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HP 48gx Quick Start Manual

1. w atta tench eenaa a CAWE View Volume The View Volume The other important parameter for three dimensional plotting is the eyepoint the point in space from which you are viewing the View Volume The eyepoint determines the way that the View Volume is projected onto the two dimensional plotting display Top View Ys annonces View Volume Vigar m View Plane parallel to xz plane A Shee 1 y axis unit Y Eyepoint Xe Ye Ze Plot Display Screen The Relationship of the Eyepoint View Volume and Plot Display Plotting Equations and Analyzing Graphs 6 7 Note that the three dimensional coordinate system on the HP 48 is somewhat constrained compared to its abstract mathematical counterpart Specifically The plot display screen does not rotate in space it always stays parallel to the zz plane and perpendicular to the y axis This means that visually height is always along the z axis width along the x axis and depth along the y axis The y axis is always oriented so that negative y values are nearer and positive y values farther away from the plot display The eyepoint must be at least one unit nearer than Ynear Ye lt Ynear 1 and can never exist within the View Volume Whenever you move the eyepoint you also move the plot display screen so that it remains exactly one unit away in the direction of the y axis You cannot plot a top view of a fu
2. Step 3 Divide the result by 3 2 yo 3GP91 G z po m7 Ls 7 1 63 MAT E MAT 0 Gr APPLY Arithmetic 3 11 Example Find the square roots of 8 6i Step 1 Type the complex number Co EEIN EMATEMAT 0 30m 1 APPLY ee gc Step 2 Find the principal square root and make an extra copy et aN THAT YMATL e oom 1 APPLY Step 3 Find the conjugate root Os e A rene an SIGN MEG CONJ Algebraics containing complex numbers can be manipulated symbolically in the same way as real number expressions Example Calculate the sine of 6 2 f aleteando 9933r 70649 EESE ENT E E ES Example Use the Equation Writer T to enter an expression representing the complex number 2 2i 3 Then evaluate the expression to get a complex result Step 1 Enter the expression i 2 Beiet3 aera GE 3 ENTER LSIGM MEG COMJ i 7 OD Step 2 Convert the expression to a number l Ceo tot 1H161514 SIGN NEG CONS O O TOO O 3 12 Arithmetic Lesson 11 Arithmetic including Units You needn t calculate with numbers separated from their natural measurement units if you use the HP 48 A unit object is a real number connected to a measurement unit with an underscore character The built in unit management feature of the HP 48 allows you to attach units to numbers and then do arithmetic with the resulting unit objects As long as you attach th
3. 15 Pow pk ewAM ff a 4 10 Understanding and Using Memory This chapter provides a brief introduction to the SOLVE application The lessons take you through examples of the primary kinds of equation solving that can be accomplished on the HP 48 including gt Numerically solving for an unknown variable when all other variables have explicit values gt Symbolically solving for a variable gt Finding all roots real and complex of a polynomial gt Solving a system of linear equations Solving Equations 5 1 Lesson 17 Solving for a Variable Numerically If you want a numeric solution for an unknown in an equation you can use the root finding application HP Solve You can solve for a value of any variable without changing the equation as long as you fill in values for all other variables in the expression or equation You can solve an equation or expression over and over tor different known values and for different combinations of known and unknown variables Example Solve the following expression for z 6 4 2 ee 9 i 6 r r r r 5246 This expression was created by the TEACH command earlier and stored as the variable RATFUNC in the EQNS directory t Step 1 Begin the SOLVE application and choose Sa ture ET g bo m pm ENTER FUNCTION TO SOLVE EDT ES oo o fvaksj o o Step 2 The Ems field is highlighted already so choose RATFUNC to be the current equation You will need t
4. HEWLETT PACKARD HP 48G Series Quick Start Guide T a Up ely oe fe Lo z Es LOA eRe So a eee ee BME ie Rae CIS Seo L oe _ TR Ge Us A 3 es es ae S 2 j Lees es Le ES Regulatory Information U S A The HP 48 generates and uses radio frequency energy and may interfere with radio and television reception The HP 48 complies with the limits for a Class B computing device as specified in Part 15 of FCC Rules which provide reasonable protection against such interference in a residential installation In the unlikely event that there is interference to radio or television reception which can be determined by turning the unit off and on try the following m Reorienting or relocating the receiving antenna a Relocating the HP 48 with respect to the receiver For more information consult your dealer an experienced radio television technician or the following booklet prepared by the Federal Communications Commission How to Identify and Resolve Radio TV Interference Problems This booklet is available from the U S Government Printing Office Washington D C 20402 Stock Number 004 000 00345 4 At the first printing of this manual the telephone number was 202 783 3238 Europe Declaration of Conformity according to ISO IEC Guide 22 and EN 45014 Manufacturer s name Hewlett Packard Co Hewlett Packard Co Manufacturer s address Corvallis Division Singapore PTE Ltd 1000 NE Circl
5. You tried to do something without supplying the pie with oa stack arguments For example executing with only one number on the stack causes this error Irese lid Card Data The HP 48 cannot read data stored on a plug in card you inserted However you will also see this message whenever a RAM car rd contains ports you ve never used Press NXT FN DT to Initialize all available RAM ports This not aire data fers stored on the card goes Wide imc Mame The HP 48 attempted to execute a command that requires numeric arguments and found a symbolic argument it could not convert into a number If the command should accept symbolic arguments then sama the Numeric Results flag 3 is set press A to check Clear it and try again If Things Go Wrong 9 1 ct hl A A A eet Lesson 39 Troubleshooting if the HP 48 is stuck in an unfamiliar state a Press CANCEL several times until you see the normal stack display To undo a mistake m To remove e the last result and get back the original data press i above the key a To aie awed press SEE To clear the entire see press Eh m To retrieve a previous command eee you exec cuted so you can above the Z key m To ag the last result and get back the original data press change it or execute it again press m Press if the calculator doesn t respond when you press the keys 1 Press CANCEL several times 2 If the keyboard
6. becomes and so forth This allows you quicker access to these operations you need not press the 4 shift key first becomes lt Introducing the HP 48 2 5 Removing Objects from the Stack Example Now remove drop objects from the stack Step I Drop just the object in level 1 Notice that all other objects drop a level in the process DROP SFT ANAS Step 2 Clear all objects from the stack Step 3 Oops You are not sure that you really wanted to do that last operation HOME 4 See a ie Si a 4 2 VECTRIMATR List HYP REAL BASE otep 4 After reviewing the stack objects again you decide that you were right the first time Press CLEAR e 2 6 Introducing the HP 48 There are over 200 characters available on the HP 48 They can be used in text strings and with a few restrictions in variable names and equations Most of these characters are available on the Alpha q keyboard and all are accessible using the CHARS feature t The a Keyboard The a key is a special shift key that converts the keyboard into a kind of typewriter Whenever you see the Gd annunciator at the top of the display the next key you press will type its alpha character instead of performing its operation Only the upper case English letters are printed on the keyboard in white at the lower right corner of the respective key You can turn on the d annunciator
7. menu VAR 5 8 Solving Equations Lesson 19 Finding all Roots of a Polynomial A polynomial has the same number of roots as its degree although not all of these roots will be real or unique The HP 48 offers an easy way to numerically calculate all roots both real and complez of a polynomial The coefficients of the polynomial may be either real or complex Sag 5 4 E r o 9 DE me Example Find all roots of xr 77 4 Og bar 4 Se 6 Step 1 Fix the re nas to two decimal places and then choose the Se Polida aa from the SOLVE choose list SEE SOLVE ANCHO N tA Head See COEFFICIENT C AM w Al AU I Mog Sener ENTER COEFFICIENTS OF PRESS SOLVE EHTA ee ee Ee Step 2 Enter the coefficients of the polynomial beginning with the coefficient of the highest degree Press between each coefficient 4 1 PC 1 GPC 2 GPC 5 CE GPO 3 GPO 6 CL Ree COLE AMH M tA LFA See COEFFICIENT AN a Al ADD t 1 1 2 5 3 6 ROOTS ENTER ROOTS OR PRESS SOLVE T tL G Step 3 Solve the polynomial BAS SOLVE AMN A AALS Se COEFFICIENTS E AM in eo AO ENTER ROOTS OF PRESS SOLVE EDIT SME Solving Equations 5 9 Step 4 Exit the SOLVE application and view the results on the Stack NXT GES or l Roots CA 14 1 896 CH io THe Ff af c fe 5 10 Solving Equations Lesson 20 Solving a System of Linear Equations The HP 48 can solve a system of lin
8. A Hi 1 RESULT Seti tee aoe CHOOSE RESULT TYPE jp CHOOSE E OK 7 4 Calculus Statistics and Advanced Mathematics Step 4 Change the RESULT field to Humeric if necessary if necessary EES INTEGRATE Sees EXPR 2 H GER S445 WAR H LO amp HE RESULT RLE DT pg ett NUMEER FORMAT Sto CHOOSE RESULT TYPE Eee CL ee ee ee Step 5 When you want to perform a numeric integration the number of digits in current display mode is used to estimate an accuracy factor Higher accuracy factors require more calculation time Sid y Bos the highest accuracy factor and Fix 0 Sci amp or Eng amp the lowest Change to Sci and ene the pa ion Wt Ia ae J displayed 1 4 SHABREH Press MODES oF MT STD to restore Std display mode Example Evaluate th a X X dX 0 If you ve already used the variable a in another example you need to purge a poo continuing Press Step 1 Select Imtecarate and enter the meena RESULT Symbol i ic ENTER EXPRESSION EDIT CHOO ANCL Ok Calculus Statistics and Advanced Mathematics 7 5 Step 2 Enter the variable and limits of integration X ENTER Ee INTEGRATE 2 ee 3 La d 0 ENTER ERPE a 2E4 SS WAR o LO 5 H a RESULT Retail tee ee ee OA CHOOSE RESULT TYPE Pp CHODS ANCL OK Step 3 Turn on symbolic mode if necessary and evaluate the integral _ if necessary RAG co
9. 192 255 Sees GMAAAARRGEEEELE RI PAHOGASaX Sus bE Saag gSsPSeGGG1 171 dAsc6satsnoGogp ys KEY coho MUM 192 ee ee ee ee ee or oF EE to switch between the four screens Press the arrow keys to move the cursor around within a screen Notice that the alpha keyboard equivalents for the highlighted character are displayed next to KEY display at the bottom of the Once you ve highlighted a desired character pressing ECHE places the highlighted character in the command line Press CANCEL to exit the CHARS feature 2 8 Introducing the HP 48 Lesson 4 Using Menus The HP 48 employs 49 keys to access over a thousand operations This greatly extended keyboard is due primarily to the use of menus A menu is a set of operations defined for the six white menu keys on the top row of the keyboard The current operations are described by the six menu labels on the bottom row of the display Menu labels oO D 3 D i Menu keys Some menu labels are displayed with a small tab attached to the top left hand side of the label These tabbed operations do not act on data they are navigational simply leading to a different menu or application The Key Menus often contain more than six operations When they do they have multiple pages The NXT key pune ui ae next nd of the current menu pak A iunat nA iS HOG Ei lonon menu O
