HP (Hewlett-Packard) HP 50g manual

HP 5 0g gr aphing calc ulator user ’s manual H Ed it io n 1 HP part number F22 2 9AA-90001[...]

Notice REG ISTER Y OUR PRODU CT A T: ww w .register .hp.com THI S MANU AL AND ANY EX AMPLES CONT AI NED HEREIN ARE PRO VIDED “ AS IS” AND ARE SUBJECT TO CHANGE WITHOUT NO TI CE. HEWLETT -P ACKARD COMP ANY MAKES N O W A R R A N T Y O F A N Y K I N D W I T H R E G A R D T O T H I S M A N U A L , INCLUD ING, BUT N O T LIMITED T O, THE IMPLIE D W A[...]

Pre face Y ou hav e in y our hands a compact sy mbolic and numer ical computer that w ill fac ilitate calc ulation and mathe matical analy sis of pr oblems in a var iety of disc iplines, f rom eleme ntar y mathemati cs to advanced engineering and sc ience sub jects. This manual cont ains ex amples that illustr ate the use of the basic calc ulator f[...]

Page TOC-1 T able of Contents Chapter 1 - Getting started Basic Ope rations , 1-1 Batteries, 1-1 Turning the calculator on and off, 1-2 Adjusting the display contrast, 1-2 Contents of the calculator’s display, 1-3 Menus, 1-3 The TOOL menu, 1-3 Setting time and date, 1-4 Introducing the calculator’s keyboard , 1-4 Selectin g calculator mo des , [...]

Page TOC-2 Editing expressions in the stack , 2- 1 Creating arithmetic expressions, 2-1 Creating algebraic expressions, 2-4 Using the Equation Writer (EQ W) to create expressions , 2-5 Creating arithmetic expressions, 2-5 Creating algebraic expressions, 2-7 Organizing data in the calculator , 2-8 The HOME directory, 2-8 Subdirectories, 2-9 Variable[...]

Page TOC-3 Available units, 3-9 Attaching units to numbers, 3-9 Unit prefixes, 3-10 Operations with units, 3-11 Unit conversions, 3-12 Physical constants in the calculator , 3-13 Defining and using functions , 3-15 Reference , 3-16 Chapter 4 - Calculations with complex numbers Definitions , 4-1 Setting the calculator to COMPLEX mode , 4-1 Entering [...]

Page TOC-4 The PROOT function, 5-9 The QUOT and REMAINDER func tions, 5-9 The PEVAL function , 5-9 Fractions , 5-9 The SIMP2 function, 5-10 The PROPFRAC function, 5 -10 The PARTFRAC function, 5-10 The FCOEF function, 5-10 The FROOTS fu nction, 5-11 Step-by-step operations with polynomials and fr actions , 5-11 Reference , 5-12 Chapter 6 - Solution [...]

Page TOC-5 Addition, subtraction, multiplication, division, 7-2 Functions applied to lists, 7-4 Lists of complex numbers , 7-4 Lists of algebraic objects , 7-5 The MTH/LIST menu , 7-5 The SEQ function , 7-7 The MAP function , 7-7 Reference , 7-7 Chapter 8 - Vectors Entering vect ors , 8-1 Typing vectors in the stack, 8-1 Storing vectors into variab[...]

Page TOC-6 Matrix multiplication, 9-5 Term-by-term multiplication , 9-6 Raising a matrix to a real power, 9-6 The identity matrix, 9-7 The inverse matrix, 9- 7 Characterizing a matrix (The matrix NORM menu) , 9-8 Function DET, 9-8 Function TRACE, 9-8 Solution of linear systems , 9-9 Using the numerical solver for linear systems, 9-9 Solution with t[...]

Page TOC-7 Chapter 12 - Multi-variate Calculus Applications Partial derivati ves , 12-1 Multiple integrals , 12-2 Reference , 12-2 Chapter 13 - Vector Analysis Applications The del operator , 13-1 Gradient , 13-1 Divergence , 13-2 Curl , 13-2 Reference , 13-2 Chapter 14 - Differential Equations The CALC/DIFF menu , 14-1 Solution to linear and non-l[...]

Page TOC-8 Reference , 15-4 Chapter 16 - Statistical Applications Entering data , 16-1 Calculating single-variable statistics , 16-2 Sample vs. population , 16-2 Obtaining frequency distributions , 16-3 Fitting data to a function y = f(x) , 16-5 Obtaining additional summary statistics , 16-6 Confidence intervals , 16-7 Hypothesis testing , 16-9 Ref[...]

