continues plotting if interrupted Aplets and their views 2 7 an SZ gt e hp40g book Page 8 F
268. is the real part y is the imaginary part and i is the imaginary constant FEE e XPI To enter i e press ALPHA or e press MATH or v keys to select Constant gt to move to the right column of the menu v to There are 10 variables available for storing complex numbers ZO to Z9 To store a complex number in a variable Enter the complex number press enter the variable to store the number in and press ENTER 04050 mzm ALPHA Z 0 ENTER 4 05620 4 92 1 29 an STA Z e hp40g book Page 30 Friday December 9 2005 1 03 AM Catalogs and editors The HP 40gs has several catalogs and editors You use them to create and manipulate objects They access features and stored values numbers or text or other items that are independent of aplets A catalog lists items which you can delete or transmit for example an aplet An editor lets you create or modify items and numbers for example a note or a matrix Catalog Editor Contents Aplet library Aplets APLET Sketch editor Sketches and diagrams See SHIFT SKETCH Chapter 20 Notes and sketches List SHIFT Lists In HOME lists are enclosed in See Chapter 19 e 7 Lists 4 Matrix SHIFT One and two dimensional MATRIX arrays In HOME arrays are enclosed in See Chapte
269. isplays the current expression in text book form Resolves all references to other definitions in terms of variables and evaluates all arithmetic expressions Displays a menu for entering variable names or contents of variables Aplets and their views an SZ gt e hp40g book Page 5 Friday December 9 2005 1 03 AM Key Meaning Continued MATH Displays the menu for entering math operations CHARS Displays special characters To enter one place the cursor on it and press HA To remain in the CHARS menu and enter another special character press Ei DEL Deletes the highlighted expression or the current character in the edit line SHIFT CLEAR Deletes all expressions in the list or clears the edit line About the Plot view After entering and selecting check marking the expression in the Symbolic view press PLOT To adjust the appearance of the graph or the interval that is displayed you can change the Plot view settings e You can plot up to ten expressions at the same time Select the expressions you want to be plotted together Setting up the plot Plot view setup Press SHIFT SETUP PLOT to define any of the settings shown in the next two tables 1 Highlight the field to edit If there is a number to enter type it in and press CENTER BIB If there is an option to choose press MI
270. ist L1 into the data column variable c1 Statistics aplet s NUM view keys The Statistics aplet s Numeric view keys are Copies the highlighted item into the edit line Inserts a zero value above the highlighted cell Sorts the specified independent data column in ascending or descending order and rearranges a specified dependent or frequency data column accordingly Switches between larger and smaller font sizes A toggle switch to select one variable or two variable statistics This setting affects the statistical calculations and plots The label indicates which setting is current Computes descriptive statistics for each data set specified in Symbolic view 10 6 Statistics aplet 4 SZ gt e hp40g book Page 7 Friday December 9 2005 1 03 AM Meaning Continued Deletes the currently highlighted value CLEAR Clears the current column or all columns of data Pregss CLEAR to display a menu list then select the current column or all columns option and press MA Moves to the first or last row or first cursor key orlast column Example You are measuring the height of students in a classroom to find the mean height The first five students have the following measurements 160cm 165cm 170cm 175cm 180cm 1 Open the Statistics aplet Select Statistics e Izd BEIGE 1
271. itled to a refund of the purchase price upon prompt return of the product with proof of purchase 4 HP products may contain remanufactured parts equivalent to new in performance or may have been subject to incidental use 5 Warranty does not apply to defects resulting from a improper or inadequate maintenance or calibration b software interfacing parts or supplies not supplied by HP c unauthorized modification or misuse d operation outside of the published environmental specifications for the product or e improper site preparation or maintenance T e P NY 4 hp40g book Page 2 Friday December 9 2005 1 03 AM HP MAKES NO OTHER EXPRESS WARRANTY OR CONDITION WHETHER WRITTEN OR ORAL TO THE EXTENT ALLOWED BY LOCAL LAW ANY IMPLIED WARRANTY OR CONDITION OF MERCHANTABILITY SATISFACTORY QUALITY OR FITNESS FOR A PARTICULAR PURPOSE IS LIMITED TO THE DURATION OF THE EXPRESS WARRANTY SET FORTH ABOVE Some countries states or provinces do not allow limitations on the duration of an implied warranty so the above limitation or exclusion might not apply to you This warranty gives you specific legal rights and you might also have other rights that vary from country to country state to state or province to province TO THE EXTENT ALLOWED BY LOCAL LAW THE REMEDIES IN THIS WARRANTY STATEMENT ARE YOUR SOLE AND EXCLUSIVE RE
272. ives Ati that is 17 42 12 Example 2 Typing PA2B2 29 gives 5 2 i that is 29 52 22 Returns the value of the nth derivative of the Digamma function at a The Digamma function is the derivative of In I x Example Typing PSI 3 1 14 67 T e P Z gt e hp40g book Page 68 Friday December 9 2005 1 03 AM Psi REORDER SEVAL SIGMA 14 68 gives BRIN ONT Returns the value of the Digamma function at a The Digamma function is defined as the derivative of In T x so we have 5 0 Psi a Example Typing Psi 3 and pressing NUM gives 922 84335098 Reorders the input expression following the order of variables given in the second argument Example Typing REORDER X2 2 X A A2 72 Z AAND X AND Z gives ar OPE SEVAL simplifies the given expression operating on all but the top level operator of the expression Example Typing SEVAL SIN 3 X X SIN X X gives sin 2 x sin 2 x Returns the discrete antiderivative of the input function that is the function G that satisfies the relation G x 1 G x f x It has two arguments the first is a function f x of a variable x given as the second argument Computer Algebra System CAS an NY e hp40g book Page 69 Friday December 9 2005 1
273. ives you an approximate measurement of the area shaded 1 Open the Function aplet The Function aplet opens in the Symbolic view 2 Select the expressions whose curves you want to e study 3 Press to plot the functions 4 Press 4 or gt to position the cursor at the starting point of the area you want to shade Press 6 Press Zaz then select Signed area and press 7 Press fz choose the function that will act as the 8 Press the lt or key to shade in the area Press 85 to calculate the area The area measurement is displayed near the bottom of the screen To remove the shading press to re draw the plot Function aplet 3 11 e NZ SN e hp40g book Page 12 Friday December 9 2005 1 03 AM Plotting a piecewise defined function Suppose you wanted to plot the following piecewise defined function 2 xs l I 1axxl 4 2 1 Open the Function SEE FUNCTION SYMBOLIC ZEE 1 W I j APLET Faim Select Function FocHoa haee pus EDIT CHE s EHHHIIEWmLI 2 Highlight the line you want to use and enter the expression You can press DEL to delete an existing 4 line or SHIFT CLEAR to clear all lines e C El 2 D FUNCTION SYMEOLIC VIEH se VFLCHI CR 2 0082 1 0 B CHARS lt 4F2ORO MB
274. ker 10 16 build your own table 2 19 cobweb 6 1 display defining function for col comparing 2 5 umn 2 17 connected points 10 17 10 19 recalculating 2 19 decimal scaling 2 14 setup 2 16 2 19 defining the independent variable 21 36 O drawing axes 2 7 off 3 3 ie grid points 2 7 c histogram 10 15 cameel 1 in Solve aplet 7 7 integer scaling 2 14 one variable statistics 10 18 overlay plot 2 13 overlaying 2 15 4 3 One Proportion Z Interval 11 17 One Sample T Interval 11 18 One Sample T Test 11 12 One Sample Z Interval 11 15 scaling 2 13 One Sample Z Test 11 8 scatter 10 15 10 17 0 online help 14 8 sequence 2 6 order of precedence 1 21 setting up 2 5 3 2 overlaying plots 2 15 4 3 split screen view 2 14 splitting 2 14 P splitting into plot and close up 138 into plot and table 2 13 PA2B2 14 67 dare ps paired columns 10 11 statistical data 10 15 parametric variables statistics parameters 10 18 axes 21 31 tvalues 2 6 connect 21 31 tickmarks 2 6 grid 21 32 to capture current display 21 21 in menu map R 8 tracing 2 8 indep 21 33 trigonometric scaling 2 14 labels 21 34 two variable statistics 10 18 recenter 21 34 plotting resolution ycross 21 37 and tracing 2 8 parentheses plot view variables to close arguments 1 21 27 94 to specity order of operation 1 21 conmnact 2 1 3 PARTFRAC 14 13 14 57 fastres 21 32 partial derivative 14 16 function 21 31 partial fraction expansion 14 13 grid 2
275. lected or the entire expression if nothing is selected How to type gt and Press to enter X and d dx to enter These symbols and are treated as prefix functions with multiple arguments They are automatically placed before the selected element if there is one hence the term prefix functions You can move the cursor from argument to argument by pressing gt or 4 Enter the expressions according to the rules of selection explained earlier but you must first go into selection mode by pressing Do not use the index i to define a summation because i designates the complex number solution of x 1 0 performs exact calculations if its argument has a discrete primitive otherwise it performs approximate calculations even in exact mode For example in both approximate and exact mode 4 Y 2 70833333334 k 0 whereas in exact mode pola lu 1 1 _ 65 I 2 3 4 24 Note that can symbolically calculate summations of rational fractions and hypergeometric series that allow a discrete primitive For example if you type 4 2 K 1 Equation Writer an Z gt e hp40g book Page 13 Friday December 9 2005 1 03 AM How to enter infix functions How to enter prefix functions Equation Writer select the entire expression and press ENTER YOU obtain 4 5 However if you type K
276. let variables Home variables are used for real numbers complex numbers graphics lists and matrices Home variables keep the same values in HOME and in aplets Aplet variables are those whose values depend on the current aplet The aplet variables are used in programming to emulate the definitions and settings you make when working with aplets interactively You use the Variable menu VARs to retrieve either Home variables or aplet variables See The VARS menu on page 17 4 Not all variables are available in every aplet S1fit S5fit for example are only available in the Statistics aplet Under each variable name is a list of the aplets where the variable can be used Plot view variables Area Contains the last value found by the Area function in Plot e Function FCN menu Axes Turns axes on or off All Aplets From Plot Setup check or uncheck _ AXES or In a program type 1 Axes to turn axes on default 0 gt Axes to turn axes off Connect Draws lines between successively plotted points From Plot Setup check or uncheck _ CONNECT arametric Polar or Solve In a program type 1 gt Connect to connect plotted points default except in Statistics where the default is off 0 gt Connect not to connect plotted points Programming 21 31 e NZ NY Coord Function Parametric Polar Seq
277. ll be shown in the form a bi or in the form of an ordered pair a b If compLex mode is not selected and an operation results in a complex number you will be asked to switch to covprgx mode If you decline the calculator will report an error Default unselected When in cowprgx mode CAS is able to perform a wider range of operations than in non complex or real mode but it will also be considerably slower Thus it is recommended that you don t select coMprgx mode unless requested by the calculator in the performance of a particular operation When is selected certain calculus applications are provided with comment lines in 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 When stepistep is selected certain operations will be shown one step at a time in the display You press to show each step in turn Default selected When incr row is selected polynomials will be listed so that the terms will have increasing powers of the independent variable which is the opposite to how polynomials are normally written Default unselected When ricorous is selected any algebraic expression of the form X i e the absolute value of X is not simplified to X Default selected When simp NON RATIONAL is selected non rational expressions will be automatically simplified Default selected Computer
278. lock programs Each building block program stands alone and it can be called from other programs Note If a program has a space in its name then you have to put quotes around it when you want to run it Programming 21 1 T 5 Y e hp40g book Page 2 Friday December 9 2005 1 03 AM Example RUN GETVALUE RUN CALCULATE RUN SHOW ANSWER This program is separated into three main tasks each an individual program Within each program the task can be simple or it can be divided further into other programs that perform smaller tasks Program catalog The Program catalog is where you create edit delete send receive or run programs This section describes how to open the Program catalog create a new program enter commands from the program commands menu enter functions from the MATH menu edit a program run and debug a program stop a program copy a program send and receive a program delete a program or its contents customize an aplet Open Program 1 Press SHIFT PROGRM Catalog The Program Catalog displays a list of program names The Program Catalog contains a built in entr g 9 called Editline Editline contains the last expression that you entered from the edit line in HOME or the last data you entered in an input form If you press from HOME without entering any data the HP 40gs runs the
279. logistic fit 10 13 display eigenvalues 18 11 loop commands displaying 18 5 BREAK 21 23 displaying matrix elements 18 5 DO UNTIL END 21 23 dividing by a square matrix 18 8 FOR 21 23 dot product 18 11 WHILE REPEAT END 21 23 M loop functions extracting a portion 21 25 TERATE 13 10 trace of a square ma RECURSE 13 11 summation 13 11 inverting nd mus low battery 1 1 matrix calculations 1C multiplying and dividing by scalar lowercase letters 1 6 18 7 multiplying by vector 18 7 M multiplying row by value and add mantissa 13 15 ing result to second row 21 25 math functions multiplying row number by value complex number 13 7 21 25 hyperbolic 13 10 negating elements 18 8 in menu map R 13 R 17 opening Matrix Editor 21 28 keyboard 13 3 raised to a power 18 7 e Na Ne NY 4 P hp40g book Page 8 Friday December 9 2005 1 03 AM redimension 21 24 replacing portion of matrix or vec tor 21 25 sending or receiving 18 4 singular value decomposition 18 13 singular values 18 13 size 18 12 spectral norm 18 13 spectral radius 18 13 start Matrix Editor 21 24 storing elements 18 3 18 5 storing matrix elements 18 6 swap column 21 25 swap row 21 25 transposing 18 13 variables 18 1 matrix functions 18 10 COLNORM 18 10 COND 18 11 N searching 1 9 minimum real number 13 8 mixed fraction format 1 11 modes angle measur
280. lue to a fraction 1 Set the number format mode to Fraction orMixed Fraction 2 Either retrieve the value from the History or enter the value on the command line 3 Press to convert the number to a fraction When converting a decimal to a fraction keep the following points in mind When converting a recurring decimal to a fraction set the fraction precision to about 6 and ensure that you include more than six decimal places in the recurring decimal that you enter In this example the BS RAD Bee FUNCTION Se fraction precision is set 55666666 ara to 6 The top 6666 calculation returns the 2223275004 correct result The bottom one does not To convert an exact decimal to a fraction set the fraction precision to at least two more than the number of decimal places in the decimal Getting started an P hp40g book Page 29 Friday December 9 2005 1 03 AM In this example the fraction precision is set ied to 6 2625 245 Complex numbers Complex results To enter complex numbers Storing complex numbers Getting started The HP 40gs can return a complex number as a result for some math functions A complex number appears as an ordered pair x y where x is the real part and y is the imaginary part For example entering 1 returns 0 1 Enter the number in either of these forms where x