10. 7 14 Calculus Statistics and Advanced Mathematics This chapter shows you how to gt Transfer objects between two HP 48s using the infrared port gt Find and use an equation set from the built in Equation Library Attach detach and use libraries Special Features 8 1 A a py tt Rt Rt Lesson 35 Transferring Objects Via Infrared The HP 48 has both wired and infrared serial input output ports to allow you to transfer objects to and from other devi LS computers and other HP 48s serial transfer requires the optional Serial Interface Cable see your HP dealer Infrared transfer between two HP 48s can be accomplished quickly and easily without any additional equipment To transfer an object from one HP 48 to another 1 Line up the infrared ports by lining up the 4 marks near the Hewlett Packard logo just above the display The calculators should be no farther apart than 2 inches S Davo yc 4157 35H HEWLETT PACKGAD Ca 2 Receiver m Change to the directory where the new object is to be stored Press 3 Sender am He 45 from the menu and press m Press m Select o HF 45 from the menu and press a Type or AEG os the name of the object to be et into the MATE field m Press SEHD 8 2 Special Features Lesson 36 Using an Equation Set from the Equation Library The Equation Library is a collection of equations and commands that enable you to solve simple sci
11. ENTER 1 ENTER M AR 1 Y MEM 5 1 H TICE BES V TICK TA yw PIHELS ENTER HORIZONTAL TICK SPACING Ts ee Ee ee ee Step 4 Set the option changes erase the picture display and draw the plot feet gaea eas saa geeen FLD Ee a ee Calculus Statistics and Advanced Mathematics 7 13 Lesson 34 Linear Algebra The HP 48 includes a number of useful linear algebra commands in the MTH MATRIX command menu You will find commands for finding the determinant inverse transpose rank trace spectral radius and norm condition number eigenvalues and eigenvectors of a matrix Additionally you can compute the reduced row echelon form of a matrix and decompose appropriate matrices using any of several different decompositions LU LQ QR Schur and single value While you should consult chapter 14 of the HP 48G Series User s Guide for details about these commands try the following example as a sample Wxample Find the eigenvalues and eigenvectors of matrix A 2 2 3 Step 1 Using the Matrix Writer enter matrix A onto the stack ENTER 2 ENTER 3 7 a7 CENTER V ENTER ENTER praetor we Mt er Step 2 Find the eigenvectors and eigenvalues of the matrix MTH 20 NXT zE cs 1 51 2a l 3 5 3 RED EGY EGVL MAGMAG gt The eigenvectors are shown on level 2 and the eigenvalues on level 1 The related command EGVL computes only the eigenvalues
12. O FINAL amp SOLN yY INIT k FINAL Pa e TOL HOH STEP DIE _ STIFF PRESS SOLVE FOR FINAL SOLN VALUE EMT ee eee Step 5 Exit the SOLVE application and view the solution on the stack NXT 2 GELS HEHEHE CHB VECTR EEE E me Example Plot the solution of the previous differential equation Y with respect to time T from t 0 tot 8 Step 1 Open the PLOT application and select the Diff Ex plot type Notice that as a shortcut for choosing a plot type typing brings up the next or only plot type beginning with the letter D SSS BLOT YP TISFCT VY See TYPE EPG pina a Peg F lec i 2 2 Yea INDEP IMIT amp FINAL 5 SOLM Y INIT _ STIFF CHOOSE TYPE OF PLOT ee GS ee ee ERASE DRAH Step 2 The proper equation is still in the F field Change the final value to 8 if necessary DOAA ENTER Se BLOT A TISPCT 49 See TYPE Diff Eq a Deg F E Lt 23 2 yam INDEP 7 IMIT amp FINAL SOLN BQ INIT A _ STIFF ENTER OLUTION VAR WARE ELITA e OPTS ERASE DRAH 7 12 Calculus Statistics and Advanced Mathematics Step 3 Change to the Plot Options form to set the tolerance 10 the horizontal plotting range 1 to amp and the vertical plotting range 0 5 to 1 Other option values are the same as the defaults for this example 16 eo ro TOL aa STEP AMES D Lee Da ENTER 8 ENTER ie ae z Ter D It zat 5
13. OK Step 2 Enter the function HO XC 3HO2 XO HO O4 INDEP mi cae MEF 6 5 6 5 _AUTOSCALE V VIEH 3 1 SB ENTER FUNCTIONS TO PLOT EDIT os a Oe ERASE DRAH Step 3 Erase the blackboard the PICTURE display and draw the function enor tx 73 TRACE FCM EDIT CaNCL Plotting Equations and Analyzing Graphs 6 13 Step 4 You can see that there are three real roots where the plot crosses the z axis but you cannot see the whole function very well Zoom the vertical scale out to display the plot better Vertical Zoom Out is one of 15 different kinds of zoom available to you Sear a at PENET p pem CE RELEE o NXT p e EEEE 200M tht TRACE FCM EDIT TANEL Step J Find a root Once the HP 48 finds a root the cursor will be positioned as close to the root as possible the calculated value will be shown on the display and a tagged copy of the root placed on the Stack a RAT Step 6 Find a different root Move the cursor over towards the left most root 4 as needed to redisplay the menu de p ErP LO En aP E ee ROOT 2 5104297636 7 Find the third root gt as needed to redisplay the menu Step PETE we 3 aar Eoen oe Save ROOT 204160529092 6 14 Plotting Equations and Analyzing Graphs Lesson 27 Finding Slope Tangents and Critical Points The following examples show you other kinds of analysis you can perform o
14. PLOT or SOLVE If you notice that the screen of your HP 48 doesn t match the screen shown in the example simply correct your screen and then continue with the keystrokes given in the example a Dont panic You can turn the HP 48 off at any time when you turn 1t on again it ll be ready to continue where you left off If you run into trouble see chapter 10 If Things Go Wrong at the end of this manual 1 2 Start Here Lesson 1 Getting Ready Here are a few things to do to prepare the HP 48 before you begin Turning the HP 48 On and Off gt Press to turn the machine on The key is highlighted in the diagram at the right key is a shafted Boe Si shift Ic lt 3 to turn it off The key the green gt Press p version of the The calculator will also turn itself off if you haven t used it for 10 consecutive minutes in order to preserve its batteries Unlike some calculators or computers you may have used the HP 48 can be turned off at any time without risking data loss Adjusting the Display Contrast b With the calculator on hold down the key and press to darken or to lighten the display Preparing the Built in Examples 1 Hold down qa highlighted in the diagram at the right 1 and while holding it press in sequence COS r Jp Geccae COO CMmMme Ca Ce PRG so that you type in the word peeese ry gh ee OCC rERIH at the bottom of the display When
15. Soon between two HP 48s or between S Printu te Doc wee ad ci Transfer joosas the HP 48 and a computer l H sie j pe CANE Using External Programs gt t The LIBRARY application helps log Qoom i a HOME 3 porono you manage and retrieve external Poono 3 S006 programs and other objects stored 3 GODT a opopo on plug in cards or in backup 1 BOOS CLEE memory Using Built In Equations gt The EQ LIB application allows you to select from over 300 Sesese built in equations and use them to Forces and Eneray GOOI Gases pooso solve problems Heat Transfer 1 soseq Esl SENGLIUNITS A Utility Environments There are four special interactive environments that help you to manage and organize your work and control the way your calculator functions You will use these environments independently and in combination with the applications Editing Previously Created Objects The EDIT environment is an Qooocno z 050000 expanded version of the command S Gooh Ga yi f Sa i Byers 3 Lee e and is used to edit objects E E TOET E8000 line and is used to edit o jects 466 HOPG 44 BANS P42 RAPES ENED scoop after they ve been entered onto G OOG OOS the stack 2 14 Introducing the HP 48 Setting Calculator Modes p gt You visited MODES in lesson 1 It is used to set the various calculator modes and to change
16. as soon as you begin typing in an object it appears below the stack on a line of its own This line is the command line Actually the command line is more than one line It expands as needed to accommodate objects of any size Objects in the process of being created stay on the command line until you press ENTER at which point they are placed onto the stack and the command line disappears Making typing errors while creating numbers and other objects is a common problem but one that is easily fixed After all the command line is designed to be a preliminary work area where you can create edit or refine an object before you decide to enter it thus declaring it ready As long as you see the command line you can edit whatever you re in the process of creating Here s a list of the editing keys and what they do CANCEL Erases the entire Command Line causing it to disappear until you start typing again Moves the cursor to the left Moves the cursor to the right Moves the cursor to the line above for objects requiring more than one line Moves the cursor to the line below for objects requiring more than one line Erases the character to the left of the cursor JHA 0 BMA L Erases the character underneath the blinking cursor Each of these keys are editing keys only while you are using the command line At other times each key performs the action printed above it W hen there s no command line
17. do they kick it How high is the ball halfway through its flight How far could they drop kick the ball if they used the same kicking velocity but changed the elevation angle to 30 degrees Ignore the effects of drag on the ball Step 1 Start solving the problem ooh RAI 8 4 Special Features Step 2 Enter the known values Define r0 and y0 as 0 Notice that the menu labels turn black as you store values vl 4 2 1 Step 3 Solve for the velocity vo Notice that pressing the left shifted version of a variable s menu key causes the HP 48 to solve for it esc NS nec ul T uA ao d4 ys EENE ae Step 4 Recall the range R divide by 2 to get the halfway distance and enter that as the z coordinate Notice that pressing the right shifted version of a variable s menu key causes the HP 48 to recall its value to the stack The small square next to the on the menu label indicates that it was used in the previous calculation 22 OD GOR WAP z5 44m5 zo ono o Yo ENAN oo Step 5 Solve for the height y Notice that the HP 48 finds values for other variables as needed shown by the small squares in order to solve for the specified variable aa pasi 19 37 y 2 oles I EEE ae Special Features 8 5 Step 6 Enter the new value for the elevation angle 30 degrees store the previously computed initial velocity vg and then solve for R 30 BE l Re ar lb m 8 6 Spec
18. finished popon O COMO COCO sees the a key CEEE 2 Press ENTER The TEACH command resets the calculator modes to their default values and loads a number of example functions data sets and other objects that are used in some of the examples in the HP 48G Series Quick Start Guide and the HP 48G Series User s Guide Whenever you wish to remove all of the objects that TEACH created type LLTERCH holding down the a key as in the example above and then press ENTER Start Here 1 3 setting the Time and Date 6 1 Open the TIME application See CET TIME AND DATE SSRA TIME Me 45 57 AM DATE ie 3 94 MeDe Y choose m y dees S ENTER Aak EotT cnoo ANL Ik Type the hour minutes and seconds pressing after each optional If you want the clock to report the time using 24 hour format press until 24 hr is displayed Press to advance the highlight and then type the day month and year pressing after each optional If you want the clock to report the date using e format press ga until amp Pia 1s displayed Press GE once everything is set as you ee Setting the Beeper Clock and Fraction Mark 1 Open the MODES utility wt 1 4 SESE CALCULATOR MODES Sees HUMBER FORMAT Bann ANGLE MEASURE Degrees COORD SYSTEM Rectangular y BEEP ELOK FML CHOOSE MUMEER DISPLAY FORMAT He A FLAG tANiL DE optional If you want to
19. or complex matrices Lessons 20 and 34 contain worked examples using the Matrix Writer Samples EDIT VEC W EHI HIDA GOs m GI O1 iaie oF KE 3 1 2 4 2 6 4 EnIT EHD AID Introducing the HP 48 2 11 Creating Pictures FICTURE PICTURE provides access to the HP 48 graphics jooSeoge T HAPS opocod blackboard called PICT Graphs are plotted and E TROD i i i eee freehand drawings are created and displayed on this acooo blackboard See chapter 6 of this guide or chapters 22 24 of the HP 48G Series User s Guide for more about plotting See chapter 9 of the HP 48G Series User s Guide for more about freehand drawing Samples 4 a a E a K 5 Kz K l Kez Application Environments Each of these applications facilitates your interaction with a particular kind of problem or activity Some use input forms and choose lists that prompt you for the necessary information and conveniently display your options To peek at an application press the appropriate keys to exit from a form or list to the stack display press CANCEL solving Equations The choose list in SOLVE allows you to select the kind of problem that you want to solve ry pa as m Solve equation Solus diff pgn Solve poly Solwe lim sus Solwe finance aed en Ea ee ee ee ANE EK 2 12 Introducing the HP 48 Plottin