Page 1-1 Chapter 1 Gett in g st art ed This c hapter pr ov ides basi c infor mation about the oper ation o f your calc ulator . It is designed to famili ari z e yo u with the basi c operati ons and settings bef or e you perfor m a calculati on. Basic Ope ratio ns Batt er ies The calc ulator us es 4 AAA (LR03) batteri es as main po wer and a CR20 3 [...]

Page 1-2 b . Insert a new CR203 2 lithium bat tery . Make sur e its positiv e (+) side is facing up . c. Replace the plate and push it to the ori ginal place. After installing the batter ies, pr ess $ to turn the p o wer o n. Wa rn i ng : When the low battery icon is displa yed , you need to r eplace the batteri es as soon as possible . Ho wev er ,[...]

Page 1-3 Contents of the calculator ’s displa y T urn yo ur cal c ulato r on o nce mo r e. At t he top of th e dis pla y y ou w ill hav e two line s of infor mation that desc ribe the s ettings of the calculator . The f irst line sho ws the c har acters: RAD XYZ HEX R= ' X' F or details on the meaning o f these s ymbols see Ch apter 2 i[...]

Page 1-4 These si x functi ons form the f irst page of the T OOL menu . This menu has actually e ight entr ies arr anged in t w o pages. The second page is av ailable by pr essing the L (NeXT menu) k ey . This k ey is the third k ey fr om the left in the thir d r ow of k ey s in the k ey board . In this case , only the firs t t w o soft menu ke ys [...]

Page 1-5 F or ex ample , the P key , key (4,4 ) , has the follo w ing six f unctio ns associated with it: P Main functi on, to ac tiv ate the S YMBolic menu „´ Le f t-shift functi on, to acti vat e the MTH (Math) men u …N R ight-shift f unction , to activ ate the CA T alog func tion ~p ALPHA func tion, to enter the upper -case letter P ~„p A[...]

Page 1-6 Of the six f unctions ass ociat e d w ith a k ey onl y the firs t four ar e shown in the ke yboar d itself . The f igure in ne xt page show s these four labels for the P ke y . Notice that the color and the position of the labels in the k ey , namely , SY MB , MTH , CA T and P , indicate w hich is the main func tion ( SY MB ) , and w hich [...]

Page 1-7 Operating Mode The ca lc ulator off ers tw o operating mode s: the Alg eb r a ic mode , and the Reverse P ol ish N ota tion ( RPN ) mode . The def ault mode is the Algebr aic m o d e ( a s i n d i c a t e d i n t h e f i g u r e a b o v e ) , h o w e v e r , u s e r s o f e a r l i e r H P calc ulators ma y be mor e famili ar with the RPN [...]

Page 1-8 Y ou could also ty pe the expr essio n directl y into the displa y w ithout using the equation w riter , as f ollow s: R!Ü3.*!Ü5.- 1/3.*3.™ /23.Q3+!¸2.5` to obtain the same result . Change the oper ating mode to RPN b y fir st pre ssing the H butto n. Select the RPN operating mode b y either u sing the k e y , o r p r e s s i n g th[...]

Page 1-9 Let's try some other sim ple operatio ns befor e trying the mor e complicat ed expr essi on used earlier f or the algeb r aic oper ating mode: Note the positi on of the y and x in the last tw o operati ons. T he base in the e xponential oper ation is y (stac k leve l 2) while the e xponent is x (stac k lev el 1) bef or e the ke y Q is[...]

Page 1-10 T o select between the AL G v s. RPN operating mode , y ou can a lso s et/ clear s ys tem flag 9 5 thr ough the follo w ing k e ystr ok e sequence: H @FLAGS! 9˜˜ ˜˜ ` Number F ormat and dec imal dot or comma Changing the numbe r form at allow s yo u to cus tomi z e the wa y real numbers ar e displa yed b y the calculator . Y ou w ill [...]

Page 1-11 Pr ess the ri ght arr ow k e y , ™ , to highlight the z er o in front o f the option Fix . Pr ess the @ CHOOS soft menu k ey and , using the up and dow n arr ow keys, —˜ , select , say , 3 dec imals. Pr ess the !!@@OK#@ soft m enu k ey to comp lete the sele ction: Pr ess the !!@@OK#@ so ft men u k e y r e tur n t o th e ca lc ula to [...]