281. lutions appear on the display In the example at the right the solver was able to find solutions for x y and z as soon as the first co efficient of the last equation was entered 8 2 Linear Solver aplet 4 zz gt e hp40g book Page 3 Friday December 9 2005 1 03 AM As you enter each of E LIMERR EQUATION the remaining known Je 907 225 pu lag 214 values the solution Bie uiae ele changes The example w 2 25 z 2 541056 at the right shows the final solution once all the co efficients and constants are entered for the set of equations we set out to solve Linear Solver aplet 8 3 PN 0 X iG e hp40g book Page 4 Friday December 9 2005 1 03 AM T an ad e iG e hp40g book Page 1 Friday December 9 2005 1 03 AM Triangle Solve aplet About the Triangle Solver aplet The Triangle Solver aplet allows you to determine the length of a side of a triangle or the angle at the vertex of a triangle from information you supply about the other lengths and or other angles You need to specify at least three of the six possible values the lengths of the three sides and the size of the three angles before the solver can calculate the other values Moreover
282. m and maximum independent values Polar Appears as the URNG field in the Plot Setup input form From the Plot Setup input form enter values for URNG or In a program type nib Umin n gt Umax where n n Ustep Sets the step size for an independent variable Polar From the Plot Setup input form enter values for USTEP or In a program type nb Ustep where n 0 Programming 21 35 e 21 X iG e hp40g book Page 36 Friday December 9 2005 1 03 AM Tmin Tmax Parametric Tracing All Aplets Tstep Parametric Xcross All Aplets Ycross All Aplets 21 36 Sets the minimum and maximum independent variable values Appears as the TRNG field in the Plot Setup input form From Plot Setup enter values for TRNG or In a program type n b Tmin n gt Tmax where n n Turns the tracing mode on or off in Plot view In a program type 1 gt Tracing to turn Tracing mode on default 0 gt Tracing to turn Tracing mode off Sets the step size for the independent variable From the Plot Setup input form enter values for TSTEP or In a program type nb Tstep where gt 0 Sets the horizontal coordinate of the crosshairs Only works with TRACE off In a program type nb Xcross Sets the vertical coordinate of the crosshairs Only works with TRACE off In a program type nb Ycross Progr
283. mainder from the division of the two polynomials A X and B X divided in decreasing order by exponent Example Typing REMAINDER X 1 X 1 gives x 1 Note that in step by step mode synthetic division is shown with each polynomial represented as the list of its coefficients in descending order of power For n gt 0 TCHEBYCHEFF returns the polynomial T such that 7n x cos n arccos x 4 For n 2 O we have 5 Ee Tx on EDU k 0 For gt 0 we also have 1 x T_ x 2T x n T x 0 For n gt 1 we have ac If n lt TCHEBYCHEFF returns the 2nd species Tchebycheff polynomial sin n arccos x T x sin 14 59 T e P iG e hp40g book Page 60 Friday December 9 2005 1 03 AM Example 1 Typing TCHEBYCHEFF 4 gives 8x 8x 1 Example 2 Typing TCHEBYCHEFF 4 gives 8 4x Real menu CEILING See CEILING on page 13 14 e FLOOR See FLOOR on page 13 14 e FRAC See FRAC on page 13 14 INT See INT on page 13 15 MAX See MAX on page 13 15 MIN See MIN on page 13 15 Rewrite menu All the functions on this menu are also available on the AIA menu in the Equation Writer See REWRI menu on page 14 28 for a description of these functions Solve menu All the functions on this menu are also available
284. mal or numeric but the result is usually in symbolic form not a number You will find the symbols for the symbolic functions and where in the CHARS menu SHIFT CHARS as well as the MATH menu Sets an equality for an equation This is not a logical operator and does not store values See Test functions on page 13 19 expression expression2 Isolates the first occurrence of variable in 0 and returns a new expression where variable newexpression The result is a general solution that represents multiple solutions by including the formal variables S1 to represent any sign and n1 to represent any integer ISOLATE expression variable 13 17 4 4 P hp40g book Page 18 Friday December 9 2005 1 03 AM LINEAR QUAD QUOTE where 13 18 Examples ISOLATE 2 X 8 X returns 4 ISOLATE A B X C X returns A C B Tests whether expression is linear for the specified variable Returns 0 false or 1 true LINEAR expression variable Example LINEAR X 2 1 X 1 X returns 0 Solves quadratic expression 0 for variable and returns a new expression where variable newexpression The result is a general solution that represents both positive and negative solutions by including the formal variable 5 to represent any sign or QUAD expression variable Example QUAD X 1 7 X returns
285. me real number and keyboard functions Enter complex numbers in the form where x is the real part and y is the imaginary part ARG Argument Finds the angle defined by a complex number Inputs and outputs use the current angle format set in Modes ARG x Example ARG 3 3 returns 45 Degrees mode CONJ Complex conjugate Conjugation is the negation sign reversal of the imaginary part of a complex number CONJ x y Example CONJ 3 4 returns 3 4 IM Imaginary part y of a complex number x y IM x Using mathematical functions 13 7 e NZ NY RE Constants MAXREAL MINREAL Conversions e hp40g book Page 8 Friday December 9 2005 1 03 AM Example IM 3 4 returns 4 Real part x of a complex number x y RE x y Example RE 3 4 returns 3 The constants available from the MATH FUNCTIONS menu are mathematical constants These are described in this section The HP 40gs has two other menus of constants program constants and physical constants These are described in Program constants and physical constants on page 13 24 Natural logarithm base Internally represented as 2 71828182846 Imaginary value for 1 the complex number 0 1 Maximum real number Internally represented as 9 99999999999 x 10477 MAXREAL Minimum real number
286. mple POLYFORM X 1 2 1 returns 2 2 2 POLYROOT Polynomial roots Returns the roots for the nth order polynomial with the specified 1 coefficients POLYROOT coefficients Example For x4 2x3 25x7 26x 120 POLYROOT 1 2 25 26 120 returns 2 3 4 5 e HINT The results of POLYROOT will often not be easily seen in e HOME due to the number of decimal places especially if they are complex numbers It is better to store the results of POLYROOT to a matrix For example POLYROOT 1 0 0 8 BW M1 will store the three complex cube roots of 8 to matrix M1 as a complex vector Then you can see them easily by going to the Matrix Catalog and access them individually in calculations by referring to M1 1 M1 2 etc Probability functions COMB Number of combinations without regard to order of n things taken rata time n r n r COMB n r Example COMB 5 2 returns 10 That is there are ten different ways that five things can be combined two at a time 13 12 Using mathematical functions 4 NY 4 P hp40g book Page 13 Friday December 9 2005 1 03 AM PERM RANDOM HINT UTPC UTPF UTPN Using mathematical functions Factorial of a positive integer For non integers T x 1 This calculates the gamma function value Number of permutations with regard to order of n things t
287. n a variable of this kind must have a name like S1 S5 51 55 nl n5 but not X which is assigned to a real value By default X is assigned to O To store symbolic expressions you must use the variables EO E1 E9 In the Equation Writer all the variables may or may not be assigned For example X is not assigned to a real value by default so computing X X will return 2X Moreover Equation Writer variables can have long names like XY or ABC unlike in HOME where implied multiplication is assumed For example ABC is interpreted as A x B x C in HOME For these reasons variables used in the Equation Writer cannot be used in HOME and vice versa Using the PUSH command you can transfer expressions from the HOME screen history to CAS history see page 14 8 Likewise you can use the POP command to transfer expressions from CAS history to the HOME screen history see page 14 8 The current variable 14 4 In the Equation Writer the current variable is the name of the symbolic variable contained in VX It is almost always X The current variable is always S1 in HOME Some CAS functions depend on a current variable for example the function DERVX calculates the derivative with respect to the current variable Hence in the Equation Writer DERVX 2 X Y returns 2 if VX X but 1 if VX Y However in the HOME screen DERVX 2 S1 S2 returns 2 but DERIV 2 S1 S2 S2 returns 1 Computer Algebra System CAS
288. n Note view NoteText Use NoteText to recall text previously entered in Note All Aplets view Sketch variables The following aplet variables are available in Sketch view Page Sets a page in a sketch set The graphics can be viewed All Aplets one at a time using the FE and keys The Page variable refers to the currently displayed page 4 of a sketch set In a program type graphicname gt Page PageNum Sets a number for referring to a particular page of the All Aplets sketch set in Sketch view In a program type the page that is shown when SHIFT SKETCH is pressed gt PageNum Programming 21 43 4 X iG e hp40g book Page 44 Friday December 9 2005 1 03 AM T an ad e iG e hp40g book Page 1 Friday December 9 2005 1 03 AM 22 Extending aplets Aplets are the application environments where you explore different classes of mathematical operations You can extend the capability of the HP 40gs in the following ways Create new aplets based on existing aplets with specific configurations such as angle measure graphical or tabular settings and annotations Transmit aplets between HP 40gs calculators via a serial or USB cable Download e lessons teaching aplets from Hewlett Packard s Calculator web site Program new apl
289. n access the on line help in Numeric view Display a graphic view of the test results PLOT FE Z 1 644854 CRIT Z Horizontal axes are Test 2 5 presented for both the 1 n distribution variable and the test statistic A generic bell curve represents the probability distribution function Vertical lines mark the critical value s of the test as well as the value of the test statistic The rejection region is marked lt and the test numeric results are displayed between the horizontal axes Importing sample statistics from the Statistics aplet The Inference aplet supports the calculation of confidence intervals and the testing of hypotheses based on data in the Statistics aplet Computed statistics for a sample of data in a column in any Statistics based aplet can be imported for use in the Inference aplet The following example illustrates the process Inference aplet an Y e hp40g book Page 5 Friday December 9 2005 1 03 AM Open the Statistics aplet Enter data HINT Calculate statistics Inference aplet A calculator produces the following 6 random numbers 0 529 0 295 0 952 0 259 0 925 and 0 592 l If the Decimal Mark setting in the Modes input form SHIFT modes is set to Comma use instead of 3 Open the Statistics aplet and reset
290. n of the equation Therefore the solution was not a real number or it caused an error Constant The value of the equation is the same at every point sampled HINT _ It is important to check the information relating to the solve process For example the solution that the Solve aplet finds is not a solution but the closest that the function gets to zero Only by checking the information will you know that this is the case The Root Finder Youcon watch the process of the rootfinder calculating at work and searching for a root Immediately after pressing to start the rootfinder press any key except ON m You will see two intermediate guesses and to the left the sign of the expression evaluated at each guess For example 2 2 219330555745 1 21 31111111149 You can watch os the rootfinder either finds a sign reversal or converges on a local extrema or does not converge at all If there is no convergence in process you might want to cancel the operation press ON and start over with a different initial guess Plotting to find guesses The main reason for plotting in the Solve aplet is to help you find initial guesses and solutions for those equations that have difficult to tind or multiple solutions Consider the equation of motion for an accelerating body 2 X V T Solve aplet 7 7 e e SZ gt e hp40g book Page 8 Fr
291. n real mode x V2 OR x N2 and in complex mode x V2 i OR x N2 OR x N2 i OR x V2 Computer Algebra System CAS am ad T NY 4 LDEC LINSOLVE Computer Algebra System CAS hp40g book Page 35 Friday December 9 2005 1 03 AM Linear differential equations having constant coefficients LDEC enables you to directly solve linear differential equations having constant coefficients The parameters are the second member and the characteristic equation Solve E Typing LDEC X EXP 3 X X 6 X49 gives 3 exp 3 x cCO and cC1 are integration constants y 0 cCO and y 0 1 Solve linear system LINSOLVE enables you to solve a system of linear equations It is assumed that the various equations are of the form expression O LINSOLVE has two arguments the first members of the various equations separated by AND and the names of the various variables separated by AND Example 1 Typing LINSOLVE X 3 AND X Y 1 X AND Y gives x 2 AND y 1 or in Step by step mode CFG etc 12 L2 L1 113 1 11 14 35 T e X iG e hp40g book Page 36 Friday December 9 2005 1 03 AM L1 2L1 L2 1 0 2 2 ENTER Reduction Result 7 0 0 2 2 then
292. nce for a selected hypothesis against the null hypothesis The null hypothesis is that the sample mean has some assumed value Ho H po You select one of the following alternative hypotheses against which to test the null hypothesis H H lt uo 7 uo Hi uz o Inference aplet am a T NY Inputs Results Inference aplet e hp40g book Page 13 Friday December 9 2005 1 03 AM The inputs are Field name Definition z SX n LO Ol Sample mean Sample standard deviation Sample size Hypothetical population mean Significance level The results are Result Description Test T T Test statistic Prob Probability associated with the T Test statistic Critical T Boundary value of T associated with the level that you supplied Citical s Boundary value of x required by the a value that you supplied am ad 11 13 T e hp40g book Page 14 Friday December 9 2005 1 03 AM e NY Two Sample T Test Menu name T Test ul u2 The Two sample T Test is used when the population standard deviation is not known On the basis of statistics from two samples each sample from a different population this test measures the strength of the evidence tor a selected hypothesis against th
293. nd DIFF SV Example This example aplet is designed to demonstrate the process of customizing an aplet The new aplet is based on the Function aplet Note This aplet is not intended to serve a serious use merely fo illustrate the process 21 10 Programming e hp40g book Page 11 Save the aplet Configuring the Setviews menu option programs Programming Friday December 9 2005 1 1 03 AM Open the Function qplet and save it os EXPERIMENT The new aplet appears in the Aplet library Select Function Create a program called EXP ME1 with contents as shown This program configures the plot ranges then runs a program that allows HPLET LIERARY BEBE Funct 1 RB Inference BKE Parametric BKE Folar HEB IEESETI SORT ISEHD S TART 1 PROGRAM la bsmin LAR Amex ebimin BR max RUM ETUR SPACE 1 ne TER SP you to set the angle format Create a program called EXP ME2 with contents as shown This program sets the numeric view options for the aplet and runs the program that you can mode Create a program called EXPANG which the previous two programs call Create a program called EXP S which runs when you start the aplet as shown This program sets the angle mode to degrees and
294. nd cos SINCOS takes an expression containing complex exponentials as an argument SINCOS then rewrites this expression in terms of sin x and cos x Typing SINCOS EXE QL X gives after turning on complex mode if necessary cos x i gt sin x Transform tan x with sin 2x and cos 2x TAN2CS2 has a trigonometric expression as an argument Computer Algebra System CAS am ad T NY TAN2SC e TAN2SC2 TCOLLECT Computer Algebra System CAS e e hp40g book Page 41 Friday December 9 2005 1 03 AM TAN2CS2 transforms this expression by replacing tan x 1 cos 2 x with sin 2 x Typing TAN2CS2 TAN X gives 1 cos 2 x sin 2 x Replace tan x with sin x cos x TAN2SC has a trigonometric expression as an argument TAN2SC transforms this expression by replacing tan x with 5260 cos x Typing TAN2SC TAN X gives sin x cos x Transform tan x with sin 2x and cos 2x TAN2SC2 has a trigonometric expression as an argument TAN2SC2 transforms this expression by replacing tan x sin 2 x 1 cos 2 x with Typing TAN2SC2 TAN X gives sin 2 x 1 cos 2 x Reconstruct the sine and the cosine of same angle TCOLLECT has a trigonometric expression as an argument 14 4 T e P NY