20. sometime after you ve created it This too can be easily accomplished using the Variable Browser Example Store the text strmg HP 48SX under the name TXT Then change it to HP 48GX updating TXT in the process Step I Open the Variable Browser and select CHERS SHEH EHEH VARIABLE eee DE JECT ji E aS MAME HRELTORY ENTER MEH DEJECT EMT CHOOS CANEL DK Step 2 Enter the text string and then the name FXT Press THE to complete the process Notice that two different melee for alpha entry are shown P HP ASS X SORUECTS IN HOME EXAMPLES 13 TATE SHE ABSA a hold TXT release PRGS DIR XTILE ee Step 3 Bring the stored object into the editing environment EDET ERLT HP 4855 O T Too aafo Step 4 Move the cursor to the letter S then delete it and insert the letter G 6 times DEL a G HP 464 Gi as ee CT Faad Step 3 Rca Rens SSQEWECTS IM HOME EXAMPLES 338 ENTER TAT CHP 436 PROS DIR xTILE Gin PE Oe m Pm T m 3 im Tt Save the changes and return to the Variable Browser 4 8 Understanding and Using Memory The Variable Browser also allows you to purge variables several at a time if you wish so that unneeded variables don t occupy valuable memory space Example Return to the HOME directory and purge the variables tl and t2 Step 1 Return to the HOME directory cHOCS OK Sp oF ec k en p1 1 En EXAMPL Ik
21. to redisplay the menu a ee ee or ee er TTT ee bed PP EP be Magn 3 305 8 Sant Son t s 200M C840 TRACE FEN EDIT TANEL 6 18 Plotting Equations and Analyzing Graphs This chapter shows you a few examples of the high powered mathematics of which the HP 48 is capable The examples you ll explore are gt Finding symbolic derivatives gt Finding symbolic integrals gt Entering and summarizing data Performing a regression analysis on a set of data gt Solving the initial value problem for a first order differential equation gt Plotting a phase plane for a differential equation gt Finding the eigenvalues of a matrix Calculus Statistics and Advanced Mathematics 7 1 Lesson 29 Finding Derivatives Example Find the slope of f x 52x 2 at eS ac Step I Select Differentiate from the SYMBOLIC menu Sees DIFFERENTIATE Se eee Eurr WAR RESULT Symbolic ENTER EXPRESSION EDIT CHOOS STEP CANCL OK Step 2 Enter the expression 5 a X 07 2 e n E SEN WAR RESULT Symbolic ENTER EXPRESSION EDIT CHOOS STEP CAMEL Step 3 Enter the variable of differentiation X Pe DIFFERENTIATE ees EXPR Bahoga WAR i RESULT SYS elnp ee CHOOSE RESULT TYPE CMOS STEP CANCL OK Step 4 Berges you want a numerical oe ative make sure that Murai ic is displayed in the FESHI field if necessary EEE DIFFERENTIATE See
22. turn the beeper off move the cursor to the EEFEE field and press EHE so that the check mark disappears optional If you want to continuously display the date an time on the main calculator screen move the cursor to the ELITE field and press THE so ihat the check mark appears optional If you want to use the comma instead of a decimal ae as 3 the fraction mark move the cursor to the FM field and press E so that the check mark appears Ones you aan set the options as you wish press 55 Start Here This chapter provides a brief introduction to the HP 48 an overview of its design operating fundamentals and far ranging mathematical power Specifically you will learn how to gt gt Use the stack and command line Enter mathematical objects numbers equations matrices units Enter text including non English and mathematical characters ea a s Correct input errors and edit objects Use menus and navigate within them Explore the various user friendly environments of the HP 48 Introducing the HP 48 2 1 The mathematical and scientific disciplines use a wide variety of objects in the process of describing and solving problems real numbers sometimes with units attached complex numbers vectors matrices functions variables equations plots of many kinds points sequences words and sentences programs and so forth The HP 48 can use all of these objects and more Concep
23. CT iamen eed So ber Sa ro So ee WAHE _ DIRECTORY ENTER NEW DEJECT RESET CALC TYPES CAMEL DK Step 4 Enter the name 42 and press GE You will see t with its contents at the top of the cal variable list MOCT 2 ENTER BR EDIT CHODS 4 CHE NEH COPY MOVE Step 5 Exit the Variable Browser by pressing CANCEL Understanding and Using Memory 4 5 Lesson 14 Organizing Variables Whenever a variable is created it is put into the current directory Directories let you organize variables into meaningful collections They allow you to work with only with one collection of variables rather than all variables at once Only one directory at a time is active or current The current directory is shown in the stack display in the line above the stack levels At the moment it shows that HOME is the current directory Managing and organizing the contents of the current directory is the primary purpose of the Variable Browser Example Review the contents of the current directory acne DE JECTS IN HOME See tes Tira a eo HORS ar ti 1 41421356237 ESAMNPLES DIF PRGS then A and as needed EDIT CHOOS CHE MEME COPY MOVE If the particular variable you re seeking is not in the current directory you can always switch to a different directory and look for it there Example Display the contents of the EXANFLES directory This directory and its contents were created by
24. E V VER 3 ENTER FUNCTIONS TO PLOT EDIT CHODE SOPTA ERASE DRAH Step 2 Enter the function into the Ef field O Git X ENTER Setanta ei Re my aie peee x eter TYPE Funct ion a neg EG SINCS INDEP H VIEk 6 5 6 5 _AUTOSCALE V VEW 3 1 3 2 ENTER INDEPENDENT VAR MAME EDIT OPTS ERASE DRAH 6 2 Plotting Equations and Analyzing Graphs Step 3 The aod aeons variable and its default range in H E need no changing To let the calculator eae scale the vertical axis for you make sure that there is a check mark in the ALTO field V 4 CHE SES BL T See TYPE Funct ion Et MSIHCwa INDEP x H WEM 6 5 6 5 FUAUTOSCALE V WER Auto AUTOSCALE VERTICAL PLOT RANGE ne Be v CHk OPTS ERASE DRAH Step 4 Change the angle mode from Degrees to Radi ans 64 G CHOOSE V ENTER TYRE Funct ion EQ SINGH INDEP H HEM 6 5 6 5 YAUTOSCALE Y VIEH Aut c CHOOSE ANGLE MEASURE a ee Oe ERASE DRAH Step 5 Erase any previous plots and draw the new one he oe ETHECEA TRACE FCM EDIT CARCEL Return to the PLOT application by pressing CANCEL Plotting Equations and Analyzing Graphs 6 3 Lesson 22 Modifying the Display of a Plot There are several display options that are set on the PLOT OPTIONS screen The default settings are shown in the figures below ee PLOT OPTIONS See INDEP Lo DF 1t we DF lt vf AMES w CONNECT
25. ER VECTRA MATR LIZT HYP REAL ERSE Step 2 Get the REAL submenu find the command and calculate 15 of 145 Example Find 6 6 factorial The command is in the probability MTH PROB menu Step 1 Clear the stack and key in 6 Then get the MTH PROB menu 6 MTH NXT ERGE G Step 2 Execute the command to find 6 Arithmetic 3 7 Lesson 8 Arithmetic with Fractions Fractions whether they are proper improper or mixed can be represented on the HP 48 as algebraic expressions Use the Equation Writer to enter fractions Example Add 5 and 13 12 Step 1 Begin the Equation Writer and type in the first fraction 0 COME FERM RAND Roe Step 2 Type in the second fraction Note that when you enter a mixed fraction you must include the between the integer and fractional parts 14 3G 4 COME PERM RAND RBZ Step 3 Evaluate the expression It will display as a decimal l 6666666667 EOmTERAINARA Step 4 Convert the decimal to a fraction DEAE NXT i 13 6 PMATeMAT e sem 1 JAPPLY Foie 3 8 Arithmetic Lesson 9 Arithmetic with symbols Arithmetic using symbolic variables is very much like arithmetic using numbers You can make symbolic calculations on the stack the same way you make numeric calculations except you use algebraic objects and tick mark delimiters instead of just numbers Example Use symbolic math
26. EXPR Sako 7h Wak Si RESULT R E Ul ae eee VALUE CHOOSE RESULT TYPE jo CHOOS STEP CANCEL OK 7 2 Calculus Statistics and Advanced Mathematics Step 5 Enter the value at which you are evaluating the derivative and calculate F 5 ENTER 1 29 WECTRIMATR LIST HYP REAL BASE ce 6 Example Find the symbolic derivative of f x 5x Step L Reselect Differentiate from the SYMBOLIC menu and repeat the previous example making sure to set the RESULTS field to Sumboabic ENTER eee DIFFERENTIATE See Jhd GX Gite EXPR TEK Z i i WAR if necessary REZULT AETI etme es Em CHOOSE RESULT TYPE CHODS STEP CAMCL OK Step 2 Calculate the symbolic derivative Le Pelee tbr AOE VECTALMATR LIST HYP REAL BASE Calculus Statistics and Advanced Mathematics 7 3 The examples in this lesson illustrate how to find numerical and symbolic integrals Example Evaluate 1 J 2X 6 Xf 5 dX 0 Step 1 Select Integrate from the SYMBOLIC menu E INTEGRATE Eee aoa o oo WAR LO HI RESULT Symbolic ENTER EXPRESSION EDIT jCHOOS cANiL OK Step 2 Enter the integrand D EQUATION 2 CX 6 XK OQ am B RESULT Symbolic ENTER EXPRESSION EDIT CHOOS foo HEL OR Step 3 Enter the variable and limits of integration MOX ENTER 0 ENTER ENTER Sees INTEGRATE ase EXPR Dee Be4 445 Wak H LO
27. SIMULT STEP Dlt _ PINES H TICK 6 oV TIK 6A PINELS ENTER INDEPENDENT YAR MAME EMIT es ee Dk The Plot Options Screen The options available on this allow you to b Set a plotting domain 1 0 to HI that is different from the displayed horizontal view This is particularly useful with POLAR plots gt Choose to display the plotted function with e CONHET or without _ EGH HHECT connecting lines between sample points gt Choose to display the plots of multiple functions either simultaneously SIMULT or sequentially _ SIMULT Choose to display the plotted function s with RHES or without _ SES the coordinate axes Choose the step size STEF between Sauer ee during plotting in either pixels Iti idle mark e FISELS or coordinate units FISELS gt Choose your own spacing for the tick marks on the axes H TICK and TICE in either pixels e F TMEL S or coordinate units o FIXELS ae ae to the main plot screen after changing some options press or ENTER Press CAMEL or CANCEL if you don t want A save ahs changes 6 4 Plotting Equations and Analyzing Graphs Lesson 23 Plotting Several Functions To plot several eon on the same display you must enter a list of functions in the Ef field of the Plot screen The easiest approach is to create and name ach function and then use the Variable Browser to select which group to plot The following example uses function
28. Select Solve diff eq m the SOLVE application ENTER Ree COLE YCTISECT t See ee INDEP INIT G FINAL G 5 SOLA YO INIT H FIHAL ToL GAAL STEP DELE STIFF ENTER FUNCTIOW OF INDEP AME SOLH EDIT CHOOS oo SINIT EDLYVE Step 2 Enter the right hand expression arn 2Y into F Notice that the variables appear in the menu as soon as you begin the command line so that you can use them as typing aids uHe wak eee SOLVE YC TISF CT 1 A oes yr F t Fa Ca a F Eada wr j 2 Q 2 2 oT ae emi ciao E INDEP T INIT ERR FINAL S ENTER T ENTER ENTER SOLN Y INIT FINAL TOL AGAI STEP DEFIE STIFF EMTER IMITIAL INDEP VAR VALUE EDIT pe INIT SOLVE Step 3 Check the remaining fields You are using the default values for the solution y variable name as well as for the initial values 2 and amp You can use the default value for BTEF the iterative step size as well Change the final value for T to amp and the tolerance to E F em 8 ENTER SES SOLVE VCTISPCT Y See 1 7_ ENTER F IA LIT gaye SOLM Y IMIT amp FINAL TOL MH STEP ERRA _ STIFF ENTER INITIAL STEP IZE EBIT p INIT SOLVE Caiculus Statistics and Advanced Mathematics 7 11 Step 4 Highlight the FINAL seo amg ok opporre tenet EE Sowme 8 ove Sane donee 3 Fave solution field and solve the problem eS SOLVE YC TISPCT V 1 Ses F eC T 2r a INDEP T INIT
29. THT aT EMIT CHOOS CHE NEH COPY MOVE Step 2 Select the variables to be purged by placing a check mark in front of each of them xe F aR P EE eee EJECTS IM HORE 1 fti2 1 r r320502079r tl 1 414215356237 ESAMPLES DIF TAT a EDIT CHOO2 CHE MEM COPY HOVE Step 3 Purge the selected variables from memory NXT PURE SSCS ORIECTS IM HOME IIS EXAMPLES DIR THT ORCL PURG SIZE JAMEL OK Step 4 Exit the Variable Browser by pressing CANCEL Understanding and Using Memory 4 9 Lesson 16 Using Variables in Calculations The variables in the current directory are conveniently available to be used in calculations and expressions Pressing the key brings up a menu of the variables in the current directory As with all menus the and keys allow you move through the variables one page at a time forwards and backwards respectively Example Store the width and length of a 3 by 5 rectangle in W and L then use those values to find the area Step 1 Enter and store the width and length Notice that STO can 5 be used to store an object in a variable without using the Variable Browser Press when you ve finished to bring up the menu of variables in the current directory a ee a 3 O L 5 W VAR Step 2 Recall the two values to the stack using their variable names EvaM ft Step 3 Multiply to find the area