Page 1-12 K eep the number 3 in fr ont of the Sc i . (T his number can be c hanged in the same fashi on that we c hanged the Fix e d number of decimals in the e xample abo ve). Pr ess the !!@@OK#@ so ft men u k e y r etu rn t o t he c alc ul at or d isp la y . T he nu mbe r now is sho wn as: This r esult , 1.2 3E2 , is the calc ulator ’s versi on[...]

Page 1-13 Pr ess the !!@@OK#@ so ft men u k e y r e tur n t o th e ca lc ula to r di spl a y . T he n um ber now is sho wn as: Becaus e this number has thr ee fi gures in the integer part, it is sho wn w ith four si gnifi cativ e figur es and a z er o pow er of ten, while using the Engineer ing format . F or e xample , the number 0. 00 2 56 , w ill[...]

Page 1-14 Angle Measure T rigonometr ic fu nctions, f or e xample , req uire ar guments r eprese nting plane angles . The calc ulator pro vi des three diff eren t Angle Measure modes f or wor ki ng wi th an gl e s, n a me ly: • Degr ees : T her e are 360 degr ees ( 360 ° ) in a co mp le t e ci rcum fe ren ce. • Radi ans : Ther e are 2 π r adi[...]

Page 1-15 soft men u ke y to complete the oper ation . For e xample , in the follo wing scr een , the P olar co or dinate mode is selected: Selec ting CA S set tings CA S stands fo r C omputer A lgebr aic S ys tem. T his is the mathematical core of the calculator w her e the s ymboli c mathema ti cal op er ations and func tions are pr ogrammed . T [...]

Page 1-16 Non-Rati onal o pti ons above). Unselected options w ill show no chec k mark in the underline pr eceding the option of inter est (e.g ., the _Numeri c, _Appr ox , _Comple x, _V erbos e, _St ep /S tep, _Inc r P ow options abov e) . • After ha ving s elected and unse lected all the options that y ou wan t in the CA S M OD E S input form ,[...]

Page 1-17 Selec ting Displa y modes The calc ulator displa y can be cu stomi zed to your pr ef erence b y selecting differ ent displa y modes. T o see the optional displa y settings use the follo w ing: •F i r s t , p r e s s t h e H button to activ ate the CAL CULA T OR MODE S in put fo rm. W ithin the CAL CUL A T OR MODES in put for m, pr ess t[...]

Page 1-18 Selec ting the displa y font Fi r st, p r es s t h e H button to activate the CAL CUL A T O R MODE S i nput fo rm. W ithin the CAL CULA T OR MODE S input for m, pr ess the @@DISP@ soft menu k ey t o display the DISP L A Y MODE S input for m. T he Fo nt : fi eld is highlighted , and the option Ft8_0: sy stem 8 is selected . This is the def[...]

Page 1-19 Selecting properties of the Stack Fi r st, p re s s th e H but ton to activ ate t he CAL CULA T OR MOD E S input for m. W ithin the CAL CUL A T OR MODES inpu t form , pre ss the @@DISP@ soft menu k ey ( D ) to display the DISPLA Y MODES in put for m. Pr ess the do wn arr ow k ey , ˜ , t w ice , to get to the St ack line. T his line show [...]

Page 1-20 Selecting properties of the equation writer (E QW ) Fi r st, p r es s t h e H button to activate the CAL CUL A T O R MODE S i nput fo rm. W ithin the CAL CULA T OR MODE S input for m, pr ess the @@DISP@ soft menu k e y to display the DISPLA Y MODE S input f orm . Pres s the dow n arr ow k e y , ˜ , three time s, to get to the EQ W (E qua[...]

Page 2-1 Chapter 2 Intr oduc ing the calc ulat or In this chapte r we pr esent a number o f basic oper ations of the calc ulator including the us e of the E quation W riter and the manipulati on of data obje cts in the calc ulator . Study the e xample s in this chapter to get a good gr asp of the capab ilities of the calc ulator fo r futur e applic[...]

Page 2-2 Notice that , if y our CAS is set to EXA CT (see Appendi x C in user ’s guide) and y ou enter y our expr essi on using integer numbers f or integer v alues, the r esult is a s ymboli c quantity , e.g ., 5*„Ü1+1/7.5™/ „ÜR3-2Q3 Bef ore pr oduc ing a re sult, y ou w ill be asked t o change to Appr ox imate mode . Accept the change t[...]