295. negative number To enter 25 press 25 Note this is not the same operation that the subtract button performs Enters the independent variable by inserting X T 0 or N into the edit line depending on the current active aplet DEL Deletes the character under the cursor Acts as a backspace key if the cursor is at the end of the line CLEAR Clears all data on the screen On a settings screen for example Plot Setup CLEAR returns all settings to their default values gt Moves the cursor around the display Press first to move to the beginning end top or bottom _ Getting started 1 5 e 0 SZ gt e hp40g book Page 6 Friday December 9 2005 Shifted keystrokes 1 03 AM Key Meaning Continued CHARS Displays a menu of all available characters To type one use the arrow keys to highlight it and press Ha To select multiple characters select each and press Ham then press HH There are two shift keys that you use to access the operations and characters printed above the keys and ALPHA Key Description ALPHA Press the key to access the operations printed in blue above the keys For instance to access the Modes screen press SHIFT then press HOME MODES is labeled blue above the key You do not nee
296. ng a dataset comprising two variables advertising minutes and resulting sales Enter data 3 Enter the data into the columns 2 ENTER 1 ENTER 3 ENTER 5 ENTER 5 ENTER 4 ENTER ET ELE IEHEFT EIG gt jo move to the next column 1400 920 1100 2265 2890 2200 10 2 Statistics aplet e 0 Y e hp40g book Page 3 Friday December 9 2005 1 03 AM Choose fit and 4 Select a fit in the Symbolic setup view data columns SETUP SYMB SERESTATISTICS S MEOLIC SETUP SEE A LES jee Linear Ly POH CS saFIT L 1rvear 1r18 ar7 Select Linear SSFIT Linear CHOOSE STATISTICS MODEL TYPE hm You can create up to five explorations of two variable data named S1 to S5 In this example we will create just one S1 5 Specify the columns that hold the data you want to analyze SYMB SES STATISTICS VIEH See 451 C2 You could have entered 1 mxE b your data into columns Fit2 m b other than C1 and C2 ENTER INDEPENDENT EDIT Jw CHE Explore statistics 6 Find the mean advertising time MEANX and the O mean sales MEANY 4 NUM a vak S1 aen 3 MEANX is 3 3 minutes RW m and MEANY is about fva aa Byags 796 3 33333333333 7 Scroll down to dis
297. ng aid for the column variables or for the Fit expressions 8 10 8 Statistics aplet gt 9 zz gt e hp40g book Page 9 Friday December 9 2005 1 03 AM Meaning Continued Displays the current variable expression in standard mathematical form Press BIB when done Evaluates the variables in the highlighted column C1 etc expression Displays the menu for entering variable names or contents of variables MATH Displays the menu for entering math operations DEL Deletes the highlighted variable or the current character in the edit line CLEAR Resets default specifications for the data sets or clears the edit line if it e was active Note If SHIFT CLEAR is used the data sets will need to be selected again before re use To continue our example suppose that the heights of the rest of the students in the class are measured but each one is rounded to the nearest of the five values first recorded Instead of entering all the new data in C1 we shall simply add another column c2 that holds the frequencies of our five data points in C1 Statistics aplet 10 9 e NZ Z gt e hp40g book Page 10 Friday December 9 2005 1 03 AM 9 SRS STATISTICS SYMBOLIC 5 into the right column of
298. ng and splitting the graph on page 2 13 Divides horizontal and vertical scales by the X factor and Y factor For instance if zoom factors are 4 then zooming in results in 1 4 as many units depicted per pixel see Set Factors Out Multiplies horizontal and vertical scales by the X factor and Y factor see Set Factors X Zoom In Divides horizontal scale only using X factor X Zoom Out Multiplies horizontal scale using X factor Aplets and their views 2 9 e NZ e PN hp40g book Page 10 Friday December 9 2005 1 03 AM NY Option Meaning Continued Y Zoom In Divides vertical scale only using Y factor Y Zoom Out Multiplies vertical scale only using Y factor Square Changes the vertical scale to match the horizontal scale Use this after doing a Box Zoom X Zoom or Y Zoom Set Sets the X Zoom and Y Zoom factors Factors for zooming in or zooming out Includes option to recenter the plot before zooming Auto Scale Rescales the vertical axis so that the display shows a representative piece of the plot for the supplied x axis settings For Sequence and Statistics aplets autoscaling e rescales both axes The autoscale process uses the first selected function only to determine the best scale to use Decimal Rescales both axes so each pixel 0 1 units Resets
299. nline help about any CAS command To display the contents of the online help press 2 Press v to navigate to the command yOU want help Euren with and then press gd cH gt AND As 2 A 2 Id MAD EEE ICHIHFEM ECHO EE1 SS CAS HELP OM Chinese remainder far You can also get CAS help Bee from the HOME screen Type Computer Algebra System CAS 4 4 P hp40g book Page 9 Friday December 9 2005 1 03 AM TIP CAS functions NOTE Computer Algebra System CAS HELP and press enter The menu of help topics appears Each help topic includes the required syntax along with real sample values You can copy the syntax with the sample values to the HOME screen or to the Equation Writer by pressing IaH If you highlight a CAS command and then press 2 help about the highlighted command is displayed You can display the online help in French rather than English For instructions see Online Help language on page 15 4 in the Equation Writer You can display a menu of CAS functions in four ways by displaying the MATH menu from HOME and then pressing pt Or opening the Equation Writer and pressing MATH eN opening the Equation Writer and selecting a function from a soft key menu or opening the Equation Writer and pressing
300. ns For example these can be sub programs that menu 21 14 Programming T a PN NZ Z gt e hp40g book Page 15 Friday December 9 2005 1 03 AM options use or the program that defines the aplet s VIEWS menu You can include a Start option in the VIEWS menu to specify a program that you want to run automatically when the aplet starts This program typically sets up the aplet s initial configuration The START option on the menu is also useful for resetting the aplet Command syntax The syntax for the command is as follows SETVIEWS Prompt ProgramName 1 ViewNumber1 Prompt2 ProgramName2 ViewNumber2 You can repeat as many Prompt ProgramName ViewNumber trios of arguments as you like Within each Prompt ProgramName ViewNumber trio you separate each item with a semi colon Prompt PNI Prompt is the text that is displayed for the corresponding 4e entry in the Views menu Enclose the prompt text in double quotes Associating programs with your aplet IF Prompt consists of a single space then no entry appears in the view menu The program specified in the ProgramName item is associated with the aplet and transferred whenever the aplet is transmitted Typically you do this if you want to transfer the Setviews program with the aplet or you want to transfer a sub program that other menu programs use Auto run pr
301. ns is different from the numbers in HOME s display history A value in Ans is stored internally with the full precision of the calculated result whereas the displayed numbers match the display mode 1 23 e NZ Z e hp40g book Page 24 Friday December 9 2005 1 03 AM HINT When you retrieve a number from ans you obtain the result to its full precision When you retrieve a number from the HOME s display history you obtain exactly what was displayed Pressing evaluates or re evaluates the last input whereas pressing ANS copies the last result as Ans into the edit line Storing a value You can save an answer in a variable and use the in a variable variable in later calculations There are 27 variables available for storing real values These are A to Z and 0 See Chapter 17 Variables and memory management for more information on variables For example 1 Perform a calculation 45 8 3 45 8 8 2 Store the result in the A variable An kA 3 5 2 ALPHA A e 1 24 Getting started e 0 GIN e hp40g book Page 25 Friday December 9 2005 1 03 AM Accessing the Pressing enables the highlight bar in the display display history history While the highlight bar is active the following menu and keyboard keys are very useful
302. nt has been tested and found to comply with the limits for a Class B digital device pursuant to Part 15 of the FCC Rules These limits are designed to provide reasonable protection against harmful interference in a residential installation This equipment generates uses and can radiate radio frequency energy and if not installed and used in accordance with the instructions may cause harmful interference to radio communications However there is no guarantee that interference will not occur in a particular installation If this equipment does cause harmful interference to radio or television reception which can be determined by turning the equipment off and on the user is encouraged to try to correct the interference by one or more of the following measures Reorient or relocate the receiving antenna Increase the separation between the equipment and the receiver Connect the equipment into an outlet on a circuit different from that to which the receiver is connected Consult the dealer or an experienced radio or television technician for help The FCC requires the user to be notified that any changes or modifications made to this device that are not expressly approved by Hewlett Packard Company may void the user s authority to operate the equipment Connections to this device must be made with shielded cables with metallic RFI EMI connector hoods to maintain compliance with FCC rules and regulations This dev
303. nter to turn recenter on default 0 gt Recenter to turn recenter off Contains the last value found by the Root function in the PlotFCN menu Sets the mark to use for scatter plots From Plot Setup for two variable statistics Slmark S5mark then choose a mark or In a program type n gt Slmark where n is 1 2 3 5 Enables you to choose types of sequence plot Stairstep or Cobweb From Plot Setup select SeqPlot then choose Stairstep or Cobweb or In a program type 1 gt SeqPlot for Stairstep 2 gt SeqPlot for Cobweb Programming am ad T X iG e hp40g book Page 35 Friday December 9 2005 1 03 AM Simult Enables you to choose between simultaneous and Function sequential graphing of all selected expressions Parametric From Plot Setup check or uncheck _STMULT Polar Sequence er In a program type 1 gt Simult for simultaneous graphing default 0 gt Simult for sequential graphing Slope Contains the last value found by the Slope function in the Function Plot FCN menu StatPlot Enables you to choose types of 1 variable statistics plot Statistics between Histogram or Box and Whisker From Plot Setup select Stat Plot then choose Histogram or BoxWhisker or In a program type 1 gt StatPlot for Histogram 2 gt StatPlot for Box and Whisker Umin Umax Sets the minimu
304. nts in list IILIST list Example IILIST 2 3 4 returns 24 POS Returns the position of an element within a list The element can be a value a variable or an expression If there is more than one instance of the element the position of the first occurrence is returned A value of O is returned if there is no occurrence of the specitied element POS list element Example POS 3 7 12 19 12 returns 3 REVERSE Creates a list by reversing the order of the elements in a list REVERSE list 19 8 Lists n adii SIZE gt LIST SORT e hp40g book Page 9 Friday December 9 2005 1 03 AM Calculates the number of elements in a list SIZE list Also works with matrices Calculates the sum of all elements in list EELIST list Example XLIST 2 3 4 returns 9 Sorts elements in ascending order SORT list Finding statistical values for list elements Example Lists 2 In HOME store Ll into To find values such as the mean median maximum and minimum values of the elements in a list use the Statistics aplet In this example use the Statistics aplet to find the mean 4 median maximum and minimum values of elements in the list L1 1 Create L1 with values 88 90 89 65 70 and 89 sHiFT 88 L 90 L ALPHA L1 B JH B3 53 70 99 11 CA K OB
305. ocedure If the calculator still does not turn on please contact Customer Support for further information 1 Press and hold the ON key for 10 seconds 2 Press and hold the ON key and the third menu key simultaneously Release the third menu key then release the ON key Press and hold the ON key the first menu key and the sixth menu key simultaneously Release the sixth menu key then release the first menu key and then release the ON key 4 Locate the small hole in the back of the calculator Insert the end of a straightened metal paper clip into the hole as far as it will go Hold it there for 1 second then remove it Press the ON key 5 Remove the batteries see Batteries on page R 4 dX press and hold the ON key for 10 seconds and then put the batteries back in Press the ON key Operating details Batteries Operating temperature 0 to 45 32 to 113 F Storage temperature 20 to 65 C 4 to 149 F Operating and storage humidity 9075 relative humidity at 40 C 104 F maximum Avoid getting the calculator wet Battery operates at 6 0V dc 80mA maximum The calculator uses 4 AAA LRO3 batteries as main power and a CR2032 lithium battery for memory backup Before using the calculator please install the batteries according to the following procedure 4 42 e hp40g book Page 5 Friday December 9 2005 1 03 AM To install
306. ogramming Sets the width of histogram bars From Plot Setup 1 VAR stats set a value for Hwidth or In a program type n b Hwidth Defines the value of the independent variable used in tracing mode In a program type nb Indep Toggles between solid crosshairs or inverted crosshairs Inverted is useful if the background is solid From Plot Setup check or uncheck _ nyCross or In a program type 1 gt InvCross to invert the crosshairs 0 gt InvCross for solid crosshairs default Contains the last value found by the Intersection function in the PlotFCN menu Draws labels in Plot view showing X and Y ranges From Plot Setup check or uncheck _ Labels or In a program type 1 piabe1s lo turn labels 0 ptabe1s lo turn labels off default 21 33 am ad T 4 P hp40g book Page 34 Friday December 9 2005 1 03 AM Nmin Nmax Sequence Recenter All Aplets Root Function S1mark S5mark Statistics SeqPlot Sequence 21 34 Defines the minimum and maximum independent variable values Appears as the NRNG fields in the Plot Setup input form From Plot Setup enter values for NRNG or In a program type Nmin n Nmax where n n Recenters at the crosshairs locations when zooming From Plot Zoom Set Factors check or uncheck __ Recenter or In a program type 1 gt Rece
307. ograms If the Prompt item is Start then the ProgramName program runs whenever you start the aplet This is useful for setting up a program to configure the aplet Users can select the Start item from the VIEWS menu to reset the aplet if they change configurations You can also define a menu item called Reset which is view Programming 21 15 e NZ NY hp40g book Page 16 Friday December 9 2005 1 03 AM ProgramName ProgramName is the name of the program that runs when the corresponding menu entry is selected All programs that are identified in the aplet s SETVIEWS command are transferred when the aplet is transmitted ViewNumber ViewNumber is the number of a view to start after the program finishes running For example if you want the menu option to display the Plot view when the associated program finishes you would specify 1 as the ViewNumber value Including standard menu options To include one of an aplet s standard VIEWS menu options in your customized menu set up the arguments trio as follows The first argument specifies the menu item name Leave the argument empty to use the standard Views menu name for the item or Enter a menu item name to replace the standard name The second argument specifies the program to run Leave the argument empty to run the standard menu option Inserta