30. a library from memory 1 Make sure that the library is no longer attached to any directory Detach it if necessary 2 Type in the library identifier port number for the library you want to remove and pices ENTER ENTER Y ot 3 wad MEMORY J to remove any tempor ary references to 8 8 Special Features A library is a collection of pre programmed commands that act as extensions to the built in command set The HP 48 does not have the built in capacity to create libraries but it can install and use libraries that have been created elsewhere on other computers and transferred to the HP 48 If you have an HP 48G model you must download a library into your machine using either the infrared port from another HP 48 or the serial port from a personal computer Refer to chapter 27 of HP 48G Series User s Guide for details about serial port transfer If you have an HP 48GX model you have the additional option of installing a plug in card containing the library into one of the two expansion card slots Refer to chapter 28 of HP 48G Serves User s Guide for more details about plug in cards Libraries like any other object can be placed on the stack or stored in user memory However libraries cannot be used while stored on the stack or in user memory To use a library it must be a Stored in port memory Port 0 for the HP 48G or Ports 0 32 for the HP 48GX All libraries that are distributed on plug in cards are
31. ack to view the value of the expression labeled Expr HOME EXAMPLES EQHS 4 J vt 1 5 e oy 3 BBRRRRRRREL l Expr 133333333333 CE e E E a eee Because the value of the expression is not close to zero in all likelihood there is a discontinuity at z 3 You can confirm this by substituting 3 into the original equation and observing that it generates denominators equal to zero a sign of a potential discontinuity In general whenever you expect multiple solutions you ll probably save yourself some time and effort by plotting the expression and using the graphical analysis tools instead of the SOLVE application see lesson 26 for an example Press SOLVE GK to return to the SOLVE application and try solving another equation this time keying it in yourself Example Find the measure in degrees of the largest angle in a triangle with sides of 4 7 and 9 with as the largest angle and c as the largest side Use the Law of Cosines esa h 2ab cosh Solving Equations 5 5 Step l Move the highlight to the Et field if necessary and enter JF or selecting it the equation 0 can be typed using amp from CHARS sesame SOLVE EQUATION See Eo co cee 2 S 6 p E AARS 5 EMTER VALLE OF PRESS SOLVE EDIT sf ARS SOLVE Step 2 Store the known values ENTER VALUE OR PRESS SOLVE ees Cris as ST Step 3 Solve for the angl
32. already in port memory whenever the card is installed in its slot Libraries that are downloaded into the current directory must be moved into port memory by you a Attached to a directory Most libraries are self attaching that 1s they automatically attach themselves to the HOME directory as soon as you turn on the HP 48 again after installing them in port memory Others will need to be explicitly attached by you To store a library into port memory manually _ Put the library object on the stack Note its number and name _ Enter the port number for storing the library 0 1 2 32 _ Press STO Optional Purge the original library object from user memory a Special Features 8 7 Whenever you run into problems either following examples in this manual or solving your own problems you can use these hints to get back on track Lesson 38 Error Messages The HP 48 indicates that it can t do something by sounding a beep if the beeper is enabled and displaying a error message A complete list of these messages and their meanings can be found in Appendix B of the HP 48G Series User s Guide Clear the message by pressing CANCEL or any other key Here are the meanings of four of the more common error messages Bad Argument Tupe You tried to do something to or with an ae thes isn t valid ee dal kind of operation For example dividing by a text string causes this error ae 7 Pao Pen Mroument
33. ample Using the EquationWriter find a real number approximation for the following expression Step 1 Create the large parenthetical expression Arithmetic 3 5 rs IMATE LIST HYP REAL EASE Step 2 Advance the cursor until it is outside of the closing parenthesis Currently it is buried within layers of subexpressions square roots and quotients gt 8 times gt J as a shortcut Step 3 Finish entering the expression Notice that you begin a numerator with more than one term by using the A key The formula is displayed on stack level 1 in its one line form which is the form in which you must enter it if you didnt have the Equation Writer to help you 2n Ga 1G 1b C2134 gt 4 amp or 11 Eee 123 ievaee ENTER VECTRIMATR List HYP REAL EASE Step 4 Make a copy of the expression by entering it again Then evaluate the copy ef IELAS 2 014 Coec l bWrdotol tr WECTR MATE List HYP REAL BASE 3 6 Arithmetic Functions The HP 48 has many more math functions than can be fit onto the keyboard even using the two shift keys The others are collected and organized into menus that you can access using the key in the second row of the keyboard Example Find 15 percent of 145 The command is in the MTH REAL menu Step 1 Clear the stack and enter 145 and 15 Then get the MTH menu CLEAR ie 145 145 ENTER 15 J a ENT
34. an create an animation of them to help you visualize a moving slice through the surface Shown F x4 4x7y yt Gridmap Plots a rectilinear grid as it is distorted under the mapping of a complex valued function F x iy Shown F sin x 1y Parametric Surface Plots a perspective wireframe model of a parametrized surface F u v r u vj y u vj z u vk Shown z u v sin 3x ty y t v 5y z u v cos 3z MLE EE Sa bem te oa e TE on 1 oh x Pg i fe I ie ai x i N fem 4 I ie Lv filam fA Pree AT EE eae 4 A t i Ta pa ty man Bka h mh mo 6 12 Plotting Equations and Analyzing Graphs Ma i l P o ry ae itar n ie F a A oF EE eer EL it HE eee EVs Lesson 26 Finding Roots Graphically In Lesson 17 you found all of the roots of a polynomial using the SOLVE application This lesson shows you how to use the special analytic tools in the PICTURE environment to find the roots of a function visually as well as search for other information about a function Example Plot the function X X4 5X3 2N 24 NX 4 and find its real roots Step 1 Begin the PLOT application and reset the plot display options ee THRE aee ion Er E uae vets yyh 27 3 I INDEP bs H VIEW 6 5 6 amp _AUTOSCALE Y EM 3 1 3 2 ENTER FUMCTIONCS TO PLOT RESET CALC TYPES CAMEL
35. anced calculator However when considering its memory it is better to think of it as a computer The basic unit of storage on a desktop computer is the named file On the HP 48 the basic unit of storage is the named object or variable Unnamed objects can exist on the stack but like computer files must be named in order to be saved Envision a variable as a named storage area containing an object Variables reflecting the objects they contain vary widely in both size and type Like stored computer files variables are organized into directories file folders that make it convenient to find them later Example Determine the amount of memory in bytes currently available to store HP 48 variables mou BOC UAE SCL Pcie bees Variables on the HP 48 are stored in SYSRAM or on a plug in card in the case of the expandable HP 48 models SYSRAM memory is like a desktop computer s Random Access Memory RAM except that it is ron volatile it isn t erased when the HP 48 is turned off The figure below shows how the HP 48 divides up the SYSRAM and the type of variables in parentheses stored in each section Partitions move depending on current allocation of memory system Available Memory system I F f 1 i I t t f f i H H t Schematic view of SYSRAM in the HP 48 4 2 Understanding and Using Memory Notice that there are several kinds of variables indicated in the diagram a System va
36. bles that you wish to compare CPI and PPI are located in columns and 2 of MDAT respec tiv ely SO make sure that COL contains and Change the regression model type to Sees FIT DATA Se IDAT CE 3 1 3 2 Cu H COL 1 Y COL 2 MODEL ee aa CHOOSE STATISTICAL MODEL a CS ee tANiL DE Calculus Statistics and Advanced Mathematics 7 9 Step 3 Enter the target value for CPI v variable and predict the PPI value y variable using the best fitting model Note that the HP 48 determined that an Exponential model has the best fit i e the highest correlation coefficient of any of the four models PRED A 8 5 SET Re PREDICT VALUES Seer sr LE Sak ee ak Lan H COL 9 COL 2 MOEL Exponential Fit t EBCEESG A ENTER DEP VALUE OR PRESS PRED EDIT foe BRED Step 4 Put the computed regression model along with the correlation coefficient and covariance onto the stack CANCEL ARo BAG KIME LL 34613092 e bel epi eid peg L 2lssebon2ot ECTRIMATR LIST HYP REAL EASE 7 10 Calculus Statistics and Advanced Mathematics Lesson 33 Differential Equations The examples in this lesson show you how to solve an initial value problem for a first order differential equation and how to plot a phase plane solution of a differential equation Example Find y t for t 8 where Y T gt OY and 0 0 Find the answer to within an error tolerance of 10 Step 1
37. card box The object on the first card is said to be on stack level 1 the object on the second card is on stack level 2 and so forth The stack can contain any number of objects from zero to as many as available memory permits The main display of the HP 48 is the stack display It is merely a window showing you a portion of the stack at a time aE SS Stack Display Window Envisioning the Stack Objects enter and leave the stack at level 1 When you enter a new object you place it in the front of the card box stack level 1 thereby pushing objects already in the box farther to the back increasing their stack levels each by one in the process Introducing the HP 48 2 3 Example Enter some objects onto the stack 39 3 1248 4 5 7 99479 Step 1 Enter the first number 39 3 HOMIE q J 39 3 MECTRIMATR LIST HYP REAL EASE Step 2 Type the delimiters 4 for the list as Ea it VECTR MATR LIST HYF REAL EASE Step 3 Type in the contents of the list separating each with a space O21 GOs 39 3 Ll 2 4 83 WECTEIMATRT CTT WET Eat TEREE Step 4 Enter the list Step 5 Enter the remaining objects HOME 3 4 oe a ee ee J Ch ci r EERE WECTRIMATR LIST HYP REAL EASE 2 4 Introducing the HP 48 Editing an Object in the Command Line You probably noticed that
38. ccasionally you will want to quickly oscillate between two different menus Pressing p gt immediately before the Pen one brings up the menu displayed Introducing the HP 48 2 9 Lesson 5 A Brief Tour of the HP 48 As compact and powerful as the stack is for manipulating objects there are many kinds of problem solving situations which demand special working environments tailored to specific needs This lesson takes you on a short tour of the various user friendly environments that comprise the HP 48 Entry Environments You have already seen the main entry environment on the HP 48 the command line However among the mathematical objects handled by the HP 48 are objects whose natural format is not well suited to the command line display Creating Equations Algebraic equations and expressions can be entered as you are accustomed to seeing them using a special entry environment the Equation Writer The EquationWriter is handy for writing any equation in a familiar form see lesson 6 for a worked example x 6 l 1 5 T 19 ry l T 4 R ae i TnL 5 0 1 19 4 Po We WECTRIMATE HYP PROE REAL re 2s A a pitiy r y 5 MECTRIMATE HVP_ PROE REAL BASE 2 10 Introducing the HP 48 Creating Matrices You can also enter a matrix in a form similar to its depiction in books using the special Matrix Writer entry feature It can create either real