Page 2-3 If the CAS is s et to Exact , you w ill be ask ed to appro ve c hanging the CAS setti ng to Appr ox . Once this is done , you w ill get the same result a s bef ore . An alter nativ e wa y to ev aluate the expr essi on enter ed earlie r bet w een quote s is b y using the option …ï . W e will no w ente r the expr essi on used abo v e when[...]

Page 2-4 Creating algebraic e x pr essions Algebr aic e xpres sions include n ot only number s, but also v aria ble names. As an ex ample , we w ill enter the follo w ing algebraic e xpr ession: W e set the calculat or operating mode to A lgebrai c, the CA S to Ex act , and the display to Te x t b o o k . T o enter this algebr aic e xpres sion we u[...]

Page 2-5 Using the Equation W riter (EQW) to create ex p re s s i o ns The equati on wr iter is an extr emely po w er f ul tool that not only let y ou enter or see an equati on, but als o allow s yo u to modify and wor k/apply functi ons on all or part of the equation. The Equati on W r iter is launched by pr essing the k e ystr ok e combination ?[...]

Page 2-6 Suppose that y ou w ant to replace the quan tit y betw een parenthes es in the denominator (i.e ., 5+1/3) with (5+ π 2 /2). Fir st , we u se the delet e ke y ( ƒ ) delete the c urr ent 1/3 expr essi on, and then w e replace that fr action wit h π 2 /2 , as follo ws: ƒƒƒ„ìQ2 When hit this point the s cr een looks as follo ws: In or[...]

Page 2-7 F irst , we need to highlight the entire f irst ter m by using either the r ight arr ow ( ™ ) or the upper arr ow ( — ) ke ys , repeatedl y , until the entire e xpres sion is hi ghlighted , i .e., s ev en times, produc ing: Once the e xpressi on is highligh ted as show n abov e , type +1/ 3 to add the fr action 1/3 . Re sulting in: Cre[...]

Page 2-8 ~„y———/~‚tQ1/3 This r esults in the output: In this e xample w e used se ver al low er -case English letter s, e .g., x ( ~„x ), se v er al Gr ee k l e tt er s , e .g ., λ ( ~‚n ), and even a combinati on of Greek and English le tters, namel y , ∆ y ( ~‚c~„y ) . K e e p i n m i n d t h a t t o e n t e r a l o w e r - c[...]

Page 2-9 Subdirectories T o store y our data in a w ell or ganiz ed direct or y tr ee yo u may w ant to cr eate subdir ector ies under the HOME dir ectory , and more subdir ectori es w ithin subdirec tori es, in a hier arc hy o f direct ories similar t o folders in modern co mputers . T he subdir ector ies w ill be giv en names that may r ef lect t[...]

Page 2-10 T o unlock the upper -case lock ed ke yboar d, pr ess ~ . T r y the f ollow ing ex er cis es: ~~math` ~~m„a„t„h` ~~m„~at„h` The calc ulator dis play w ill sho w the follo wing (l eft -hand side is A lgebrai c mode , righ t -hand side is RPN mode): Creating v ariables The si mp les t way to creat e a varia bl e i s by us ing t he[...]

Page 2-11 The fo llow ing are the k eys trok es for ente ring the remaining var iables: A12: 3V5K~a 12` Q: ~„r/„Ü ~„m+~„r™™ K~q` R: „Ô3‚í2‚í1™K~r` z1: 3+5*„¥K~„z1` (Accep t cha nge to Com pl ex mode if asked). p1: å‚é~„r³„ì* ~„rQ2™™™ K~„p1` . The sc reen , at this po int , will loo k as follo ws: Y o[...]

Page 2-12 T o enter the value 3 × 10 5 i n t o A 1 2 , w e c a n u s e a s h o r t e r v e r s i o n o f t h e pr ocedu r e: 3V5³~a12`K Here is a w ay to enter the contents of Q: Q: ~„r/„Ü ~„m+~„r™™³~q`K T o enter the v alue of R, w e can use an ev en shorter versio n of the pr ocedu r e: R: „Ô3#2#1™ ³~rK Notice that to s epar[...]

Page 2-13 Chec king v ariables contents The si mp les t way to ch eck a va riab le co nte nt i s by pres si ng th e sof t men u k ey label f or the var iable . F or ex ample , for the v ari ables listed abo ve , pr ess the follo w ing ke ys to see the conte nts of the var iables: Algebraic mode T ype thes e ke ystr okes: J @@z1@@ ` @@@R@@ ` @@@Q@@@[...]