308. om a CAS soft menu but you can select it from from CAS FUNCTIONS menu while you are in the Equation Writer by pressing MATH choosing the INTEGER menu and scrolling to 1S PRIME function To prove that b 1999 is a prime number it is necessary to show that 1999 is not divisible by any of the prime numbers less than or equal to 1999 As 1999 lt 2025 45 that means testing the divisibility of 1999 by n 2 3 5 7 11 13 17 19 23 29 31 37 41 1999 is not divisible by any of these numbers so we can conclude that 1999 is prime Step by Step Examples 4 Z gt e hp40g book Page 11 Friday December 9 2005 1 03 AM Now consider the product of two of the definitions entered above B N x C N ALPHA B ALPHA N gt J x C 0 ALPHA N ENTER 4EXFTNLNC16T 1 Press Hl v v v to select EXP2POW and press iis P2POH 4HEXP NLHCLaD Press to evaluate the expression yielding the result of B N x C N Consider now the decomposition of A 6 into its prime factors P Press tia v WP to select FACTOR and press e Bm FACTOR ACE 3 Now press ALPHA 6 Finally press to get the result The factors are listed separated by a medial period In this case the factors are 3 23 29 and 1999 Now let s consider whether b and c are relatively prime Here the calc
309. or the missing St TRIANGLES MUMERIC VIEH value amp 33 5 The length of the ladder Erm orn mn EN 7 73 7T is approximately 8 72 metres Resetting an aplet Resetting an aplet clears all data and resets all default settings To reset an aplet open the Library select the aplet and press BESETE You can only reset an aplet that is based on a built in aplet if the programmer who created it has provided a Reset option Extending aplets 22 3 e NZ ZN NY e hp40g book Page 4 Friday December 9 2005 1 03 AM Annotating an aplet with notes The Note view NOTE attaches a note to the current aplet See Chapter 20 Notes and sketches Annotating an aplet with sketches HINT The Sketch view SHIFT SKETCH attaches a picture to the current aplet See chapter 20 Notes and sketches Notes and sketches that you attach to an aplet become part of the aplet When you transfer the aplet to another calculator the associated note and sketch are transferred as well Downloading e lessons from the web In addition to the standard aplets that come with the calculator you can download aplets from the world wide web For example Hewlett Packard s Calculators web site contains aplets that demonstrate certain mathematical concepts Note that you need the Graphing Calculator Connectivity Kit in order to load aplets from a PC
310. orm SOLV menu The menu contains functions that enable you to solve equations linear LBEE systems and differential LIHSOLVE equations TRIG menu The menu contains functions that enable you to transform trigonometric expressions NOTE You can get online help about any CAS function by pressing 2 and selecting that function as explained in Online Help on page 14 8 0 Configuration menus La You can directly see and change CAS modes while working with the Equation Writer The first line in each of the Equation Writer menus except indicates the current CAS mode settings In the example at the right the first line of the menu reads CFG R X S CFG stands for configuration and the symbols to the right of it indicate various mode settings CANEL OK first symbol R indicates that you are in real mode If you were in complex mode this symbol would be C The second symbol indicates that you are in exact mode If you were in approximate mode this symbol would be The third symbol x in the above example indicates the current independent variable Equation Writer 15 3 e 0 Online Help language NOTE e hp40g book Page 4 Friday December 9 2005 1 03 AM The fourth symbol s in the above example indicates that you are in step by step mod
311. ory takes by default the value of X This is the name of the preferred independent variable for algebraic and calculus applications If you use another independent variable name some functions for example HORNER will not work properly Selecting the The option on CAS MODES screen lets you modulus specify the modulo you want to use in modular arithmetic The default value is 13 Approximate vs When the approx mode is selected symbolic operations Exact mode for example definite integrals square roots etc will be calculated numerically When this mode is unselected exact mode is active hence symbolic operations will be e Computer Algebra System CAS 14 5 an 4 hp40g book Page 6 Friday December 9 2005 1 03 AM Num Factor mode Complex vs Real mode Verbose vs non verbose mode Step by step mode Increasing powers mode Rigorous setting Simplify non rational setting 14 6 calculated as closed form algebraic expressions whenever possible Default unselected When the num rAcron setting is selected approximate roots are used when factoring For example x 5x 1 is irreducible over the integers but has approximate roots over the reals With numractor set the approximate roots are returned Default unselected When comptex is selected and an operation results in a complex number the result wi
312. osine 13 4 inverse hyperbolic 13 9 cotangent 13 20 covariance statistical 10 15 creating aplet 22 1 lists 19 1 matrices 18 2 notes in Notepad 20 6 programs 21 4 sketches 20 3 critical value s displayed 11 4 cross product vector 18 11 curve fitting 10 12 10 17 CYCLOTOMIC 14 63 D data set definition 10 8 date setting 21 27 debugging programs 21 7 decimal changing format 1 10 scaling 2 14 2 15 decreasing display contrast 1 2 DEF 14 10 definite integral 13 6 deleting aplet 22 6 lists 19 6 matrices 18 4 programs 21 9 statistical data 10 11 delimiters programming 21 1 DERIV 14 16 derivative 14 16 derivatives definition of 13 6 in Function aplet 13 22 in Home 13 21 DERVX 14 16 DESOLVE 14 33 determinant square matrix 18 1 1 DIFF menu 14 16 differential equations 14 33 14 35 14 57 hp40g book Page 3 Friday December 9 2005 1 03 AM an ad differentiation 13 6 14 33 digamma function 14 67 14 68 display 21 21 adjusting contrast 1 2 annunciator line 1 2 capture 21 21 clearing 1 2 date and time 21 27 element 18 5 elements 19 4 engineering 1 10 fixed 1 10 fraction 1 10 history 1 22 line 1 23 matrices 18 5 parts of 1 2 printing contents 21 25 rescaling 2 13 scientific 1 10 scrolling through history 1 25 soft key labels 1 2 standard 1 10 DISTRIB 14 28 distributivity 14 12 14 28 14 30 divide 13 4 DIVIS 14 47 DIVMOD 14 52 DIVPC 14 17 drawing circles 20 4 keys 20 4 line
313. over the whole screen The Plot Table view gives you two simultaneous views of the plot 1 Press VIEWS Select Plot Table and press BIB The screen pl 395167 displays the plot on the EEEH left side and a table of numbers on the right side 2 To move up and down the table use the 4 and gt cursor keys These keys move the tra ce point left or right along the plot and in the table the corresponding values are highlighted 3 To move between functions use the and v cursor keys to move the cursor from one graph to another 4 To return to a full Numeric or Plot view press NUM or PLOT If you want to plot over an existing plot without erasing that plot then use Overlay Plot instead of PLOT Note that tracing follows only the current functions from the current aplet Decimal scaling is the default scaling If you have changed the scaling to Trig or Integer you can change it back with Decimal Integer scaling compresses the axes so that each pixel is 1 x 1 and the origin is near the screen center Use trigonometric scaling whenever you are plotting an expression that includes trigonometric functions Trigonometric plots are more likely to intersect the axis at points factored by 2 15 an Z e hp40g book Page 16 Friday December 9 2005 1 03 AM About the numeric view After entering and select
314. owever if you use special characters and then run the program by typing it in HOME you must enclose the program name in double quotes Don t use the symbol within your program name 3 Type your program PROGRAM name then press uic When you press i MPROG 9 we Editor fez CCL ok lt 4 Enter your program When done start any other activity Your work is saved automatically Entercommands Until you become familiar with the HP 40gs commands the easiest way to enter commands is to select them from the Commands menu from the Program editor You can also type in commands using alpha characters 1 From the Program editor press SHIFT CMDS to open the Program Commands menu SHIFT CMDS SESS PRIGEREA COMMANDS ESSE CHECK SELECT SETVIEHS Graphic w UHCHECK InNLLOE 21 4 Programming gt 9 zz gt e hp40g book Page 5 Friday December 9 2005 1 03 AM 2 On the left use v or to highlight a command category then press gt to access the commands the category Select the command that you want w v gt v PROGRAM COMMANDS SERRE HP let Branch ERASE Graphic w FEEEZE ok H PEDG PROGRAM Box STO ES
315. p40g book Page 22 Friday December 9 2005 1 03 AM T an ad e 4 hp40g book Page 1 Friday December 9 2005 1 03 AM 16 Step by Step Examples Introduction Example 1 Step by Step Examples This chapter illustrates the power of CAS and the Equation Writer by working though a number of examples Some of these examples are variations on questions from senior math examination papers The examples are given in order of increasing difficulty If A is 1 NIU 1 1 calculate the result of A in the form of an irreducible fraction showing each step of the calculation Solution In the Equation Writer enter A by typing e 3 620 CJ 1 9 gt GJ 1 3 2 1 Now press gt to select the denominator as shown above Press ENTER to simplify the denominator Now select the numerator by pressing 4 16 1 an STA Example 2 16 2 e hp40g book Page 2 Friday December 9 2005 1 03 AM Press to simplify the numerator Press a to select the entire fraction Press to simplify the selected fraction giving the result shown at the right Given that C 24 45 3 12 20 6 3 write C in the form d 5 where
316. ph will be of Parametric type To summarize If you choose Function Aplet the highlighted expression is copied into the chosen function Fi and the current variable is changed to X the Parametric Aplet the real part and the imaginary part of the highlighted expression are copied into the chosen functions Xi Yi and the current variable is changed to T Polar Aplet the highlighted expression is copied into the chosen function Ri and the current variable is changed to 0 Pressing NUM in the Equation Writer causes the highlighted expression to be replaced by a numeric approximation puts the calculator into approximate mode Pressing NUM in the Equation Writer causes the highlighted expression to be replaced by a rational number NUM puts the calculator into exact mode Pressing in the Equation Writer enables you to move the cursor with the gt and 4 arrow keys to see the entire highlighted expression Press gis return in the Equation Writer Equation Writer an NZ DS e hp40g book Page 21 Friday December 9 2005 1 03 AM Short cut keys In the Equation Writer the following are short cut keys to the symbols indicated SHIFT 0 for 1 for i SHIFT 3 for x SHIFT 5 for lt 6 for gt 8 for lt 9 for gt e am S SZ X iG e h
317. play the input form for setting the aplet s plot settings Angle measure is controlled using the MODES view Plot Setup Numeric Setup Symbolic Setup Press SETUP PLOT Sets parameters to plot a graph Press SETUP NUM Sets parameters for building a table of numeric values This view is only available in the Statistics aplet in mode where it plays an important role in choosing data models Press SHIFT SETUP SYMB GIVER A 1 AWD D ld s FIND THE VALUE OF B E AAD FUMCTIOM PLOT SETUP Esci TRNG 12655 7 95 1 YTICK 1 RES Faster EDITT _ EE FUNCTION MUMERIC SETUP ENTER MINIMUM HORIZONTAL VALUE PhSE MUMSTART MUMSTEP 1 MUHTYPE Automatic 200 4 ENTER STARTING VALUE FOR TRELE EWT jlPLmnTkl ZEN STATISTICS SYMEOLIC SETUP ANGLE MEASURE s1FIT L i near s FIT L i near s5FIT L innear CHOOSE ANGLE MEASURE HH _ sgFIT L 1 near sHFIT L i near Getting started an Z gt e hp40g book Page 19 Friday December 9 2005 1 03 AM To change views To save aplet configuration Each view is a separate environment To change a view select a different view by pressing NUM keys or select a view from the VIEWS menu To change to HOME press HOME You do not explicitly close the current view you just enter
318. play the value for the correlation coefficient CORR The CORR value indicates how well the linear model fits the data 9 times geddBz285 41545 The value is 8995 y DR CORR ELD Dm 699530930561 O Statistics aplet 10 3 PN N 4 hp40g book Page 4 Friday December 9 2005 1 03 AM Setup plot 8 Change the plotting range to ensure all the data points are plotted and select a different point mark if you wish SHIFT SETUP PLOT SENZ STATISTICS PLOT SETUP 2 YENG 166 o 7 S1MBRE EE 3MhRKE SUMARE so SSMARK I 100 CHOOSE FOR SCATTER PLOT CHOOS PHGE 4000 Plot fhe graph 9 Plot the graph FLE 11 8 1400 Draw the 10 Draw the regression curve a curve to fit the data regression curve points HEHU This draws the regression line for the ETRE EEE best linear fit Display the 11 Return to the Symbolic view equation for SEE STATISTICS SVYMEOLIC ZEE linear fit SYMB Hl est TI b dz5 8r5 H 3T6 Fite meX b Ent 12 Display the equation for the best linear fit to move to the FTT1 field 425 875448376 25 wt The full FIT1 Tm exp
319. plet For example if in the Function aplet you define F1 X X 10 you can enter F1 X 50 in the Solve aplet to solve the equation 2 10 50 Solve aplet 4 GIN e hp40g book Page 1 Friday December 9 2005 1 03 AM Linear Solver aplet About the Linear Solver aplet The Linear Solver aplet allows you to solve a set of linear equations The set can contain two or three linear equations In a two equation set each equation must be in the form ax by k In a three equation set each equation must in the form k You provide values for a b and k and c in three equation sets for each equation and the Linear Solver aplet will attempt to solve for x and y and z in three equation sets te The hp40gs will alert you if no solution can be found or if there is an infinite number of solutions Note that the Linear Solver aplet only has a numeric view Getting started with the Linear Solver aplet The following example defines a set of three equations and then solves for the unknown variables Open the 1 Open the Linear Sequence aplet Linear Solver SelectLinear LINEAR EQUATION SOLVER aplet Solver z The Linear Equation Solver opens Choose the 2 Ifthe last time you used equation set the Linear Solver aplet you solved for two equations the two equation input form is displayed as in the
320. plet 79 PN N GIN e hp40g book Page 10 Friday December 9 2005 1 03 AM Using variables in equations You can use any of the real variable names A to Z and 0 Do not use variable names defined for other types such as 1 a matrix variable Home variables All home variables other than those for aplet settings like Xmin and Ytick are global which means they are shared throughout the different aplets of the calculator A value that is assigned to a home variable anywhere remains with that variable wherever its name is used Therefore if you have defined a value for T as in the above example in another aplet or even another Solve equation that value shows up in the Numeric view for this Solve equation When you then redefine the value for T in this Solve equation that value is applied to T in all other contexts until it is changed again This sharing allows you to work on the same problem in different places such as HOME and the Solve aplet without having to update the value whenever it is recalculated O HINT As the Solve aplet uses existing variable values be sure amp to check for existing variable values that may affect the solve process You can use SHIFT CLEAR to reset all values to zero in the Solve aplet s Numeric view if you wish Aplet variables Functions defined in other aplets can also be referenced in the Solve a
321. pogar name to run the Er pam before the standard menu option is executed The third argument specifies the view and the menu number for the item Determine the menu number from the View numbers table below Note SETVIEWS with no arguments resets the views to default of the base aplet Programming an ad T a e hp40g book Page 17 Friday December 9 2005 1 03 AM e NY View numbers The Function aplet views are numbered as follows 0 HOME 11 List Catalog Plot 12 Matrix Catalog 2 Symbolic 13 Notepad Catalog 3 Numeric 14 Program Catalog 4 Plot Setup 15 Plot Detail 5 Symbolic Setup 16 Plot Table 6 Numeric Setup 17 Overlay Plot 7 Views 18 scale 8 Note 19 Decimal 9 Sketch view 20 Integer 10 Aplet Catalog 21 Trig View numbers from 15 on will vary according to the parent aplet The list shown above is for the Function aplet Whatever the normal VIEWS menu for the parent e aplet the first entry will become number 15 the second number 16 and so on UNCHECK Unchecks unselects the corresponding function in the current aplet For example Uncheck 3 would uncheck F3 it the current aplet is Function UNCHECK n Branch commands Branch commands let a program make a decision based on the result of one or more tests Unlike the other programming commands the branch commands work in logical groups