39. ding Slope Tangents and Critical Poni 6 15 Lesson 28 Areas Under Curves 0a a aa aa 6 17 7 Calculus Statistics and Advanced Mathematics Lesson 29 Finding Derivatives T Lesson 30 Finding Integrals 7 4 Lesson 31 Data and Statistics l T T Lesson 32 Regression Analysis a Paed Data T 9 Lesson 33 Differential Equations 000a 7 11 Lesson 34 Linear Algebra 7 14 Contents 2 8 9 Special Features Lesson 35 Transferring Objects Via Infrared Lesson 36 Using an Equation Set from the Equation Library da van iat in fe pe MS Lesson 37 Adding and Using Libraries If Things Go Wrong Lesson 38 Error Messages Lesson 39 Troubleshooting Contents 3 Welcome to the community of problem solvers As easy to use as a calculator The HP 48G Series calculators use a special graphical interface inspired by current generations of desktop computer software This interface guides you through your problem solving applications smoothly and quickly W hether you are solving simultaneous equations plotting parametric equations symbolically solving an integral or analyzing a set of data both HP 4 amp models work in a familiar intuitive way performing tasks and producing readable results As powerful as a computer The HP 48G Series calculators come with 512K of built in ROM and up to 128 KBytes of built m RAM All HP 48 models offer you the problem solving power of specialized computer software costing h
40. e i ae a a1 JaaKCR regi VECTRA Step 4 Simplify the expression by collecting terms until it doesn t simplify further OO SE 7 6 Calculus Statistics and Advanced Mathematics Statistical data for the HP 48 are represented by matrices Such a matrix contains a row for each data point and a column for each variable measured at that point point points p omt n Cnm The Statistics application uses the data stored in the current statistical matriz stored in reserved variable VYDAT You change the current statistical matrix each time you work with a different set of data Example Find the mean and standard deviation for each variable in the following set of sample data The two variables are the consumer price index CPI and the producer price index PPI for the United States over a 5 year period Year CPI PPI 1 9 1 9 2 2 5R 4 6 3 6 5 6 1 4 7 6 T 8 5 hae 1933 Step 1 Select Simale war from the STAT menu Bees CIMGLE VARIAELE STATISTICS Ske Pet nT a col _ MEAN TE DEY _ VARIANCE TOTAL MAINURM _ MISMO ENTER STATISTICAL DATA EDIT CROO CACL OK Calculus Statistics and Advanced Mathematics 7 7 Step 2 If you had already entered this eats set as a matrix and stored it with a name pressing HES would allow you to select it now for statistical ee ae However to enter new data you must create a new data matrix now Call up the Matrix Writer a
41. e 0 1 j 4g eel Fewer foes Ti e E ENTER VALUE OR PRESS SOULYE oe ee ee ee Step 4 How long would side c be if the obtuse angle 6 was 120 degrees Enter 120 into amp and solve for x 120 SOLVE ENTER VALUE UR PRESS SOLVE ae ee INED SOLVE Step 5 Exit the SOLVE py ere Notice that the labeled results of each execution of f ve 5 6 Solving Equations Lesson 18 Solving for a Variable Symbolically The HP 48 also allows you to isolate a variable symbolically that 1s rearrange an expression so that the desired variable is isolated on one side of the equal sign Once a variable is isolated it is easy to save the rearranged expression as Its definition Example Solve for Ty im the following heat transfer equation then create variable TH containing the resulting equation WAR RESULT Symbolic PRINCIPAL ENTER EXPRESSION a Cs oo RT f OE Step 2 Create and enter the equation anette RESULT Symbolic PRINCIPAL IEE _ O GAWD _ a TH GC TL ENTER EXPRESSIOM EMIT CHOD CAMEL OK Step 3 Specify the variable of solution and solve for it T H ENTER Solving Equations 5 7 Step 4 Define a new variable TH from this equation stores the expression to the right of the equal sign H lt U A TL in the variable name to the left of the equal sign Press afterwards to view the new entry in the
42. e Blvd 72 Bendemeer Rd Corvallis OR 97330 01 01 07 07 Singapore 1233 declares that the following products Product name HP 48G Series calculators conform to the following product specifications EMC CISPR 22 1985 EN 55022 1988 Class B IEC 801 2 1991 prEN 55024 2 1992 3 kV CD 8 kV AD IEC 801 3 1984 prEN 55024 3 1991 3 V m Safety IEC 950 1986 A1 A2 EN 60950 1988 A1 A2 Quality Department Hewlett Packard Company Corvallis Division LA Packar HP Part No 00048 90126 Printed in Singapore Edition 5 Notice This manual and any examples contained herein are provided as is and are warranty of any kind with regard to this manual including but not limited to the implied warranties of merchantability 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 herein Hewlett Packard Co 1993 AH rights reserved The programs that control your HP 48 are copyrighted and all rights are reserved Reproduction adaptation or translation of those programs without prior written permission of Hewlett Packard Co is also prohibited Trustees of Columbia University in the City of New York 1989 Permission is granted to any individual or institution to use copy or redistribute Kermit software so long as it is not sold for profit provid
43. e correct units it will keep track of the units as you calculate and report the answer In any appropriate measurement you want Example Create the unit object S2_ka m e s 2 Step 1 Enter the Units Catalog key in the value and append the first unit Ll Jeka CEG pea LE De Sue LET Step 2 Append the second unit This requires that you return to the main Units Catalog screen and select a different category Note that appending a unit to an object with a unit already attached implies a multiplication of the units Le ae ken 2 CSCW CS BC REED Step 3 Append the remaining units in the denominator Note that pressing the right shift before the desired unit implies a diviston that you want to append the unit in the denominator instead of the numerator of the compound unit se kate ees 2 Pak fo HT MIN 5 He Arithmetic 3 13 Converting Units Example Convert 1 amp _ atm atmospheres to maHa millimeters of mercury Step I Create the unit object 18 atr l 16 atm PA ATM EAR PSI TOER MMH Step 2 Convert to millimeters of mercury Note that pressing the left shift before the new unit converts the previous unit object to the new unit rogi mig OPRL ATM EAR OPSE TORR MMH As you perform arithmetic with unit objects the HP 48 keeps track of the units for you When different unit objects of the same category are added or subtracted the result is automatically co
44. e the z coordinate of the eyepoint to zero and the z coordinate to 8 and redraw the plot This view shows the effect of changing the horizontal component TPT 8 e 0 e Then plotting Plotting Equations and Analyzing Graphs 6 9 Lesson 29 Introducing the Plot Types There are fifteen different kinds of plots that the HP 48 can draw Each of them is discussed in detail in the HP 48G Series User s Guide but the table below gives you a brief introduction to each HP 48 Plot Types Plot Type and Description Example Function Plots true functions of a single variable y as a function of x on an zy coordinate system Shown y 2 sin 2 x Polar Plots polar functions of a single variable r as a function of on an xy coordinate system Shown r 2 cos 48 Parametric Plots the curve determined by two parametric functions x t and y t that are combined a complex valued function f t x t iy t Shown f t 3sin 3t 12 sin 4t Differential Equation Plots a phase plane of a first order differential equation at given initial oneone Shown yt phase of y t ae 2y Conic Plots both solutions to the quadratic equation representing a conic section Shown f x y 527 37 18 6 10 Plotting Equations and Analyzing Graphs HP 48 Plot Types continued Plot Type and Description Example Truth Plots truth valued functions such W as inequalities by testi
45. ear equations To create your system of equations you can either choose them from among those you ve stored or enter them directly As you solve a system of equations remember that a system of equations can be represented by a single matrix equation of the form AX B Equation Form Matrix Form 3z y 2z 13 3 1 2 x 13 r y 8 l om 1 1 8 lyj 1 z 2y 5 13 1 2 5 Z 13 The HP 48 makes use of this representation to solve systems of linear equations rapidly and efficiently Example Solve the system of linear equations shown above This example assumes that the current display mode is Std Step 1 Select Solve lin sus from the SOLVE menu sete SOLUTE SYSTEM A H E BER peor EMTER COEFFICIENTS MATRIN A TEES ie Pe eg Step 2 Enter the matrix of coefficients Matrix A using the Matrix Writer eg EE SYSTEM fi ol J a ee oe ENTER COEFFICIENTS MATRIX A EDIT choni o a ENTER 2 Solving Equations 5 11 Step 3 Enter the vector of constants B and solve the system Me eE EA 69 13 ENTER CEO EE aaa i la 1 13 pens E ne rma fr f a SOLUTIONS OR PRESS SOLVE ees Ee ee TT ENTER EMT jCHOO3 Step 4 Exit the SOLVE application and view the results on the stack 5 12 Solving Equations l ouin This chapter provides a brief introduction to the PLOT application The lessons take you through examp
46. ed this copyright notice is retained Hewlett Packard Company Corvallis Division 1000 N E Circle Blvd Corvallis OR 97330 U S A Acknowledgements Hewlett Packard gratefully acknowledges the members of the Education Advisory Committee Dr Thomas Dick Dr Lynn Garner Dr John Kenelly Dr Don LaTorre Dr Jerold Mathews and Dr Gil Proctor for their assistance in the development of this product Special thanks are also due to Donald R Asmus Scott Burke Bhushan Gupta and his students at the Oregon Institute of Technology and Carla Randall and her AP Calculus students Edition History PE OED As Sapte alana deh Screen eat as ih Per dra eafe eile nd mated ocean tnt April 1993 DOU Dn tap ali ohare Basis Boe ni nd Boonies Maeaacd don a Bain June 1993 FLUO ae han eect i ean Ae oe eee August 1993 FG OMe EE EEE S E a ec ead ae hake b October 1993 EOE cas Resign arene ec eae Pender eo UU eae ts Ae i January 1994 Start Here About the Quick Start Guide Lesson 1 Getting Ready Turning the HP 48 On and Off Adjusting the Display Contrast Preparing the Built In Examples Setting the Time and Date Setting the Beeper Clock and Traction Mere Introducmg the HP 48 Lesson 2 Mathematical Objects and the HP 48 Editing an Object in the Command Line Removing Objects from the Stack Lesson 3 Entering Characters The Keyboard Special Characters Lesson 4 Using Menus The NXT Key Lesson 5 A Brief Tour of she HP 48 Entry Env
47. ed to enter the denominator and divide 1 3 ENTER 1 1 Aroaz fir ME TE FEE The next few examples use a keystroke saving shortcut that you haven t seen yet When calculating with the stack mathematical keys such as causes an automatic before it executes its action This allows you to use the sequence 8 9 7 2 instead of 8 9 Te to subtract 7 2 from 8 9 In short it saves you a keystroke Work the following short examples of stack arithmetic that use the fourth row mathematical keys Notice in particular how each operation leaves the results ready for the next operation Example Calculate l 3 62 5 L AIG REAL EASE Example Calculate 207 7 CLEAR 20 ENTER 2 L HZS WECTRIMATR LIST HYP_ REAL BASE Example Calculate 4e 2V5 Le n H Liat WECTRIMATR List HYP REAL BASE Arithmetic 3 3 15 06x14 5 Example Calculate 15 06 M5 QO Algebraic method The HP 48 is as proficient with algebraic arithmetic as it is with stack arithmetic Unlike the direct immediate approach of stack arithmetic the HP 48 also allows you to enter a computation as an algebraic formula so that you can inspect it or store it for later use This method also has two steps first create and enter the formula then evaluate it to compute the result You must surround an algebraic formula with CEECEE er g255999 trek marks s
48. ee evaluating it Stack Method Look at an example of the way the stack works during a calculation It works very much like the pencil and paper arithmetic taught in elementary school For example to find the difference of two numbers such as 8 9 and 7 2 you first write them both onto the paper and then subtract 9 9 2 saad eee LF Using the stack for arithmetic on the HP 48 exactly mirrors the manual process Enter the numbers or arguments first then perform the operation Example Subtract 7 2 from 8 9 on the HP 48 Step 1 Enter the numbers Notice that you enter numbers in the same order that you would write them on paper 8 9 ENTER 72 ENTER 2 3 9 1 7 Poe im VECTR MATR LIST ae REAL BAZE Step 2 Perform the subtraction The subtraction operation removes the objects on the first two stack levels noting the order and returns the difference back to level 1 ir MECTRIMATRT LIST MYP REAL T ERSE O 3 2 Arithmetic This process of entering numbers onto the stack and using numbers from the stack during calculations underlies everything the HP 48 does This approach makes it easy for the calculator to work very efficiently because the results of one calculation are left sitting on the top of the stack ready to be used by any other command Example Divide the previous result by 1 3 The numerator the result of the previous calculation is already entered so you only ne