Page 2-14 This pr oduces the f ollow ing scr een (A lgebraic mode in the left , RPN in the rig ht ) Notice that this time the contents of pr ogr am p1 are lis ted in the scr een . T o see the r emaining var iables in this dir ectory , pre ss L . Listing the contents of all var iables in t he screen Use the k ey str oke comb ination ‚˜ to list th[...]

Page 2-15 Y ou can us e the PURGE command t o erase mor e than one v aria ble by plac ing their names in a list in the ar gument of P URGE . F or ex ample , if now we wan te d to pu rg e va ria bl es R and Q , simultaneously , w e can try the follo wing e xer cis e. Pr ess : I @PURGE@ „ä³J @@@R!@@ ™‚í³J @@@Q!@@ At this po int, the scr een[...]

Page 2-16 UNDO and CMD functions F unctions UNDO and CMD are us eful for r ecov er ing r ecent commands, or to r ev ert an operati on if a mistak e was made . The se functi ons are ass oci ated w ith the HIS T k ey : UNDO re sults fr om the k ey str ok e sequ ence ‚¯ , whi le CMD re sults fr om the k ey str ok e seque nce „® . CHOOSE bo xes v[...]

Page 2-17 Ther e is an alter nativ e wa y to access these menus as soft MEN U keys, by sett ing sy stem f l ag 117 . (F or infor mation on F lags see Chapt ers 2 and 2 4 in the calc ulator’s user ’s guide) . T o set this flag try the fol low ing: H @FLAGS! ——————— The s cr een sho w s flag 117 not se t ( CHOOSE bo xe s ) , as sho [...]

Page 2-18 Pr ess B to sel ect the MEMOR Y soft me nu ( ) @@MEM@ @ ). T h e di s pl a y n o w sho ws: Pr ess E to sele ct the DIR E CTOR Y sof t menu ( ) @ @DIR@@ ) The ORDER command is not sho wn in this sc reen . T o f ind it we us e the L key to fi n d i t : T o a c tiv ate the ORD ER command w e pres s the C ( @ORDER ) soft menu ke y . Refe renc[...]

Page 3-1 Chapter 3 Calculations with real numbers This c hapter demons trates the use of the calc ulator for ope ratio ns and functi ons rel ated to real n umbers. T he user should be acq uainted with the k ey boar d to iden tify ce rtain functi ons av ailable i n the ke ybo ard (e .g ., SIN , CO S, T AN, etc .) . Als o, it is assumed that the r ea[...]

Page 3-2 6.3#8.5- 4.2#2.5* 2.3#4.5/ • P arentheses ( „Ü ) can be us ed to gr oup oper ations, a s well as to enclose argum ents of fun ctions. In AL G mode: „Ü5+3.2™/„Ü7- 2.2` In RPN mode , you do not need the par enthesis, calc ulatio n is done dir ectly on the s tack: 5`3.2+7`2.2-/ In RPN mode , t y ping the e xpres sion betwee n sin[...]

Page 3-3 • The po w er function , ^, is availa ble through the Q key . Wh en calc ulating in the s tack in AL G mode, ente r the base ( y ) fo llow ed by the Q k ey , and then the e xponent ( x ), e .g . , 5.2Q1.25` In RPN mode, ente r the number firs t, then the f unction , e.g ., 5.2`1.25Q • The r oot functi on, XROO T (y ,x) , is a vailable [...]

Page 3-4 2.45`‚¹ 2.3`„¸ • Thr ee tri gonometr ic functi ons are r eadily a vailable in the k ey board: sine ( S ), co si ne ( T ), and tangent ( U ). Ar guments of thes e functi ons ar e angles in either degrees , radi ans, gr ades. The f ollo wing e xample s us e angles in degr ees (DE G): In AL G mode: S30` T45` U135` In RPN mode: 30S 45[...]

Page 3-5 Real number functions in th e MTH menu The MT H ( „´ ) menu include a number of mathemati cal func tions mostl y applicable to r eal numbers . With the defa ult setting of CHOOSE bo xes for sy s tem fl ag 1 17 (see Chap ter 2 ) , th e MTH men u shows th e foll ow i ng fu nct ions : The f unctions ar e gr ouped by th type of argument (1.[...]

Page 3-6 F or e xample , in AL G mode, the k ey str ok e sequence to calc ulate , say , tanh( 2 .5 ) , is the fo llow ing : „´4 @@OK @@ 5 @@OK@@ 2.5` In the RPN mode , the ke ys trok es to perfo rm this calculati on are the follo wing: 2.5`„´4 @@OK@@ 5 @@OK@@ The oper ations sho wn a bov e assume that y ou are u sing the defaul t setting fo r[...]