322. pp 3 1 Getting started with the Function 3 1 T 5 e hp40g book Page iv Friday December 9 2005 1 03 AM Function aplet interactive 3 9 Plotting a piecewise defined 3 12 Parametric aplet About the Parametric aplet pp 4 1 Getting started with the Parametric 4 1 Polar aplet Getting started with the Polar aplet pp 5 Sequence aplet About the Sequence 6 1 Getting started with the Sequence aplet 6 Solve aplet AboubihecSolve BIG 7 1 Getting started with the Solve aplet pp 7 2 Use amimia gues Si utes iocis Poet 7 5 7 6 Plotingto tind es 7 7 Using variables in equations 7 10 Linear Solver aplet About the Linear Solver 8 1 Getting started with the Linear Solver aplet 8 Triangle Solve aplet About the Triangle Solver aplet 9 Getting started with the Triangle Solver aplet 9 10 Statistics aplet About the Statistics apjef cus tdt te
323. ppose you finance the purchase of a car with a 5 year loan at 5 5 annual interest compounded monthly The purchase price of the car is 19 500 and the down payment is 3 000 What are the required monthly payments What is the largest loan you can afford if your maximum monthly payment is 300 Assume that the payments start at the end of the first period Solution The following cash flow diagram illustrates the loan calculations PV 16 500 FV 0 I YR 5 5 N 5x12 60 P YR 12 End mode 1 2 59 60 PMT 2 Start the Finance Solver selecting P YR 12 and End payment option e Enter the known TVM variables as shown in the diagram above Your input form should look as follows TIME VALUE OF ENTER PAYMENT AMOUNT OR SOLVE ET nhHohT 130LE Highlighting the PMT field press the soft menu key to obtain a payment of 315 17 i e PMT 315 17 To determine the maximum loan possible if the monthly payments are only 300 type the value 300 in the PMT field highlight the PV field and press the Ba soft menu key The resulting value is PV 15 705 85 Using the Finance Solver 12 5 T am S SZ SZ e hp40g book Page 6 Friday December 9 2005 1 03 AM Example 2 Mortgage with balloon payment Suppose you have taken out a 30 year 150 000 house mortgage at 6 5 annual intere
324. press ENTER The following is then written to the Equation Writer x 2 AND y 1 Example 2 Type 2 2 1 AND 2 2 1 AND X 2 Y Z 4 Then invoke LINSOLVE and type the unknowns X AND Y AND 2 and press the ENTER key The following result is produced if you are in Step by step mode CFG etc 12 2L2 L 1 211 1 112 1 121 4 ENTER 13 213 11 211 1 013 1 121 4 and so on until finally Reduction Result 800 4 08 0 20 00 8 4 1436 Computer Algebra System CAS am ad T a e hp40g book Page 37 Friday December 9 2005 1 03 AM then press ENTER The following is then written to the Equation Writer anv y 5 ano z SOLVE Solve equations SOLVE has as two parameters 1 either an equality between two expressions or a single expression in which case is implied and 2 the name of a variable SOLVE solves the equation in R in real mode and in C in complex mode ignoring REALASSUME Typing SOLVE X 1 3 X gives in real mode x N2 OR x V2 or in complex mode e x V2 OR x V2 OR x i V2 OR x iv2 Solve systems SOLVE also enables you to solve a system of non linear equations if they are polynomials If they are not polynomials use MSOLV in the HOME screen to get a numerical solution It is assumed that the various equat
325. quences with integer domains Or define the nth term as a non recursive expression in terms of n only In this case the calculator inserts the first two terms based on the expression that you define Note You will have to enter the second term if the hp40gs is unable to calculate it automatically Typically if Ux N depends on Ux N 2 then you must enter Ux 2 Aplets and their views an SZ e hp40g book Page 3 Friday December 9 2005 1 03 AM Evaluating expressions In aplets In the Symbolic view a variable is a symbol only and does not represent one specific value To evaluate a function in Symbolic view press If a function calls another function then resolves all references to other functions in terms of their independent variable 1 Choose the Function ic FUME TION z THEDLIC aplet Fick Select Function F EDIT lecHE 2 Enter the expressions in the Function aplet s Symbolic view ALPHA A x El SEES FUNCTION SMEOLIC VEH Fl ix32H xX DT PECK ISB Familie on ALPHA MA 406 ALPHA F B D EDIT TEE EVAL EO ORE ALPHA F2 0E D BIB 3 Highlight F3 X EE FUNCTION IMEDLIC VIEH 4 WFICKISAeAe 4 Press Note how the values for F1 X and F2 X are substituted into F3 X FUNCTION SYMEOLIC VIEH
326. r 18 Matrices Notepad SHIFT Notes short text entries See Chapter 20 Notes and sketches Program SHIFT Programs that you create or l associated with user defined aplets See Chapter 21 u n rogramming Equation Writer The editor used for creating 88 expressions equations CAS See Chapter 15 Equation Writer 1 30 Getting started e 0 GIN e hp40g book Page 1 Friday December 9 2005 1 03 AM Aplets and their views Aplet views This section examines the options and functionality of the three main views for the Function Polar Parametric and Sequence aplets Symbolic Plot and Numeric views About the Symbolic view The Symbolic view is the defining view for the Function Parametric Polar and Sequence aplets The other views are derived from the symbolic expression You can create up to 10 different definitions for each Function Parametric Polar and Sequence aplet You e can graph any of the relations in the same aplet lt simultaneously by selecting them Defining an expression Symbolic view Choose the aplet from the Aplet Library APLET 1 Press A or v to Inference ar ametric select an aplet Eran are Sequence RE ZAME SHETIEEHD RECY START The Function Parametric Polar and S
327. r 9 2005 1 03 AM Using programs Runa program From HOME type RUN program name or From the Program catalog highlight the program you want to run and press Regardless of where yov start the program all programs run in HOME What you see will differ slightly depending on where you started the program If you start the program from HOME the HP 40gs displays the contents of Ans Home variable containing the last result when the program has finished If you start the program from the Program catalog the HP 40gs returns you to the Program catalog when the program ends Debug a IF you run a program that contains errors the program program will stop and you will see an error message Invalid Sunt ax Edit program To debug the program 1 Press to edit the program The insert cursor appears in the program at the point where the error occurred 2 Edit the program to fix the error 3 Run the program 4 Repeat the process until you correct all errors Stop a program You can stop the running of a program at any time by pressing CANCEL the ON key Note You may have to press it a couple of times Programming 21 7 e 0 Copy a program Transmit a program 21 8 hp40g book Page 8 Friday December 9 2005 1 03 AM HINT You can use the following procedure
328. r other household waste Instead it is your responsibility to dispose of your waste equipment by handing it over to a EE designated collection point for the recycling of waste electrical and electronic equipment The separate collection and 1 recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that it is recycled in a manner that protects human health and the environment For more information about where you can drop off your waste equipment for recycling please contact your local city office your household waste disposal service or the shop where you purchased the product e e X iG e hp40g book Page 8 Friday December 9 2005 1 03 AM T an ad e NY P hp40g book Page 1 Friday December 9 2005 1 03 AM Index A CHECK 21 14 ABCUV 14 62 SELECT 21 14 ABS 1445 SETVIEWS 21 17 absolute value 13 6 ACOS2S 14 38 add 13 4 ADDTMOD 14 51 ALGB menu 14 10 algebraic entry 1 19 alpha characters typing 1 6 alphabetical sorting 22 6 angle measure 1 10 in statistics 10 12 setting 1 11 animation 20 5 creating 20 5 annunciators 1 3 Ans last answer 1 24 antiderivative 14 68 14 69 antilogarithm 13 4 13 10 aplet attaching notes 22 4 clearing 22 3 copying 22 4 definition of R 1 deleting 22 6 Function 13 21 Inf
329. r substitute value substitutes the specified value for the variable in the expression Typing X 1 ya9 gives atai Computer Algebra System CAS am a T NY SUBST TEXPAND e UNASSIGN Computer Algebra System CAS e hp40g book Page 15 Friday December 9 2005 1 03 AM Substitute a value for a variable SUBST has two parameters an expression dependent on a parameter and an equality parameter substitute value SUBST substitutes the specified value for the variable in the expression Typing SUBST A 41 A 2 gives 2 1 Develop in terms of sine and cosine TEXPAND has a trigonometric expression or transcendental function as an argument TEXPAND develops this expression in terms of sin x and cos x Example e Typing TEXPAND COS X Y gives cos y sin y sin x Example Typing TEXPAND COS 3 gives 4 cos x 3 cos x Clear a variable UNASSIGN is used to clear a variable for example UNASSIGN ABC 14 15 T e e hp40g book Page 16 Friday December 9 2005 1 03 AM NY DIFF menu DERIV Derivative and partial derivative DERIV has two arguments an expression or a function and a variable DERIV returns the derivative of the expression or the
330. r substitutes values for any variables For example if you enter A B on the command line and press the calculator retrieves the values for A and B from memory and substitutes them in the calculation To pertorm symbolic calculations for example symbolic ditferentiations and integrations you need to use formal Using mathematical functions an P hp40g book Page 21 Friday December 9 2005 1 03 AM names The HP 40gs has six formal names available for use in symbolic calculations These are S1 to S5 When you perform a calculation that contains a formal name the HP 40gs does not carry out any substitutions You can mix formal names and real variables Evaluating 4 8 51 2 will evaluate A B but not 51 If you need to evaluate an expression that contains formal names numerically you use the where command listed in the Math menu under the Symbolic category For example to evaluate S1 S2 when S 2 and 52 4 you would enter the calculation as follows CSle5202 5152 52 45 64 BI 1 The symbol is in the CHARS menu press CHARS The sign is listed in the MATH menu under Symbolic functions 4 Symbolic You can perform symbolic operations in the Function calculations in qplefs Symbolic view For example to find the derivative of a function in the Function aplet s Symbolic view you the
331. rams in the Program catalog that belong to each aplet See Aplet naming convention on page 21 10 e NZ e hp40g book Page 10 Friday December 9 2005 1 03 AM NY 4 Develop a program that uses the SETVIEWS command to modify the aplet s VIEWS menu The menu options provide links to associated programs You can specify any other programs that you want transferred with the aplet See SETVIEWS on page 21 14 for information on the command 5 Ensure that the customized aplet is selected then run the menu configuration program to configure the aplet s VIEWS menu 6 Test the customized aplet and debug the associated programs Refer to Debug a program on page 16 7 Aplet naming convention To assist users in keeping track of aplets and associated programs use the following naming convention when setting up an aplet s programs Start all program names with an abbreviation of the aplet name We will use APL in this example Name programs called by menu entries the VIEWS menu number after the entry for example APLME for the program called by menu option for the program called by menu option Name the program that configures the new VIEWS menu option APL SV where SV stands for SETVIEWS For example a customized aplet called Differentiation might call programs called DIFF ME1 DIFF ME2 a
332. regression curve Hides and displays the menu key labels When the labels are hidden any menu key displays the x y e coordinates Pressing mamm redisplays the menu labels Calculating predicted values The functions PREDX and PREDY estimate predict values for X or Y given a hypothetical value for the other The estimation is made based on the curve that has been calculated to fit the data according to the specified fit Find predicted 1 In Plot view draw the regression curve for the data values set 2 Press to move to the regression curve 3 Press and enter the value of X The cursor jumps to the specified point on the curve and the coordinate display shows X and the predicted value of Y In HOME Enter PREDX y value to find the predicted value for the independent variable given a hypothetical dependent value 10 20 Statistics aplet e 0 e PN hp40g book Page 21 Friday December 9 2005 1 03 AM NY Enter PREDY x value to find the predicted value of the dependent variable given a hypothetical independent variable You can type PREDX and PREDY into the edit line or you can copy these function names from the MATH menu under the StotTwo category HINT In cases where more than one fit curve is displayed the PREDY function uses the most recently calculated curve In order to avoid errors wit
333. ression is shown The slope m is 425 875 The y intercept b is 376 25 10 4 Statistics aplet an e hp40g book Page 5 Friday December 9 2005 1 03 AM Predict values 13 To find the predicted sales figure if advertising were to go up to 6 minutes DB Ea RAL STATISTICS MATH S to highlight Stat Two 2 oie gt fo highlight TI PREDY fa 14 Return to the Plot view lcHnFHITFHCmlGHTH FIT DEFN 15 Jump to the indicated point on the regression line Erin 6 DB Observe the predicted y value in the left bottom corner of the screen Statistics aplet an STA 10 5 WB PRED BH31 5 MEHU GIN e hp40g book Page 6 Friday December 9 2005 1 03 AM Entering and editing statistical data The Numeric view NUM is used to enter data into the Statistics aplet Each column represents a variable named CO to C9 After entering the data you must define the data set in the Symbolic view A HINT A data column must have at least four data points to provide valid two variable statistics or two data points for one variable statistics You can also store statistical data values by copying lists from HOME into Statistics data columns For example in HOME L1 C1 stores a copy of the l
334. riday December 9 2005 1 03 AM Key Meaning Continued HEHU Turns menu key labels on and off When the labels are off pressing ZIXZII turns them back on Pressing once displays the full row of labels Pressing Mam a second time removes the row of labels to display only the graph Pressing a third time displays the coordinate mode Displays the ZOOM menu list TRACE Turns trace mode on off A white box appears over the DATA Opens an input form for you to enter an X or Tor N or 0 value Enter the value and press 9 The cursor jumps to the point on the graph that you entered Function aplet only turns on menu list for roottinding functions see Analyse graph with FCN functions 4 3 4 Displays the current defining expression Press to restore the menu Trace a graph You can trace along a function using the lt or gt key which moves the cursor along the graph The display also shows the current coordinate position x y of the cursor Trace mode and the coordinate display are automatically set when a plot is drawn Note Tracing might not appear to exactly follow your plot if the resolution in Plot Setup view is set to Faster This is because RES FASTER plots in only every other column whereas tracing always uses every column In Function and Sequence Aplets You
335. right corner and the body of the screen lists each category the memory it uses and the percentage of the total memory it uses 2 Select the category with which you want to work and 3 To delete variables in a category Press DEL to delete the selected variable Press CLEAR to delete all variables in the selected category Variables and memory management 17 9 e e X iG e hp40g book Page 10 Friday December 9 2005 1 03 AM T an ad e e hp40g book Page 1 Friday December 9 2005 1 03 AM NY 18 Matrices Introduction You can perform matrix calculations in HOME and in programs The matrix and each row of a matrix appear in brackets and the elements and rows are separated by commas For example the following matrix 123 456 is displayed in the history as 1 2 3 4 5 6 If the Decimal Mark mode is set to Comma then separate each element and each row with a period e You can enter matrices directly in the command line or 0 create them in the matrix editor Vectors Vectors are one dimensional arrays They are composed of just one row A vector is represented with single brackets for example 1 2 3 A vector can be a real number vector or a complex number vector for example 1 2 7 3 Matrices