49. ence and engineering problems The library consists of more than 300 equations grouped into 15 technical subjects containing more than 100 problem titles Each problem title contains one or more equations that help you solve that type of problem Example Examine the equation set for Frajeciiie Motion Phan ht h Pudi fe Step 1 Fix the display to 2 eu ae saree and then open the EQ LIB application If 1 and UAT T aren t flagged with small squares press i of the corresponding menu keys once ore Forces and Energy Gates Heat Transfer J 51 m ENGL UNIT j euT Step 2 Select the ot ion subject area and open its catalog M M ENTER LS Prae l Motion Angular Motion Circular Motion Terminal Yelocity Be EGM VARS ee Step 3 Select Projectile Motion and look at the diagram that describes the soe TE T Special Features 8 3 43 Step 4 View the five equations in the Fredectile Mot ion set All five are used interchangeably in order to solve for missing variables see the next example inal x posit ion WHF init y position ue final y position HG initial angle WA initial velocity FTE BS VARS PIC STEK ENIT Now try using this equation set to answer a question or two Example You estimate that an average professional goalkeepers can punt a soccer ball a distance R of 65 meters downfield at an elevation angle 9 of 50 degrees At what velocity vo
50. flag settings Storing Retrieving and Organizing Variables MEMORY allows you to name store view retrieve purge and rearrange any objects stored in your user memory STACK allows you to view and manipulate the objects in RTE i i i temporary storage on the stack and Organizing Objects on the Stack Ree CALCULATOR MOLES Skee HUMEER FORMAT ere HNGLE MEASURE egress COORD S STEM Rect angular WEEEPER CLOCK 9 _ FM CHOOSE MUMEER MIZPLAY FORMAT Poss OHDOS po PRLAG CANCE OK SeQEUECTS IM T HOME EXAMPLES 758 PROS DIR MEDIAN 3 FLOTS DIR HSIN Ra EQNS DIR ONE SINC STILE SWAP SORT w PURGES HOME EsR HOME pea Sb Tee Cee S4 4 Cbtk COS CS 82 T6 ECHO MEH Cee IROLLDJSLIST et PN introducing the HP 48 2 15 This chapter shows you how to gt Calculate using real numbers gt Calculate using fractions Calculate using symbolic variables gt Calculate using complex numbers gt Calculate using units Arithmetic 3 1 Lesson 6 Doing Arithmetic There are actually two different ways that you can do arithmetic on the HP 48 The stack method is most convenient when you want to perform immediate calculations involving one or more numbers The algebraic method is most convenient when you wish to describe your calculation as a formula so that you can verify it or reuse it before
51. g Functions PLOT allows you to select any one of 15 plot types The input form you see adjusts to show the SSS PLOT Gage See TYPE Function a De EQ INDER H H HEH 6 o 6 5 _AUTOSCALE Y HERE 3 1 3 2 ENTER FUMCTIOMNG TO PLOT EDIT Gs eee ee ERASE DRAH options available for your selected plot type The SYMBOLIC application contains special calculus tasks as Differentiate l Taylor polya Tsoalate var Solve quad pe fp e ANL OK well as general purpose symbolic manipulation bet PALI Pe first lesson to set the time and qf a a 5et alarme date You can also use alarms to 3 Set time daten help manage your time eeens panei pises poetit RAMEE ES DRE The STAT application allows you to enter data into a matrix and to Single var oar oe 4 Frequencies collect descriptive statistics or run 3 Eit datan aoe Ci Summary stats a regression on it Li C e eee ANOLE OK UNITS allows you to attach any aie Ace t of over 100 units to real numbers Jf The HP 48 can keep track of units 3 during calculations LENG AREA VOL ETIME SPEED HASS introducing the HP 48 2 13 Printing and Data Transfer gt The I O application allows you to or Mend to HP 48 print objects or to transfer data 4 Get from HP 48 000 OC HE fel sites i a S o J Pr int display
52. ial Features To attach a library to user memory manually 1 Change to the directory to which you want to attach the library m Io access the library from all directories move to HOME m To limit access move to the desired directory The library will be available only in this directory and its subdirectories 2 Enter the brary identifier for the library it has the form port number where number is a unique number associated with the hbrary 3 Press LIBRARY AT TAC There is no limit to the number of libraries that can be attached to the HOME directory However every other directory is limited to one attached library To use a library that is attached in the current path 1 Press This brings up the Library Catalog a menu of all currently av ailable libraries This is similar to the way the key brings up a menu of all variables in the current directory 2 Press NXT or Q PREV as necessary to find the desired library 3 Press the menu key corresponding to the desired library to open the menu of commands contained in the library To detach a library from a directory Change to the directory where the library is attached Enter the eons library number for the library you are detaching Press Y E to detach it from the current directory Press and examine the menu The library should have disappeared If it didn t it may be attached to a second directory in the current path To purge
53. ironments Application Environments Utility Environments Arithmetic Lesson 6 Doing Arithmetic Stack Method Algebraic method Using the Equation Writer l Lesson 7 Finding and Using More M a koee Lesson 8 Arithmetic with Fractions Lesson 9 Arithmetic with Symbols Lesson 10 Arithmetic with Complex Numbers 1 2 1 3 1 3 1 3 1 3 1 4 1 4 Contents 1 Lesson 11 Arithmetic including Units 2 2 3 13 Converting Units 4 2 0 6 4 84 oP Ga ey Bela 4 Understanding and Using Memory Lesson 12 Understanding Memory 4 9 Lesson 13 Creating Naming Variables 2 4 4 Lesson 14 Organizing Variables 2 2 2 1 4 6 Lesson 15 Editing and Purging Variables 2 4 8 Lesson 16 Using Variables in Calculations 4 10 5 Solving Equations Lesson 17 Solving for a Variable Numerically 5 2 Searching for Multiple Solutions 5 3 Interpreting the Results a 5 4 Lesson 18 Solving for a Variable Syml sleali 5 7 Lesson 19 Finding all Roots of a Polynomial 5 9 Lesson 20 Solving a System of Linear Equations 5 11 6 Plottmg Equations and Analyzing Graphs Lesson 21 Plotting a Function E Soh te 6 2 Lesson 22 Modifying the Display of a Plot oe ee 6 4 Lesson 23 Plotting Several Functions 6 5 Lesson 24 Plotting Functions in Three Dimensions 6 7 Lesson 25 Introducing the Plot Types 2 2 6 10 Lesson 26 Finding Roots Graphically 6 13 Lesson 27 Fin
54. is locked or the X annunciator won t turn off perform a system halt a Press and hold ON b Press and release the C menukey c Release ON The empty stack display should appear 3 If the HP 48 doesn t respond to the system halt from the keyboard try to halt the pia directly without using the keyboard as described on page 5 17 of HP 48G Series User s Guide 4 If the problem still exists perform a memory reset See page 9 17 of HP 48G Series User s Guide If these steps fail to restore operation the calculator requires service To reset the calculator and erase all memory 1 If there s anything in memory you want to keep don t reset the calculator 2 Press and hold ON 9 2 If Things Go Wrong Cn Aa At the same time press the left and right menu keys A and F then release them Release the ON e ON key Press The above steps also erase the contents of a plug in RAM card but only if its RAM is merged with the calculator s main memory if the calculator 2 2 TT O i 3 u ro on Press and release ON If the display is still blank hold down and press several times until characters become visible then release ON If no characters appear in the display check for too light of a display If nothing appears in the display install three new AAA batteries as described under Changing Batteries in Appendix A of HP 48G Series User s Guide The
55. les of gt p d Plotting a simple function Modifying how a plot is displayed Plotting several functions at once Plotting functions of two variables in three dimensions Using various plot types Finding the roots of a function graphically Finding the slope of a function at a point Finding the line tangent to a function at a pomt Finding a local maximum Finding and shading the area under a curve Plotting Equations and Analyzing Graphs _ 6 1 Pn A A a a a a a nN te Lesson 21 Plotting a Function A function takes one or more arguments as inputs and transforms them mathematically into exactly one output A function can be plotted by graphing a series of outputs against a corresponding series of inputs Plotting functions on the HP 48 is a matter of doing the following gt Entering or choosing the function to plot gt Declaring the independent variable and the horizontal range of that you want to view gt Either declaring the vertical range to be displayed or choosing to let the HP 48 automatically scale it for you gt Making sure that the angle mode Degrees Radians Grads is properly set gt Setting the other plot display options All of these steps can be accomplished smoothly and quickly in the PLOT application Example Plot f z sing Step 1 Open the PLOT application You may or may not already have a function entered in Em TYPE ae ion EQ INDEP H VIEH 6 5 _AUTOSCAL
56. ly not recommended EE Bee See ees BLOT E TYPE miale ag a Fe Ea C SINEK SeSI a s gt if necessary TC CHEN ENTER INDEP 5 H VEH 6 5 6 5 AUTOZCALE Y WER 4 4 CHOOSE TYPE OF PLOT fcnoos OPTS ERASE ORAL Example Plot the list of functions you just selected Plot them simultaneously Step 1 Set the Simultaneous plot option eee PLOT OPTIONS sees INDEP Lo 6 50 Wb BS wf AES ee fa SIMULT STEP DF 14 _ PINELS H TICK 16 na 1A wf PIELS PLOT FUNCTIONS SIMULTAMEDUSLY CHE ACL OK m spe ary Rae He Step 2 Erase the PICTURE display and draw the plot bf 200M iNY TRACE FCM EDIT CAMEL Return to the main PLOT screen by pressing CANCEL when you ve finished viewing the plot You may plot as many functions simultaneously as memory allows as long as they are all gathered together in a list You may either build this list from a group of already created variables as in the previous example or enter the list from scratch using the command line 6 6 Plotting Equations and Analyzing Graphs Lesson 24 Plotting Functions in Three Dimensions There are six different plot types that can be used to help you visualize functions of two variables Some of these only plot the given function within a region in 3 dimensional space called the View Volume defined by ranges on each of the three coordinate axes Z vi high
57. n repeat the previous steps H changing the batteries did not solve the problem turn the HP 48 over Remove the top right as you face the bottom of the machine rubber foot You should see a small hole with the letter R next to it Insert the end of an ordinary metal paper clip into the hole as far as it goes Hold for one second and remove Press ON Repeat the previous steps oma EE oOo o N R Reset hole 5 If all of this doesn t work your calculator needs repair Contact the HP Calculator Support department see the inside back cover lf Things Go Wrong 9 3 if you suspect that your calculator is malfunctioning 1 Run the self test a Turn on the calculator b Press and hold ON c Press and release the E menukey d Release ON The diagnostic self test tests the internal ROM and RAM and generates various patterns in the display The test repeats continuously until you perform a system halt 2 Halt the self test system halt a Press and hold ON b Press and release the C key the key with C next to it c Release ON The empty stack display should appear If the self test indicates an internal ROM or RAM failure Gf PROM OE and IRAH OE are not displayed the calculator requires service If the calculator passes the self test you may have made a mistake operating the calculator Reread appropriate sections of the documentation and Answers to Common Que
58. n the currently plotted function Example Using the same polynomial you just plotted in the previous lesson Y X4 5X3 2X74 X 4 find the slope at x 0 4 and draw a tangent line to the function at z 0 3 Step 1 Turn on TRACE mode and move the cursor using the 4 and gt keys NXT y the menu T Z lt 4 and gt i ad l 200M CHN EDIT Step 2 Display the cursor coordinates and move the cursor over until the r coordinate equals 0 4 gt or lt as needed Y 4 58464 Step 3 Find the slope to redisplay the menu SF CE SLOPE SLOPE of Plotting Equations and Analyzing Graphs 6 15 Step 4 Move the cursor to x 0 3 and draw the line tangent to the function at that point 7 times als fo gt redisplay the menu md 7 TAMLINE 1 4015 4 3 5B403 Example Determine the point where the current function has a local maximum in the region near the y axis Step 1 Magnify the display to show the target region more clearly Move the cursor to one corner of the target region and use Box Zoom A 3 times lt 6 times a a E the menu a aa GEE i PET ovg D 5 elis oe 12 times j n E ETA Step 2 Execute the zoom move the cursor near the local maximum point and find an extremum A in ESTRM 1594839 06477 3 91091 8662 Gace ae Poa te T De or Ds as neede Step 3 Return to the stack Notice tha
59. nction looking down onto the zy plane simply by moving the eyepoint You may simulate this by transforming coordinates however Example Plot a wireframe view of f X Y X Y XY Step d Change the plot type to Hireframe and enter the function DWD OX 63 OW Y O KX DOY OF 3 ENTER THRE ieee fame lt lt Rad ER l een Seis T ae i INDEF PS STEPS 14 DEPND STEPS 9 ENTER INDEPENDENT YAR WAHE EDIT f OPTS ERASE DRAH Step 2 Set the number of horizontal and vertical steps or frames to plot A 12 ENTER O 12 ENTER TYPE a Rad EQ gar eee INDEP STEPS 12 DEPNE y STEPS 2 CHOOSE TYPE OF PLOT o es a OPTS Ga Oe 6 8 Plotting Equations and Analyzing Graphs Step 3 Set the size of the View Volume and location of the eyepoint ECTS 1 ENTER 1 Sees BLOT OPTIONS Sees ENTER 1 4 ENTER 1 H LEFT H RIGHT Y MEAR Y FHE i 2 LOW 4 Z HIGH HE A VE 2 ZE ENTER MINIMUM 4 VIEM VOLUME YAL EDIT fe MEL OK one plotting Step 5 Return to the plot input form and change the z coordinate of the eyepoint to 20 to see what the function looks like from a high vantage point Remember that you are still looking forwards as well as downwards at the function OPTS 20 Torn SPOT ere See eke EE Me pec SEDIE PEETA AYS lites Step 6 Return to the plot input form and chang
60. nd enter the data REE SIMGLE VARINELE STATISTICS See EDAT ere COL j TYPE Sample PERM STE DEY _ VARIANCE _ TOTAL PASH _ MINIMUM ENTER STATISTICAL DATA EDIT choos KANL DK Step 3 By default the column for which you will be calculating the mean and standard deviation shows 1 i e the CPI data Accept the default for now Put a check mark 1 next to each statistic that you want to calculate and press OE to calculate The labeled results are put onto the cae Meant 9 1 st Dey em an in J 35e F 1 i a a WECTRIMATR L ENA a Step 4 Repeat the procedure for the PPI this time changing the column number to 7 8 Calculus Statistics and Advanced Mathematics Lesson 32 Regression Analysis of Paired Data The HP 48 can fit any one of four statistical models to a set of data pairs Once again the data must be in the VYDAT matrix Example Using the same data as the previous example calculate the correlation and covariance between the CPI and PPI variables using the best fitting regression model of the four available Then predict the PPI value for a CPI value of 8 5 using the calculated model Step L Open the STAT application and select Fil Data TOAT HerOh Y CDL a MODEL Linear Fit ENTER STATISTICAL DATA EDIT SS ee jCANIL OK Sten 2 Check vour regression options The correct data is in MDAT v r already The two varia
61. ng each point in the range to determine 1f the function is true or false and that pomt Shown x y mod4 lt 2 Histogram Plots the data in a designated ms AA a ele column of the current statistical matrix after it has been sorted into numerical ranges or bins A Histogram is a Bar plot where each bar represents the number of data points that fall into a particular bin Bar Plots the value of each data pomt in a designated column of the current statistics matrix as a vertical bar Scatter Plots the data in one column of the current statistics matrix versus the data in a second column Slopefield For a function F x y z plots a lattice of line segments whose slopes represent the function value 2 at their centerpoint x y Shown F sin ry Plotting Equations and Analyzing Graphs 6 11 HP 48 Plot Types continued Example Plot Type and Description Wireframe Plots a perspective wireframe view of the surface determined by a function of two variables Shown F x 4r7y y Pseudo Contour For a function F x y plots a lattice of line segments that are each tangent to a contour of the function a curve satisfying F x y constant This allows your eye to pick out the contours without actually plotting them Shown F z 1 y 1 Y Slice Plots a series of cross sections of the surface determined by the current function of two variables and c
62. no parity 8 bits 1 stop bit m via the Internet Access as hpcvbbs external hp com 192 6 221 13 using telnet ftp or World Wide Web browser http hpcvbbs external hp com hp48g html Contents Start Here Introducing the HP 48 Arithmetic Understanding and Using Memory Solving Equations Plotting Equations and Analyzing Graphs Calculus Statistics and Advanced Mathematics Special Features If Things Go Wrong h HEWLETT Part Number 00048 90126 Edition 5 PACKARD For HP internal use only 00048 90105 English Printed in Singapore 12 94
63. number is a single object Many functions that work with real numbers also work with complex numbers You can use complex numbers as arguments for arithmetic operations and you can use them in symbolic expressions Example Enter the number 3 4 rectangular coordinates Use the SPC key to separate the two coordinates CD 3 GPO 4 It 2 4 Example Enter the number with magnitude 5 39 and phase 158 2 degrees polar coordinates Step L Set the angle mode to Degrees then type in the number Note that the A character is located above the key oe ERS 5 392158 2 Me MAT MAT Q gt am APPLY 3 10 Arithmetic Step 2 Enter the polar number on the stack It s converted to match the current coordinate mode in this case Rectangular mode es 3 43 I 5 00453860689 2 DO16 253362 AAT MAT gt o 90m 1 APPLY Step 3 Now change the coordinate mode and watch how the O complex number changes POLAR is located above the MTH key S33 l7 SB1B2354 3 PEEL 156 7 Mat 0 som 1 APPLY va L Change the coordinate mode back to Rectangular press again before you go on Try some examples to see how easy complex numbers are to use In calculations Example Calculate Step 1 Enter the first two complex numbers CLEAR c34 D 9 E ENT D 4 CA SPC 3 Step 2 You do not need to press ENTER before pressing LA Char ra MAT MAT 0 7 i APPLY
64. nverted to the units of the last unit object entered the level 1 object Example Add up the following lengths and report the answer in centimeters 41 mm 19 in 5 ft and 12 cm Step 1 Enter the unit objects onto the stack cl m byt Step 2 Add up the units Because the level 1 object has cm as its unit each addition converts the total to centimeters rs 1 16 rcm SN On 3 14 Arithmetic One final example illustrates the ability of the HP 48 to factor the unit expression Example Factor H Newtons out of 3 3 ko ges Step 1 Enter the unit object 3 5 ken ese ee ee ee eee Step 2 Wey in the unit to be factored using i as its value ot 3 5 koe 205 1_N CEYN GF KIP LEF POL Siena pees the unit factoring using the Units Commands menu l aa 5 Mem E UVAL UFACT gt UNIT Arithmetic 3 15 with one press of the CLEAR key A better place to store information for later use is in User Memory This chapter explains how memory 1s organized and how you manage it Specifically you ll learn to gt Understand the memory in the HP 48 gt Understand variables and directories gt Create variables gt Organize your variables gt Edit and purge variables gt Use variables in calculations Understanding and Using Memory 4 1 Lesson 12 Understanding Memory Thus far it has been convenient to think of the HP 48 as a calculator albeit an adv
65. o switch to the EQNS directory first tienes SOLVE EQUATION Sees E CHoe 9 47 EHH EMTER FUNCTION TO SELYE EDIT CHOOS VARS ERPR 5 2 Solving Equations Step 3 Since RATFUNC only has one variable it must be the unknown variable Solve for by highlighting its field and pressing SOLVE Kornig Se SHAE ok it aoe OR es Dawe paces TOLRE EGUATION See EQ Gr Oe 2 99td i Gta n PEE EHTER VALUE OF PRESS SOLVE EDIT a a CE INFO ZOLVE Step 4 Press HEG to determine the nature of the most recent luon found by the root finder The eru message indicates that the solver found a solution a point where the expression evaluates to exactly that is to 12 significant digits zero THEO eee SOLVE EQUATION Rees Ee Erix 2g te een h Zer ENTER YALUE OK PRESS SOLVE ee Lok Step 5 Press fk to remove the message box ee ie lt Searching for Multiple Solutions Although an equation or expression may have more than one solution the calculator stops when it finds one Because there was no value listed for x before you chose to solve for z the solver began looking for an answer at x 0 and reported the first solution it found However you can tell une solver to eee its search o a different var iab le e Example Re solve RATFUNC beginning with a guess of x 2 it Solving Equations 5 3 Step 1 You re already working with RATFUNC and the x va
66. o that the HP 48 understands that you eooc want to treat the mathematical operations as a formula OOOH A cc 33 22500 instead of as a series of direct commands The tick key cen eeess C is highlighted in the diagram to the left Example Calculate ass using the algebraic method Step 1 Enter the algebraic expression 1 62 5 ENTER 1762 9 O1 VECTREMATEE LIET HYP REACT ERSE Step 2 Evaluate the expression to obtain a numerical result EVAL H16 EVAL Ca a LIST HYP REAL EASE Example Calculate 207 CED 20 6 2 AD l A125 WECTRIMATR LIST H P REAL EASE Example Calculate 4e2V5 CLEAR C 4 amp 5 l J34 VECTRIMATR LIST 3 4 Arithmetic Example Calculate gecjas 6 11 5 ED Using the EquationWriter When the equations or calculations get more complicated the HP 48 offers a special way to enter algebraic expressions the Equation Writer You don t use tick marks in the Equation Writer because everything you create there is an algebraic Try some examples to see how it works Example Repeat the previous example using the Equation Writer Step 1 Call up the EquationWriter and enter the equation n ATION 15 Yer 6 x 14 5 an O 13 66 14 50 MATRI LIST HYP REAL BASE Step 2 Evaluate the expression leet VECTRIMATR LIST HYP REAL E E d a Ca ee m 0a wri x Li m Ex
67. riable field is highlighted so you are ready to enter the guess 2 CO ENTER se SILVE EQUATION ENTER FUNCTION TO SOLVE EMT chons VARS INFO EXPR Step 2 Solve for again and examine the new solution f a V SOLVE THRO S SOLVE EQUATION See x 3 HHBEGRHERG 1 Sion Reversal ENTER VALUE OR PRESS SOLVE E Cre E E ee TE Step J3 Press Ok Interpreting the Results The Sign Reversal message means that the solver has found two adjacent sample points at which the value of the expression is opposite in sign but hasn t found one sample point that makes the expression zero to 12 digits This can happen at a legitimate solution the finite numerical precision making it impossible for the HP 48 to find the actual zero But it can also occur at a discontinuity where the graph of the equation jumps across the x axis without ever touching it Two kinds of Sign Reversals ETHAN Actual Root Discontinuity 5 4 Solving Equations To decide which case it is you should find the value of the expression at the Sign Reversal point Example Find the value of the expression at the computed value of x in order to decide whether it is a solution to RATFUNC or represents the location of a discontinuity Step 1 Press A to move the highlight to the Et field and press EMPR The value of the expression at the computed value of x is returned to the stack Step 2 Return to the st