336. riodic payment amount The payments are the same amount each period and the TVM calculation assumes that no payments are skipped Payments can occur at the beginning or the end of each compounding period an option you control by setting the Payment mode to Beg or End PMT The future value of the transaction the amount of the final cash flow or the compounded value of the series of previous cash flows For a loan this is the FV size of the final balloon payment beyond any regular payment due For an investment this is the cash value of an investment at the end of the investment period Performing TVM calculations e 1 Launch the Financial Solver as indicated at the beginning of this section 2 Use the arrow keys to highlight the different fields and enter the known variables in the TVM calculations known value Be sure that values are entered for at least four of the five TVM variables namely N I YR PV PMT and FY 3 If necessary enter a different value for P YR default value is 12 i e monthly payments 4 Press the key to change the Payment mode Beg or End as required 5 Use the arrow keys to highlight the TVM variable you wish to solve for and press the soft menu key Using the Finance Solver 4 SZ ZNS e hp40g book Page 5 Friday December 9 2005 1 03 AM Example 1 Loan calculations Su
337. rs greater than 10 a pseudo prime is a number with a large probability of being prime Example 1 Typing ISPRIME 13 gives 1 Example 2 Typing ISPRIME 1 4 gives 0 Returns the least common multiple of two integers Example Typing ICM 18 15 gives 90 See MOD on page 13 15 Computer Algebra System CAS am ad T a e hp40g book Page 51 Friday December 9 2005 1 03 AM NY NEXTPRIME NEXTPRIME n returns the smallest prime or pseudo prime greater than n Example Typing NEXTPRIME 75 gives 79 PREVPRIME PREVPRIME n returns the greatest prime or pseudo prime less than n Example Typing PREVPRIME 75 gives 73 O Modular menu 4 All the examples of this section assume that p 213 that is you have entered MODSTO 13 or STORE 13 MODULO or have specified 13 for Modulo in CAS MODES screen as explained on page 15 16 ADDTMOD Performs an addition in Z pZ Example 1 Typing ADDTMOD 18 gives 6 ADDTMOD can also perform addition in Z pZ X Example 2 Typing ADDTMODY 1 1X 5 8X 6 gives 6x 2 e Computer Algebra System CAS 14 51 T a e P e hp40g book Page 52 Friday December 9 2005 1 03 AM NY DIVMOD Division in Z pZ or Z pZ X Example 1 In Z pZ the arguments are two integers
338. rtcut to changing NUMSTART and NUMSTEP Integer Changes intervals for the independent variable to 1 unit e Starts at zero Shortcut to changing NUMSTEP Trig Changes intervals for independent variable to x 24 radian or 7 5 degrees or 8 4 grads Starts at zero Un zoom Returns the display to the previous Zoom The display on the right is a Zoom In of the display on the left The zoom factor is 4 x 0z5 Lu uguggu da a a lrh 1741081 H 3894184 0 1986693 5 4794255 3 98834 156646BE 2 3 9885416646BE 2 EnH EIG E EGIDEFN HINT To jump to an independent variable value in the table use the arrow keys to place the cursor in the independent variable column then enter the value to jump to 2 18 Aplets and their views e 0 Z e hp40g book Page 19 Friday December 9 2005 1 03 AM Automatic You can enter any new value in the X column When you recalculation press the values for the dependent variables are recalculated and the entire table is regenerated with the same interval between X values Building your own table of numbers The default NUMTYPE is Automatic which fills the table with data for regular intervals of the independent X or N variable With the NUMTYPE option set to Build Your Own you fill the table yourself
339. rueclause if not do the falseclause IFTE expression trueclause falseclause Example IFTE X gt 0 Xx X3 NOT Returns 1 if value is zero otherwise returns O NOT value OR Returns 1 if either value or value2 is non zero otherwise returns valuel OR value2 Using mathematical functions 13 19 T a e ZN NY XOR e hp40g book Page 20 Friday December 9 2005 1 03 AM Exclusive OR Returns 1 if either value or value2 but not both of them is non zero otherwise returns O value XOR valve2 Trigonometry functions ACOT ACSC ASEC COT CSC SEC The trigonometry functions can also take complex numbers as arguments For SIN COS TAN ASIN ACOS and ATAN see the Keyboard category Arc cotangent ACOT value Arc cosecant ACSC value Arc secant ASEC value Cotangent cosx sinx COT value Cosecant 1 sinx CSC value Secant 1 cosx SEC value Symbolic calculations In HOME Using formal variables 13 20 Although CAS provides the richest environment for performing symbolic calculations you can perform some symbolic calculations in HOME and with the Function aplet CAS functions that you can perform in HOME such as DERVX and INTVX are discussed in Using CAS functions in HOME on page 14 7 When you perform calculations that contain normal variables the calculato
340. s graphicname arguments The position argument takes the form x y Position coordinates depend on the current aplet s scale which is specified by Xmin Xmax Ymin and Ymax The upper left corner of the target graphic graphic2 is at Xmin Ymax You can capture the current display and store it in GO by simultaneously pressing ON DISPLAY Stores the current display in graphicname DISPLAY graphicname e DISPLAY Displays graphic from graphicname in the display DISPLAY graphicname GROB Creates a graphic from expression using font size and stores the resulting graphic in graphicname Font sizes are 1 2 or 3 If the fontsize argument is O the HP 40gs creates a graphic display like that created by the SHOW operation gt GROB graphicname expression fontsize GROBNOT Replaces graphic in graphicname with bitwise inverted graphic GROBNOT graphicname GROBOR Using the logical OR superimposes graphicname2 onto graphicname The upper left corner of graphicname2 is placed at position GROBOR graphicname position graphicname2 where position is expressed in terms of the current axes settings not in terms of pixel postion Programming 21 21 e NZ NY GROBXOR MAKEGROB PLOT gt PLOT REPLACE SUB ZEROGROB 21 22 e hp40g book Page 22 Friday December 9 2005 1 03 AM
341. s and boxes 20 3 drawing commands ARC 21 19 BOX 21 20 ERASE 21 20 FREEZE 21 20 LINE 21 20 PIXOFF 21 20 PIXON 21 20 TLINE 21 20 DROITE 14 45 E 13 8 edit line 1 2 editing matrices 18 4 T NY notes 20 2 programs 21 5 Editline Program catalog 21 2 editors 1 30 EGCD 14 55 eigenvalues 18 11 eigenvectors 18 11 element storing 18 6 E lessons 1 12 engineering number format 1 11 EPSXO 14 29 equals for equations 13 17 logical test 13 19 Equation Writer 14 2 15 1 16 1 selecting terms 15 5 equations solving 7 1 erasing a line in Sketch view 21 20 error messages bad guesses 7 7 constant 7 7 Euclidean division 14 48 14 49 EULER 14 47 exclusive OR 13 20 exiting views 1 19 EXP2HYP 14 63 EXP2POW 14 29 EXPAND 14 12 EXPANDMOD 14 52 expansion 14 25 14 27 EXPLN 14 29 exponent fit 10 13 minus 1 13 10 of value 13 17 raising to 13 5 exponentials 14 30 14 63 expression defining 2 1 R 1 entering in HOME 1 19 evaluating in aplets 2 3 literal 13 18 plot 3 3 extended greatest common divisor 14 55 e hp40g book Page 4 Friday December 9 2005 1 03 AM extremum 3 10 FACTOR 14 12 14 47 14 56 factorial 13 13 factorization 14 12 FACTORMOD 14 53 FastRes variable 21 32 FDISTRIB 14 30 fit a curve to 2VAR data 10 17 choosing 10 12 defining your own 10 13 fixed number format 1 10 font size change 3 8 15 2 20 5
342. s as arguments Using mathematical functions 13 3 e NZ SZ e hp40g book Page 4 Friday ELELEE Ene SHIFT 10 SIN COS TAN ASIN December 9 2005 1 03 AM Add Subtract Multiply Divide Also accepts complex numbers lists and matrices value 1 value2 etc Natural exponential Also accepts complex numbers e value Example e b returns 148 413159103 Natural logarithm Also accepts complex numbers LN value Example LN 1 returns O Exponential antilogarithm Also accepts complex numbers 10 value Example 10 3 returns 1000 Common logarithm Also accepts complex numbers LOG value Example LOG 100 returns 2 Sine cosine tangent Inputs and outputs depend on the current angle format Degrees Radians or Grads SIN value COS value TAN value Example TAN 45 returns 1 Degrees mode Arc sine sin x Output range is from 90 to 90 x 2 to 1 2 or 100 to 100 grads Inputs and outputs depend on the current angle format Also accepts complex numbers ASIN value Using mathematical functions an hp40g book Page 5 Friday December 9 2005 1 03 AM SHIFT J ACOS ATAN GE Using mathematical functions Example ASIN 1 returns 90 Degrees mode Arc cosine cos x Output
343. s variable on page 20 5 for more information on storing graphic object via the sketch view ie Library Aplet library variables can store aplets that you have created either by saving a copy of a standard aplet or downloading an aplet from another source List LO to L9 For example 1 2 3 11 Matrix MO to M9 can store matrices or vectors For example 1 2 3 4 MO Modes Modes variables store the modes settings that you can configure using SHIFT MODES Notepad Notepad variables store notes Program Program variables store programs Real A to Z and 6 For example 7 45 HHE A Symbolic EO 9 51 55 51 55 and n1 n5 Variables and memory management 17 7 e NZ Y e hp40g book Page 8 Friday December 9 2005 1 03 AM Aplet variables Most aplet variables store values that are unique to a particular aplet These include symbolic expressions and equations see below settings for the Plot and Numeric views and the results of some calculations such as roots and intersections See the Reference Information chapter for more information about aplet variables Category Available names Function FO to F9 Symbolic view See Function aplet variables on page R Parametric XO YO to X9 Y9 Symbolic view See Parametric aplet variables on page R 8 Polar RO to R9 Symbolic view S
344. so handled by the Matrix catalog and editor A choice of options given in the display It can appear as a list or as a set of menu key labels across the bottom of the display The top row of keys Their operations depend on the current context The labels along the bottom of the display show the current meanings Text that you write in the Notepad or in the Note view for a specific aplet A reusable set of instructions that you record using the Program editor A drawing that you make in the Sketch view for a specific aplet The name of a number list matrix note or graphic that is stored in memory Use to store and use to retrieve A one dimensional array of values separated by commas periods if the Decimal Mark mode is set to Comma and enclosed in single brackets Created and manipulated by the Matrix catalog and editor an Z Page 3 Friday December 16 2005 11 26 views The possible contexts for an aplet Plot Plot Setup Numeric Numeric Setup Symbolic Symbolic Setup Sketch Note and special views like split screens Resetting the HP 40gs If the calculator locks up and seems to be stuck you must reset it This is much like resetting a PC It cancels certain operations restores certain conditions and clears temporary memory locations However it does nof clear stored data variables aplet databases progr
345. spect to the variable of differentiation From the command line use a formal name S1 etc for a non numeric result See Finding derivatives on page 13 21 variable expression Example 0 s1 s12 3 s1 returns 2 s1 3 J Integrates expression from lower to upper limits with respect to the variable of integration To find the definite integral both limits must have numeric values that is be numbers or real variables To find the indefinite integral one of the limits must be a formal variable s1 etc lower upper expression variable See Using formal variables on page 13 20 for further details an zz gt e hp40g book Page 7 Friday December 9 2005 1 03 AM Example 0 51 2 X43 X Ga finds the indefinite result 3 s1 2 51 2 2 See To find the indefinite integral using formal variables on page 13 23 for more information on finding indefinite integrals TAYLOR Calculates the nth order Taylor polynomial of expression at the point where the given variable O TAYLOR expression variable n Example TAYLOR 1 sin s1 s1 5 with Radians angle measure and Fraction number format set in MODES returns 1 51 2 1 3 s1 4 Complex number functions These functions are for complex numbers only You can also use complex numbers with all trigonometric and hyperbolic functions and with so
346. ssing 5 takes you into selection mode and selects the branch adjacent to the cursor Pressing it augments the selection adding the next branch to the right For example 1 2 3 4 gt selects 3 4 Pressing it again selects 2 3 4 and again selects 1 2 3 4 If you are typing a templated function with multiple arguments such as X SUBST etc pressing or 4 enables you to move from one argument to another In 15 5 an SZ gt e hp40g book Page 6 Friday December 9 2005 1 03 AM this case you have to press A to select elements in the expression The following illustration shows how an expression can be viewed as a tree in the Equation Writer It illustrates a tree view of the expression 5x 3 x 1 x43 Xx y 3 x 1 N _ ei gt k Z N e Suppose that the cursor is positioned to right of 3 f you press 4 once the component is selected If you press 4 again the selection moves up the tree with x 3 now selected f you press 4 again the selection moves up the tree and now the entire expression is selected f you had pressed gt instead of when the cursor was positioned to the right of 3 the leaves of the branch get selected that is x 3 f you press gt again the selection moves up the tree and now the ent
347. st You expect to sell the house in 10 years repaying the loan in a balloon payment Find the size of the balloon payment the value of the mortgage after 10 years of payment Solution The following cash flow diagram illustrates the case of the mortgage with balloon payment I YR 6 5 PV 150 000 N 30 x 12 360 for PMT N 10x 12 120 for balloon payment P YR 12 End mode Balloon payment FV Start the Finance Solver selecting P YR 12 and End payment option e Enter the known variables as shown in the diagram above Your input form for calculating monthly payments for the 30 yr mortgage should look as follows TIME VALUE OF bi 5 H 26H 158 AGA HE 7 345 10 15 End ni ENTER PAYMENT AMOUNT OF SOLVE LEGIT AMORT F IEDLWE e Highlighting the PMT field press the soft menu key to obtain a payment of 948 10 i e PMT 948 10 determine the balloon payment or future value FV for the mortgage after 10 years use 120 highlight the FV field and press the soft menu key The resulting value is FV 127 164 19 The negative value indicates a payment from the homeowner Check that the required balloon payments at the end of 20 years N 240 and 25 years N 300 are 83 497 92 and 48 456 24 respectively Using the Finance Solver 4 4
348. stem CAS T e 4 hp40g book Page 27 Friday December 9 2005 1 03 AM TABVAR TAYLORO Computer Algebra System CAS 1 dL 53 1 2 5 ECHO NO 16 h a h 5 h h O0 h h x Variation table TABVAR has as a parameter an expression with a rational derivative TABVAR returns the variation table for the expression in terms of the current variable Typing TABVAR 3X 8X 11 gives in step by step mode F 3 8 11 F 3 2 5 8 2 3 x 4 Variation table 8 wipe 8 X The arrows indicate whether the function is increasing or decreasing during the specified interval This particular variation table indicates that the function F x decreases for x in the interval co reaching a minimum of at x 3 Itthen increases in the interval 5 reaching a maximum of 00 Note that appearing in the variation table indicates that the function is not defined in the corresponding interval Limited expansion in the vicinity of 0 TAYLORO has a single argument the function of x to expand It returns the function s limited 4th relative order expansion in the vicinity of x 0 if x is the current variable 14 27 T e P NY Note TRUNC REWRI menu DISTRIB 14 28 a