68. riables These variables are hidden from you but are used and updated by the operating system to keep track of everything as you work Local variables These are temporary variables created by a program that only exist during the execution of that program Global variables These are variables you create by assigning a name to an object and can edit evaluate and manipulate They are stored in user memory where they are quickly and immediately accessible Global variables are hierarchically organized into directories Port variables These are like global variables except that you may not edit them and they cannot be hierarchically organized They are stored in port memory where they are in long term storage The HP 48G model only has one port Port 0 but the HP 48GX model can be configured with as many as 32 additional ports each containing up to 128 KB of memory The remaining lessons in chapter 4 illustrate some of the common things you can do with user memory and global variables The HP 48G Series User s Guide gives you more information about the boundaries within SYSRAM and otherwise managing memory chapter 5 and how to use and access port memory chapter 28 Understanding and Using Memory 4 3 jg Se A A BA BP IL SSS S an pr Lesson 13 Creating Naming Variables To name an object is to create a global variable You store an object in user memory by giving it a name You can use descrip
69. s that were created and named for you by the TEACH command when you executed it in Lesson 1 Example Gather the following functions into a list and store the list in the Eft field ONE TWO THREE and FOUR Step 1 In the main Plot screen move the highlight to the EM field and open the Variable Browser Note when you access ae Variable Browser from within PLOT it only displays objects in the current directory that can be plotted Move to the EQNS directory if necessary and use the arrow keys to highlight the ONE equation eee PRE EEF CE Wl FUNC IN f HOME Enh o row key s GHOCS O D or we Gf A OFS ln FOUR 4 5IN fF JEHOOS CHEE NEH CANIL OK Step 2 Select the desired functions by putting check marks in front of the names OOO PER PET ees TYPE FUWCS IN HOME Effi ZONE SIHEKO T eee THO 22SINC lim au THREE S 51 FOUR 4s51H EXT cuon CHK NEH CANEL OK Plotting Equations and Analyzing Graphs 6 5 ae Step 3 Enter the list of checked functions into the Ef field and set a vertical display range of 4 to 4 large Saal to display the largest function in the list You must turn off the AUTOSCALE feature if it is currently checked before you can see your eii TEL Because it uses only the first function in the list to determine the vertical scale autoscaling while plotting a list of functions can give inconvenient and surprising results and is general
70. stions in Appendix A of the HP 48G Series User s Guide 9 4 If Things Go Wrong Contacting Hewlett Packard For Information about Using the Calculator If you have questions about how to use the calculator that are not covered in this guide first check the table of contents the subject index and Answers to Common Questions in appendix A of the HP 48G Sertes User s Guide If you can t find an answer in either manual you can contact the Calculator Support Department Hewlett Packard Calculator Support 1000 N E Circle Blvd Corvallis OR 97330 U S A 503 715 2004 Mon Fri 8 00am 3 00pm Pacific time 503 715 3628 FAX For Hardware Service See appendix A of the HP 48G Series User s Guide for diagnostic instructions and information on obtaining service But before you send your unit for service please call HP Calculator Support at the number listed below Hewlett Packard Corvallis Service Center 1030 N E Circle Blvd Bldg 11 Corvallis OR 97330 U S A 503 715 2004 HP Calculator Support If you are outside the United States see appendix A in the User s Guide for how to locate your nearest service center HP Electronic Information Service This service provides information on HP 48 calculators and is free of charge you pay only for the phone call or Internet service There are two ways to connect m via modem 503 715 4448 It operates at 2400 9600 14400 baud full duplex
71. t Real Number with Unit Complex Number Polar Form Ordered Pair Coordinate Symbolic Constant Variable Vector Polar Form Matrix Text String Labeled Quantity Equation Expression Sequence Commands Program List Example 14 75 14 75 m s 3441 4 6 8 25 12 1 Begin here Volume is 6 74 ml ae 4x 5xy Ox y sin x ee es Draw the plot Find square roots 2 TWO DRAW 2 2 Introducing the HP 48 HP 48 Object ot mara ome vt Rose Tonge ae 3 pea LO anak i aad rae wt R Soke oo ions pine z eae es z3 oem m r i H ome A P HA a 7 m m urt i i we bea a ie ie err ae a rors EE i i pe pe mea g rik fad iai f ibri H Ea ERN i 2 3 z H 15 Fh ui ESEJE eas ors gm HESE 3 ist in p i se pee era Pees z ook Sheba etn Reeve ove a H H a grasa Hod fan Puli 3 t F davee Saa pe s P 2i H si i REETH Ea i ee By design the HP 48 makes it easy to move between one type of object and another as one solves a problem explores data or communicates results It accomplishes this by using an object stack or stack for short Envision the stack as a special kind of card box in which the HP 48 organizes all of the objects it uses in the course of calculating solving plotting and evaluating Each object no matter its size occupies exactly one card in the
72. t each of the analytic functions put a labeled result onto the stack several times 6 16 Plotting Equations and Analyzing Graphs Lesson 28 Areas Under Curves The AREER command in the PICTURE FCN menu finds a definite integral based on the current function That is it calculates and n the area between the current function and the x axis between Example Find the area under the current polynomial X Xt 5S 2 N 4 between x 2 2 and yearn E A Step 1 Reopen PLOT and redraw the polynomial OERD 3 ENTER 12C Joue ae bet fed ven dont i I F o Hi if F Peon CRTI TRACE FCN EDIT CANIL Step 2 Use Decimal Zoom to force each horizontal pixel to be equivalent to 0 1 units Then move the cursor to r 2 2 the lower limit and mark it Note the use of the multiplication key x to mark a cursor position to mark the cursor position i T L S04egE 1 Step 3 Find the selected area Note that for finding the numerical integral the shading is for display purposes only and is entirely optional T ti mes A O aed play the menu i ABER 5 B0050916685 Plotting Equations and Analyzing Graphs 6 17 Step 4 Optional Shade the area between the current function and the z axis and between the r values represented by the mark and the cursor Note that the shading is for display purposes only and is entirely optional to the process of finding the area under a curve
73. that is enter alpha mode several ways depending on what is most convenient for you Enters alpha mode for the next keystroke only Enters lowercase alpha mode for the next keystroke only Enters extended gt alpha mode for the next keystroke only a Locks alpha mode on until you press ENTER or CANCEL a hold Enters alpha mode for as long as you hold the a key down You can press other keys meanwhile a a 4 Locks lower case alpha mode on until you press Some examples of the alpha keyboard are shown below a A a Ba C a hold A B C release HO Introducing the HP 48 2 7 Special Characters hooooosa fos oocdl hoonagag BURTI e e a S The CHARS feature allows you to find any character and put it mto the command line as if you had typed it from the keyboard Press nar lt and go exploring The 256 characters are collected into screens of 64 characters each ARSS CHARACTERS 0 63 Rape BoP eee eee eee eS ee oe ie HLl2S456Proor 1 15207 KEY MOME MUR i e Eee eee SESE CHARACTERS 128 131 Sees Bevl SEbrasstated Tydeqhs Porte Tew i 0 5 82e 87 PERI Sige are KEY eLSPC HUM 128 ee ee ee Move around in CHARS Press o ge Se CHARACTERS 64 1 Gee GABCCEFGHIJKLMNO PORSTUVARY2O IS abcdefaghijkilmnea Pqretuvuxgzt e KEY orkLEMNTER HUM 64 ee eee eee eee Sees CHARACTERS
74. the TEACH command you executed in lesson 1 Step 1 Display a list of directories ie fod FPP Somm neee ELE a 3 D HOME EXAMPLES e A A RE OK 4 6 Understanding and Using Memory Step 2 Select the EXAMPLES directory and switch to it Notice that the directory line says HOME EXAMPLES gt This illustrates that ESAMFLES is a subset or subdirectory of HOME V pE SEOBUECTS IN HOME EXAMPLES 138 PRGS DIR MEDIAN PLOTS DIR ASIN amp Ru EONS DIR ONE SING TILE SWAP SORT PURGEX HOME EXA EMIT CHOD W CHE NEH COPY MOVE Sometimes a variable may not be stored in the directory where it is most useful You can move any variable to any directory Example Move the variable TILE to the PRGS subdirectory of ESFAFLES Step 1 Select the variable to be moved TILE and press PONES WV VY Nove MOVE VARIAELECS Sees MAME TILE MOVE To ENTER VAR MAME OR DIRECTORY PATH US ee ee DE Step 2 Choose the target directory where you want to put the variable and press iE You can also type in the new path if you prefer ER S OBJECTS IM HOME EXAMPLES 338 FRGS DIR ATILE Su PLOTS DIR SSIN Re EQNS DIR ONE SIHE PURGES amp HOME EAR LEGIT CHOO CHE NEH COPY MOVE Step 3 Press CANCEL to exit the Variable Browser Understanding and Using Memory 4 7 Lesson 15 Editing and Purging Variables You will often want to modify a variable
75. tive names for variables A name can be as short as one letter or as long as 127 Global variable names can t be identical to the names of built in commands and can t begin with a number There are two ways to create a new global variable a From the stack use STO From the Variable Browser use MEM The following two examples illustrate each method Example Find the square root of 2 and store the value in a variable named using STO Step 1 Clear the stack and find the square root of 2 1 41421356237 rsa tra Wa ca EE EASE Step 2 Enter the name t1 eT 2 WECTRIMATR LIST HYP REAL EASE 1 41421356237 ad Step 3 Store the object Level 2 in the name Level 1 It disappears from the stack STO 1 Step 4 Check your current variable menu to confirm that 42 is stored Notice that the names in the menu are displayed in upper case for legibility VAR a CS a 4 4 Understanding and Using Memory Example Find the square root of 3 and store the value in a variable named t2 using the Variable Browser Step 1 Find the square root of 3 3 a 1 Seb SHO rar ota ewan e Step 2 Open the Variable Browser and select H epa NEL VARIABLE ee Q amp JECT EE MAME HIREC TORY ENTER NEH OBJECT EMIT CHOOS O ANEL OK _ Step 3 Retrieve the object in level 1 of the stack wee NXT CARE HER eS HEH VARIABLE Sees RE
76. to create the equation y 67 Step 1 Enter y and the number 1 6 PE DY ENTER 1 ENTER z aTieMaT 30 ocr 1 APPLY Step 2 Enter the argument azr O00 oom 1 gt ae aan am AR fon I Ae TEHAT 0 S07 APPLY AR Step 3 Calculate e Ue Zia P Epi azu l Ent he atw PMATEMAT e or 1 APPLY Step 4 Subtract to calculate 1 e7 at Ls l Eak k a i MAT EMA gt o oom 1 APPLY Step 5 Form an equation from the two expressions ag g ERFC aee PPHMAT MAT gt am fo APPLY Arithmetic 3 9 RN ewe VE VELOUR waaa AAR saan rn RAL RAMANA LEO Lesson 10 Arithmetic with Complex Numbers The complex number capabilities of the HP 48 can affect the results of real number operations Certain calculations that would result in an error on most calculators yield valid complex results on the HP 48 Example Find the square root of 4 DA ae re PMATTEMAT e gt am 1 APPLY The answer is a complex number displayed as an ordered pair The first term is the real component and the second is the imaginary component This answer is 0 27 or just 22 the principal square root of 4 Complex numbers can be expressed in two forms rectangular x yi and polar r cos isin The HP 48 can handle both forms although they are entered as ordered pairs x y and 7 respectively A complex number like a real
77. undreds of dollars handheld power that you can take with you wherever you need it The HP 48 family comes with memory management tools a structured programming language and extensive input output capabilities all characteristic of full size computers Start Here 1 1 About the Quick Start Guide The HP 48G Series Quick Start Guide is designed to help you learn how to use the HP 48 It is organized into lessons each of which guides you through a series of examples that illustrate how to accomplish some task Lessons are grouped into chapters The HP 48G Series Quick Start Guide doesn t provide an example for every feature of the HP 48 But it should provide you with the understanding and confidence to explore the nooks and crannies for yourself Please refer to the HP 48G Series User s Guide if you want to explore an application in greater detail Here are some suggestions a Read lesson I first It shows you how to set up the machine so that the rest of lessons in the machine will work smoothly After this explore the lessons in any order you find convenient m Try the examples They ll give you a good idea of how you can use the HP 48 Actually pushing the keys and watching the HP 48 work while following along is the fastest easiest way to learn Occasionally an individual example will build on the results of a previous calculation or example This is especially true for parameters in the application environments such as

HP 48gx Quick Start Manual

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