349. t CAS by pressing choose the Function aplet and check F1 and EZ FUNCTION STFHEHLIE Step by Step Examples an SZ 4 P hp40g book Page 19 Friday December 9 2005 1 03 AM Now press to see the graphs 0 Fl 5 MENU 2 3 3 return to CAS type each function in turn and press ENTER You may need to press twice for further simplification Part 6 To find the values of x t and y t for t 0 n For example pressing ALPHA X 0 ENTER ER gives the result at the right Likewise pressing ALPHA X 0 33 gives this answer at the right The other results are 9 1 X n 5 Y 0 0 Qo mo 0 0 The slope of the tangents is m 25 We can find the values of for 0 by using the 1im command aM Step by Step Examples 16 19 an SZ 4 P hp40g book Page 20 Friday December 9 2005 1 03 AM The example at the right shows the case for t O Select the entire expression and press to get the answer 0 The example at the right shows the case for t 2 3 Selecting the entire expression and pressing displays the message shown at the right Accept YES and press Press again to get the result OO
350. t m Q1 First quartile median of values to left of median MEDIAN Median value of data set Q3 Third quartile median of values to right of median Maximum data value in data set When the data set contains an odd number of values the data set s median value is not used when calculating Q1 and in the table above For example for the following data set 1355 dpe poy Log 02 only the first three items 3 5 and 7 are used to calculate and only the last three terms 15 16 and 17 are used to calculate Q3 10 14 Statistics aplet E p am a e hp40g book Page 15 Friday December 9 2005 1 03 AM Two variable Plotting Statistics aplet Mean of x independent values Sum of x values Sum of x values Mean of dependent values Sum of y values Sum of y values Sum of each xy Sample covariance of independent and dependent data columns Population covariance of independent and dependent data columns Correlation coefficient of the independent and dependent data columns for a linear fit only regardless of the Fit chosen Returns a value from 0 to 1 where 1 is the best fit RELERR The relative error for the selected fit Provides a measure of accuracy for the fit You can plot histograms boxand whisker plots scatter plots HENA Once you have ent
351. t Two Math functions by category Syntax Each function s definition includes its syntax that is the exact order and spelling of a function s name its delimiters punctuation and its arguments Note that the syntax for a function does not require spaces Using mathematical functions 4 zz gt e hp40g book Page 3 Friday December 9 2005 1 03 AM Functions common to keyboard and menus These functions are common to the keyboard and MATH menu SHIFT For a description see p on page 13 8 ARG For a description see ARG on page 13 7 d dx For a description see on page 1 7 AND For a description see AND on page 13 19 For a description see COMB 5 2 returns 10 That is there are ten different ways that five things can be combined two at a time on page 13 12 e SHIFT For a description see S on page 13 11 SHIFT EEX For a description see Scientific notation powers of 10 on page 1 20 For a description see on page 1 7 The multiplicative inverse function finds the inverse of a square matrix and the multiplicative inverse of a real or complex number Also works on a list containing only these object types Keyboard functions The most frequently used functions are available directly from the keyboard Many of the keyboard functions also accept complex number
352. t torm 21 28 display ilem 21 27 display message box 21 29 halt program execution 21 29 insert line breaks 21 29 prevent screen display being up dated 21 28 set date and time 21 27 store keycode 21 28 PROPFRAC 14 58 PSI 14 67 Psi 14 68 PTAYL 14 58 Q quadratic extremum 3 6 ft 10 13 function 3 4 QUOT 14 58 QUOTE 14 13 quotes in program names 21 4 R random numbers 13 13 e p NY P hp40g book Page 11 Friday December 9 2005 1 03 AM RE 13 8 real number maximum 13 8 minimum 13 8 real part 13 8 real number functions 13 14 13 16 CHANGE 13 16 TOTAL 13 16 CEILING 13 14 DEGtoRAD 13 14 FNROOT 13 14 HMSto 13 15 INT 13 15 MANT 13 15 MAX 13 15 MIN 13 15 MOD 13 15 RADtoDEG 13 16 ROUND 13 16 SIGN 13 16 TRUNCATE 13 17 XPON 13 17 reatest common divisor 14 47 recalculation for table 2 19 receive error K 2 1 receiving aplet 22 5 lists 19 6 matrices 18 4 programs 21 8 redrawing table of numbers 2 18 reduced row echelon 18 12 regression analysis 10 17 fit models 10 13 formula 10 12 user defined fit 10 13 relative error statistical 10 18 REMAINDER 14 59 REORDER 14 68 resetting aplet 22 3 calculator R 3 memory R 3 result copying to edit line 1 22 reusing 1 22 rigorous 14 6 RISCH 14 24 root interactive 3 10 nth 13 6 variable 21 34 roottinding displaying 7 7 interactive 3 9 operations 3 10 vari
353. t variables The polar aplet variables are 1 03 AM Category Available names Plot Symbolic Numeric Note Sketch Axes Connect Coord Grid Indep InvCross Labels Recenter Simult Umin Umax Ostep Tracing Digits Format NumCol NumFont NumIndep NoteText Page XCIOSS YCross Xtick YELCK Xmin Xmax Ymin Ymax Xzoom Yxoom NumRow Nurnotart NumStep NumType NumZoom PageNum am 27 R 9 T a NY 4 hp40g book Page 10 Friday December 9 2005 Sequence aplet variables The sequence aplet variables are 1 03 Category Available name Plot Symbolic Numeric Note Sketch Axes Coord Grid Indep InvCross Labels Nmin Nmax Recenter SeqPlot Simult Angle 01 02 U3 U4 Us Digits Format NumCol NumFont NumIndep NoteText Page Tracing Xcross YCross Xtick Ytick Xmin Xmax Ymin Ymax Xzoom Yzoom U6 U7 U8 U9 UO NumRow NumStart NumStep NumType NumZoom PageNum R 10 am 27 T a e hp40g book Page 11 Friday December 9 2005 1 03 AM NY Solve aplet variables The solve aplet variables are Category Available name Plot Axes Xcross Connect
354. tepad is a collection of notes independent of all aplets These notes can also be sent to another calculator via the Notepad Catalog Aplet note view You can attach text to an aplet in its Note view To write a note in 1 In an aplet press SHIFT NOTE for the Note view Note view 2 Use the note editing keys shown in the table in the following section 3 Set Alpha lock for quick entry of letters For lowercase Alpha lock press HS 4 While Alpha lock is on To type a single letter of the opposite case press letter To type a single non alpha character such os 5 or press ALPHA first This turns off Alpha lock for one character Your work is automatically saved Press any view key SYMB PLOT VIEWS or to exit the Notes view Notes and sketches 20 1 e NZ IN SZ e hp40g book Page 2 Friday December 9 2005 1 03 AM Note edit keys Key Meaning FACE Space key for text entry EE Displays next page of a multi page note ER Alpha lock for letter entry HE Lower case alpha lock for letter entry EEEF Backspaces cursor and deletes character DEL Deletes current character Starts a new line CLEAR Erases the entire note Menu for entering variable names and contents of variables 9 MATH Menu for entering math e operations and constants CMDS Menu for entering
355. the M2 variable press Ly VARS x Graphic Library M2 List mlmPLETINnF1mlVnLUEIrmNrL HE 17 4 Variables and memory management gt 9 zz gt e hp40g book Page 5 Friday December 9 2005 1 03 AM 5 Choose whether to place the variable name or the variable value on the command line Press EETEH to indicate that you want the variable s contents to appear on the command line Press to indicate that you want the 6 Press H3 to place the value or name on the command line The selected object appears on the command line FUNCTION Note The VARS menu can also be used to enter the names or values of variables into programs Example This example demonstrates how to use the VARS menu to te gt add the contents of two list variables and to store the result in another list variable 1 Display the List Catalog LIST to select 11 2 Enter the data for L1 EDIT INS 1 1 1 1 o 3 Return to the List Catalog to create 12 us LIST CATALOG 882 BEETS m Ha v to select L2 IUE HLH TY A EDT zEhplFErw Variables and memory management 17 5 e NZ 2 zz gt e hp40g book Page 6 Friday December 9 2005 1 03
356. the main batteries To install the backup battery a Slide up the battery compartment cover as illustrated b Insert 4 new AAA LRO3 batteries into the main compartment Make sure each battery is inserted in the indicated direction a Press down the holder Push the plate to the shown direction and lift it Plate f Holder 4 b Insert a new CR2032 lithium battery Make sure its positive side is facing up c Replace the plate and push it to the original place After installing the batteries press ON to turn the power on Warning It is recommended that you replace this battery every 5 years When the low battery icon is displayed you need to replace the batteries as soon as possible However avoid removing the backup battery and main batteries at the same time to avoid data lost R 5 T am S SZ e hp40g book Page 6 Friday December 9 2005 1 03 AM FG NY Variables Home variables The home variables are Category Available name Complex VAS 0 Graphic G1 G9 GO Library Function Parametric Polar sequence Solve Statistics User named List 0 Matrix M1 M9 MO E Modes Ans Date HAngle HDidgits HFormat lerr Time Notepad User named Program Editline User named Real A Z
357. the note Assignments in the Notepad 1 In the Notepad SHIFT NOTEPAD open the note Assignments 2 Press Galway highlight Note in the left e column then press gt and highlight NoteText in the right column 3 Press DI fo recall the contents of the Note view into the note Assignments Notes and sketches T am SZ iG e hp40g book Page 1 Friday December 9 2005 1 03 AM 21 Programming Introduction This chapter describes how to program using the HP 40gs In this chapter you ll learn about using the Program catalog to create and edit programs programming commands storing and retrieving variables in programs programming variables HINT More information on programming including examples and special tools can be found at HP s calculators web e site http www hp com calculators The Contents of a An HP 40gs program contains a sequence of numbers Program mathematical expressions and commands that execute automatically to perform a task These items are separated by a colon Commands that take multiple arguments have those arguments separated by a semicolon For example PIXON xposition yposition Structured Inside a program you can use branching structures to Programming control the execution flow You can take advantage of structured programming by creating building b
358. the root value on the x axis and the resulting x value is saved in a variable named ROCT Extremum Select Extremum to find the maximum or minimum of the current function nearest the cursor This displays the coordinate values and moves the e cursor to the extremum The e resulting value is saved in a variable named EXTREMUM Slope Select Slope to find the numeric derivative at the current position of the cursor The result is saved in a variable named SLOPE Signed area Select Signed area to find the numeric integral If there are two or more expressions checkmarked then you will be asked to choose the second expression from a list that includes the x axis Select a starting point then move the cursor to selection ending point The result is saved in a variable named AREA 3 10 Function aplet T e NZ Z gt e hp40g book Page 11 Friday December 9 2005 1 03 AM Function Description Continued Intersection Select Intersectiontofind the intersection of two graphs nearest the cursor You need to have at least two selected expressions in Symbolic view Displays the coordinate values and moves the cursor to the intersection Uses Solve function The resulting x value is saved in a variable named ISECT Shading area You can shade a selected area between functions This process also g
359. this product or product family This compliance is indicated by the following conformity marking placed on the product h king is valid fo on harm d This marking is valid for non Telecom products Tel duct and EU harmonized Telecom products e g Bluetooth to the product label This marking is valid for EU non harmonize Notified body number used only if applicable refe 4 4 Japanese Notice Korean Notice Disposal of Waste Equipment by Users in Private Household in the European Union hp40g book Page 7 Friday December 9 2005 1 03 AM VCCI 0 7 7 7H8gO 2 MAA SS Se 7 7 24 FAAAIYME SE m rin Ral Q t dim gt 1 4 0 This symbol on the product or on its packaging indicates that this product must not be disposed of with you
360. through the evaluation RECURSE sequencename ferm term term Example RECURSE U U N 1 N 1 2 Ul N Stores a factorial calculating function named U1 When you enter U1 5 for example the function calculates 5 120 Summation Finds the sum of expression with respect to variable from initialvalue to finalvalue gt variable initialvalue finalvalue expression Example X C 1 5 C returns 55 These functions are for matrix data stored in matrix variables See Matrix functions and commands on page 18 10 Polynomial functions POLYCOEF POLYEVAL Using mathematical functions Polynomials are products of constants coefficients and variables raised to powers ferms Polynomial coefficients Returns the coefficients of the polynomial with the specified roots POLYCOEF roots Example To find the polynomial with roots 2 3 4 5 POLYCOEF 2 3 4 5 returns 1 2 25 26 120 representing x 2092 5x 26x 120 Polynomial evaluation Evaluates a polynomial with the specitied coefficients for the value of x POLYEVAL coefficients value 13 11 4 GIN e hp40g book Page 12 Friday December 9 2005 1 03 AM Example For x 232 25x 26x4 120 POLYEVAL 1 2 25 26 120 8 returns 299 POLYFORM Polynomial form Creates a polynomial in variable 1 from expression POLYFORM expression variable Exa
361. tion as PV 2 Enter the number of payments to amortize in the new batch Using the Finance Solver 12 7 e NZ SZ e hp40g book Page 8 Friday December 9 2005 1 03 AM 3 Press the ERIA soft menu key to amortize the new batch of payments Repeat steps 1 through 3 as often as needed Example 4 Amortization for home mortgage For the results of Example 3 show the amortization of the next 10 years of the mortgage loan First press the soft menu key Then keeping 120 in the PAYMENTS field press the soft menu key to produce the results shown below Sie comin AMORTIZE SER REUS SAU PAYMENTS 128 PRINCIPAL INTEREST r6 165 98 ERLANCE 3 497 32 EZ NN CER CC EFPY To amortize a series of future payments starting at payment p 4 1 Calculate the balance of the loan at payment p 7 m 2 Store the new balance in PV using the REJN soft menu key 3 Amortize the series of payments starting at the new PV The amortization operation reads the values from the TVM variables rounds the numbers it gets from PV and PMT to the current display mode then calculates the amortization rounded to the same setting The original variables are not changed except for PV which is updated after each amortization e 0 4 hp40g book Page 1 Friday
362. tor All Aplets From Plot ZOOM Set Factors enter the value for vzooM or In a program type n gt YZOOM The default value is 4 Symbolic view variables Angle Sets the angle mode All Aplets From Symbolic Setup choose Degrees Radians or Grads for angle measure or In a program type 1 gt Angle for Degrees 2 gt Angle for Radians 3 gt Angle for Grads F1 F9 FO Can contain any expression Independent variable is X Function Example SIN X b FI X You must put single quotes around an expression to keep it from being evaluated before it is stored Use SHIFT CHARS to type the single quote mark 21 38 Programming e 0 NY P hp40g book Page 39 Friday December 9 2005 1 03 AM X1 Y1 X9 Y9 X0 YO Parametric R1 R9 RO Polar U1 U9 UO Sequence E1 E9 EO Solve S1fit S5fit Statistics Programming Can contain any expression Independent variable is T Example OLN 442 P YLIT lt Xl1 T Can contain any expression Independent variable is Example 2 SIN 2 0 gt R1 0 Can contain any expression Independent variable is N Example RECURSE U UOGI L N l1 2 gt Uli N Can contain any equation or expression Independent variable is selected by highlighting it in Numeric View Example 2 gt EI Sets the
363. triangle type Specify the known values Open the Triangle Solver aplet Select Triangle Solver ill 2 aut oF amp The Triangle Solver nter Length oF zaide A aplet opens Note if you have already used the Triangle Solver the entries and results from the previous use will still be displayed To start the Triangle Solver afresh clear the previous entries and results by pressing CLEAR If the last time you used the Triangle Solver aplet you used the right angled triangle ill 2 out oF amp ugluez input form that input TI EDIT RECTm form is displayed again as in the example at the right If the triangle you are investigating is not a right angled triangle or you are not sure what type it is you should use the general input form illustrated in the previous step To switch to the general input form press HENE If the general input form is displayed and you are investigating a right angled triangle press to display the simpler input form Using the arrow keys move to a field whose value you know enter the value and press BIB or ENTER Repeat for each known value Note that the lengths of the sides are labeled A B and C and the angles are labeled a as ill Z out of amp udlugz and amp It is important Enter Ltensth side ELIT RECT that you enter the known values in the appropriate fields In our example we know the length of
364. two integers n1 n2 For a vector size is a list containing one integer n REDIM name size 21 24 Programming e 0 e hp40g book Page 25 Friday December 9 2005 1 03 AM NY REPLACE Replaces portion of a matrix or vector stored in name with an object starting at position start start for a matrix is a list containing two numbers for a vector it is a single number Replace also works with lists and graphics REPLACE name start object SCALE Multiplies the specified row number of the specified matrix by value SCALE name value rownumber SCALEADD Multiplies the row of the matrix name by value then adds this result to the second specified row SCALEADD name value row row2 SUB Extracts a sub object a portion of list matrix or graphic from object and stores it into name start and end are each specified using a list with two numbers for a matrix a number for vector or lists or an ordered pair x Y for graphics SUB name object start end SWAPCOL Swaps Columns Exchanges column 1 and column2 of the specified matrix SWAPCOL name column column2 SWAPROW Swap Rows Exchanges row and row2 in the specified matrix SWAPROW name row row2 Print commands These commands print to an HP infrared printer for example the HP 82240B printer PRDISPLAY Prints the contents of the display P
365. two sides and the angle at which those sides meet Hence if we specify the lengths of sides A and B we must enter the angle as since is the angle where A and B meet If instead we entered the Triangle Solve aplet an zz gt e hp40g book Page 3 Friday December 9 2005 1 03 AM Errors Triangle Solve aplet lengths as B and C we would need to specify the angle as a The illustration on the display will help you determine where to enter the known values Note if you need to change the angle neasure mode press MODES change the mode and then press NUM to return to the aplet 4 Press The solver calculates the values of the unknown variables and displays As the illustration at the right cM A shows the length of the unknown side in our example is 3 2296 The other two angles have also been calculated Note if two sides and edic ThIHM LE SOLVER an adjacent acute HEBES BEBEH A angle are entered and there are two solutions LaLa i only one will be displayed initially In this case an menu key is displayed s2 4152 8 6821 as in this example 1B us You press to hatin Found display the second solution and again to return to the first solution No solution with given data If you are using the general input form and you enter
366. type of fit to be used by the FIT operation in ee drawing the regression line From Symbolic Setup view specify the fit in the field for STFIT S2FIT etc or In a program store one of the following constant numbers or names into a variable S1fit S2fit etc 1 Linear 2 3 ExpFit 4 Power oO uacdkit 6 Cubre T LOGILSE 8 ExptFit 9 TrigFit 10 User 21 39 T PN NZ e hp40g book Page 40 Friday December 9 2005 1 03 AM AG NY Example Cubic b S2fit or 6 gt S2fit Numeric view variables The following aplet variables control the Numeric view The value of the variable applies to the current aplet only C1 C9 CO CO through C9 for columns of data Can contain lists Statistics Enter data in the Numeric view or In a program type LIST Cn wheren 0 1 2 3 9 Digits Number of decimal places to use for Number format in All Aplets the HOME view and for labeling axes in the Plot view From the Modes view enter a value in the second field of Number Format or In a program type n gt Digits where 0 lt lt 11 Format Defines the number display format to use for numeric All Aplets format on the HOME view and for labeling axes in the Plot view From the Modes view choose Standard Fixed Scientific Engineering Fraction or Mixed Fraction inthe Number Format field or In
367. type the text on the edit line To lock sketch the Alpha shift on press for uppercase or EWA for lowercase To make the label a smaller character size turn off GED before pressing GEES AH is a toggle between small and large font size The smaller character size cannot display lowercase letters Press Position the label where you want it by pressing the v x keys 4 Press BIB again to affix the label Press BITTE to continue drawing or press to exit the Sketch view To create a set of You can create a set of up to ten sketches This allows for sketches simple animation eo After making a sketch press to add a new blank page You can now make a new sketch which becomes part of the current set of sketches view the next sketch in an existing set press WAZ Hold GEA down for animation remove the current page in the current sketch series press DEL To store into a You can define a portion of a sketch inside a box and graphics variable then store that graphic into a graphics variable 1 In the Sketch view display the sketch you want to copy store into a variable Press FALTA Highlight the variable name you want to use and press MA 4 Draw a box around the portion you want to copy move the cursor to one corner press BIB then move the cursor to the opposite corner and press MA Notes and sketches 20 5
368. u option beginning with that alpha character With this method you do not need to press ALPHA first Just press the key that corresponds to the command s beginning alpha character Note that when the MATH menu is open you can also access CAS commands You do this by pressing This enables you to use CAS commands on the HOM screen without opening CAS See Chapter 14 for details of CAS commands Pressing CMDS displays the list of Program Commands See Programming commands on page 21 13 If you press a key that does not operate in the current context a warning symbol like this A appears There is no beep A menu offers you a choice of items Menus are displayed in one or two columns Center The arrow in the display means more items below Tests FIFHROOT 7 The arrow in the display means items above Getting started an SZ gt e hp40g book Page 9 Friday December 9 2005 1 03 AM To search a menu Press v or 4 to scroll through the list If you press v or A you ll go all the way to the end or the beginning of the list Highlight the item you want to select then press Erg ENTER f there are two columns the left column shows general categories and the right column shows specific contents within a category Highlight a general category in the l
369. ue closest to the position of the cursor You need to re locate the cursor to find other roots or extrema that may exist 20 Display the numeric view NUM 21 Display the numeric setup SHIFT SETUP NUM FUNCTION NUMERIC SETUP Seek HIHETHRT MUMSTEP 1 MUMTYPE Automatic HUMZOOM 4 ENTER STARTING VALUE FOR THELE EDIT PLOTE See Setting up the table Numeric view setup on page 2 16 for more information 22 Match the table settings to the pixel columns in the graph view FUNCTION NUMERIC SETUP SERSSE NUMSTART MUMSTEP MUMTYPE Automatic HUMZOOM 4 ENTER gt TARTING VALUE FOR TAELE EDIT PLOTE 23 Display the table of values NUM 3 7 4 4 To navigate around a table To go directly to a value To access the zoom options To change font size To display the symbolic definition of a column 3 8 hp40g book Page 8 Friday December 9 2005 1 03 AM 24 Move to X 5 9 6 times 25 Move directly to X 10 26 Zoom in on X 10 by a factor of 4 Note NUMZOOM has a setting of 4 The symbolic definition of F1 is displayed at the bottom of the screen Function aplet an 4 P hp40g book Page 9 Friday December 9 2005 1 03
370. uence Solve Statistics Extremum Function FastRes Function Solve Grid All Aplets Hmin Hmax Statistics 21 32 P hp40g book Page 32 Friday December 9 2005 1 03 AM Turns the coordinate display mode in Plot view on or off From Plot view use the Menu mean key to toggle coordinate display on an off In a program type 1 Coord to turn coordinate display on default 0 Pp Coord to turn coordinate display off Contains the last value found by the Extremum operation in the PlotFCN menu Toggles resolution between plotting in every other column faster or plotting in every column more detail From Plot Setup choose Faster or More Detail or In a program type 1 gt FastRes for faster 0 gt FastRes for more detail default Turns the background grid in Plot view on or off From Plot setup check or uncheck __GRID or In a program type 1 gt Grid to turn the grid on 0 gt Grid to turn the grid off default Defines minimum and maximum values for histogram bars From Plot Setup for one variable statistics set values for HRNG or In a program type nj gt Hmin n b Hmax where n n Programming am a T e NY 4 P hp40g book Page 33 Friday December 9 2005 1 03 AM Hwidth Statistics Indep All Aplets InvCross All Aplets Isect Function Labels All Aplets Pr
371. ulator is useful only for trying out different values of n To show that b and c are relatively prime it is enough to note that C DS That means that the common divisors of b and c are the common divisors of b and 2 as well as the common divisors of c and 2 b and 2 are relatively prime because b is a prime number other than 2 So e Step by Step Examples 16 11 4 4 P hp40g book Page 12 Friday December 9 2005 1 03 AM GCD c b GCD c 2 GCD b 2 1 Part 2 Given the equation b x c y 1 1 where the integers x and y are unknown and b and c are defined as in part 1 above 1 Show that 1 has at least one solution 2 Apply Euclid s algorithm to b4 and and find a solution to 1 3 Find all solutions of 1 Solution Equation 1 must have at least one solution as it is actually a form of B zout s Identity In effect B zout s Theorem states that if a and are relatively prime there exists an x and y such that a xt tb y 1 Therefore the equation b x c3 y 1 has at least one solution Now enter TEGCD 3 C 3 IEGCP B SLC S Y Note that the TEGCD function can be found on the INTEGER submenu of the MATH menu Pressing a number of times returns the result shown at the right THM AAD In other words b
372. used in this example The reduced row echelon matrix gives the solution to the linear equation in the fourth column An advantage of using the RREF function is that it will also work with inconsistent matrices resulting from systems of equations which have no solution or infinite solutions For example the following set of equations has an infinite number of solutions 2 5 2 7 2 2 2 18 14 Matrices ev e 0 Z gt e hp40g book Page 15 Friday December 9 2005 1 03 AM The final row of zeros in the reduced row echelon form of the augmented matrix indicates an inconsistent system with infinite solutions Matrices 18 15 e v bg X iG e hp40g book Page 16 Friday December 9 2005 1 03 AM T an ad e ZN NY 4 hp40g book Page 1 Lists Create a list in the List Catalog Lists Friday December 9 2005 1 03 AM 19 You can do list operations in HOME and in programs A list consists of comma separated real or complex numbers expressions or matrices all enclosed in braces A list may for example contain a sequence of real numbers such as 1 2 3 If the Decimal Mark mode is set to Comma then the separators ar
373. were equal or where the expression was zero a root within the calculator s 12 digit accuracy Sign Reversal Solve found two points where the difference between the two sides of the equation has opposite signs but it cannot find a point in between where the value is zero Similarly for an expression where the value of the expression has different signs but is not precisely zero This might be because either the two points are neighbours they differ by one in the tweltth digit or the equation is not real valued between the two points Solve returns the point where the value or difference is closer to zero If the equation or expression is continuously real this point is Solve s best approximation of an actual solution Extremum Solve found a point where the value of the expression approximates a local minimum for positive values or maximum for negative values This point may or may not be a solution Or Solve stopped searching at 9 99999999999E499 the largest number the calculator can represent Note that the value returned is probably not valid 7 6 Solve aplet e 0 GIN e hp40g book Page 7 Friday December 9 2005 1 03 AM If Solve could not find a solution you will see one of the following two messages Message Condition Bad Guess es The initial guess lies outside the domai
374. x 1000 c x 999 1 Therefore we have a particular solution x 1000 999 The rest can be done on paper C b 4 2 b 999x241 Step by Step Examples an 4 Exercise 7 Step by Step Examples P hp40g book Page 13 Friday December 9 2005 1 03 AM so b 999 x b4 1 or b x 1000 c x 999 1 The calculator is not needed for finding the general solution to equation 1 We started with b x c y 1 and have established that b x 1000 c x 999 1 So by subtraction we have b x 1000 c 999 0 or b x 1000 999 According to Gauss s Theorem c is prime with 54 so c4 is a divisor of x 1000 Hence there exists k e Z such that x 1000 kx c and y 999 k x b Solving for x and y we get x 1000 k x and 999 b for k e Z This gives us b x c y b x 1000 c x 999 I The general solution for all k Z is therefore x 1000 k x c4 y 999 b Let be point on circle C of center radius 1 Consider the image M of mdefined on their affixes by the transformation F z When m moves on 16 13 T e Sd 4 P hp40g book Page 14 Friday December 9 2005 1 03 AM Part 1 16 1
375. x 52 90 E then you get DERVX E1 S1 x 2 DERIV E1 S2 4 INTVX E1 1 3 S13 4 x 52 x 1 e Computer Algebra System CAS 14 7 e 0 2 4 hp40g book Page 8 Friday December 9 2005 1 03 AM Send expressions from HOME to CAS history Send expressions from CAS to HOME history Online Help 14 8 Symbolic matrices are stored as a list of lists and therefore must be stored in LO L1 L9 whereas numeric matrices are stored in MO M1 M9 CAS linear algebra instructions accept lists of lists as input For example if you type in HOME XQ S2 1 1 42 1 amm L1 then you have TRAN L1 S2 1 V2 1 1 Some numeric linear algebra commands do not directly work on a list of lists but will do so after a conversion by AXL For example if you enter DET AXL L1 you get S2 1 42 In the HOME screen you can use the PUSH command to send expressions to CAS history For example if you enter PUSH S 14 1 S141 is written to CAS history N In the HOME screen you can use the POP command to retrieve the last expression written to CAS history For example if S1 1 is the last expression written to CAS history and you enter POP in the HOME screen S1 1 is written to the HOME screen history and S1 1 is removed from CAS history When you are working with the Equation Writer you can display o
376. your last operation Pressing in the Equation Writer displays a menu of plot types You can choose to graph a function a parametric curve or a polar curve Xu SELECT AM APLET 2 Function Parametric Polar CAMEL OK Depending on what you choose the highlighted expression is copied into the a appropriate aplet to the F4 destination that you specify xx CHOOSE DESTINATION X 15 19 an s Z e hp40g book Page 20 Friday December 9 2005 1 03 AM NOTE NUM key SHIFT NUM key VIEWS key _ 15 20 This operation supposes that the current variable is also the variable of the function or curve you want to graph When the expression is copied it is evaluated and the current variable contained in VX is changed to X T or 9 depending on the type of plot you chose If the function depends on a parameter it is preferable to give the parameter a value before pressing PLOT If however you want the parameterized expression to be copied with its parameter then the name of the parameter must consist of a single letter other than X T or so that there is no confusion If the highlighted expression has real values the Function Aplet or Polar Aplet can be chosen and the graph will be of Function or Polar type If the highlighted expression has complex values the Parametric Aplet must be chosen and the gra

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