Page 3-7 F inally , in o rder to s elect, for e xample , the hy perboli c tangent (tanh) functi on, simpl y press @ @TANH@ . F or ex ample , to calculat e tanh(2 . 5) , in the AL G mode, w hen using SO F T menus over CHOOSE box es , f ollo w this pr ocedur e: „´ @@HYP@ @ @TANH@ 2.5` In RPN mode , the same value is calc ulated using: 2.5`„´ ) [...]

Page 3-8 Option 1. T ools.. cont ains functi ons used to operate on units (discu ssed later ) . Opti ons 2. L e n g t h . . t h r o u g h 17 .Viscosity .. contai n menus w ith a number of u nits f or each o f the quantities desc ribed . F or ex ample , selec ting option 8. F or ce.. sho ws the f ollo wing units me nu: The us er will r ecogni ze mo [...]

Page 3-9 Pr essing on the appropr iate soft men u ke y will open the sub-menu of units fo r that partic ular selecti on. F or ex ample, f or the @) SPEED sub-men u, the fo llow ing units are a vailable: Pr essing the so ft menu k ey @) UNITS w ill ta k e you back to the UNIT S menu. Recall that you can al wa ys list the f ull menu labels in the s c[...]

Page 3-10 5‚Û8 @@OK@@ @@OK@@ Notice that the under scor e is enter e d aut omaticall y when the RPN mode is acti ve . The k ey str oke sequence s to enter units when the SO FT m en u option is select ed, in both AL G and RPN modes, ar e illustr ated ne xt. F or ex ample , in AL G mode , to enter the quantity 5_N use: 5‚Ý‚ÛL @ ) @FORCE @@ @[...]

Page 3-11 123‚Ý~„p~„m Using UB ASE (type the name) to con vert to the def ault unit (1 m) results in: Operations w it h units Her e are some cal culatio n ex amples using the AL G operating mode . Be war ned that, w hen multiply ing or di viding q uantities w ith units, y ou must enc losed eac h quantity with it s units between par enthe ses[...]

Page 3-12 Additi on and subtracti on can be performed , in AL G mode, w ithout using par entheses, e .g., 5 m + 3 200 mm, can be enter ed simpl y as 5_m + 3 200_mm ` . Mor e complicated expr ession r equire the us e of parenthes es, e .g., (12_mm)*(1_cm^2)/( 2_s) ` : Stac k calculati ons in the RPN mode do not r equir e you to enc lose the differ e[...]

Page 3-13 Ph ysical constants in the calculator The calc ulator’s ph y sical const ants are con tained in a constants libr ar y acti vated w ith the command CONLIB. T o launch this command y ou could simpl y type it in the s tack: ~~conl ib` , or , you can select the command C ONLIB fr om the command cat alog, as f ollo ws: F irs t, launch the ca[...]

Page 3-14 If w e de -select the UNIT S option (pr ess @UNITS ) only the v alues are sho wn (English units select ed in this case) : T o copy the va lue of Vm to the stac k, select the vari able name , and pres s @²STK , then, press @QUIT@ . F or the calc ulator set to the AL G, the scr een w ill look lik e this: The dis play sho ws what is called [...]

Page 3-15 Defining and using functions Users can de fine their o wn f unctions b y using the DEFINE com mand av ailable thought the ke ystr ok e sequence „à (assoc iated w ith the 2 ke y). T he function mus t be ent ered in the follo w ing f ormat: F unction_name(arguments) = e xpres sion_containing_ar g uments F or ex ample, w e could define a [...]

Page 3-16 r elativ ely simple and consists of tw o par ts , contained between the pr ogram containers This is to be in terpr eted as say ing: enter a v alue that is temporar ily assigned to the name x (r eferr ed to as a local var iable), eval u ate the expr ession bet w een quotes that contain that local vari able, and sh ow the eval ua ted exp re[...]

Page 4-1 Chapter 4 Calculations with complex numbers This c hapter sho ws e xamples o f calcul a ti ons and applicati on of func tions to comple x number s. Definitions A comple x number z is a number z = x + iy , whe re x and y ar e r eal number s, and i is the imaginary unit def ined by i ² = –1. T he complex num ber x + iy ha s a r eal part, [...]

Page 4-2 Pr ess @@OK @@ , t w ice, to r etu rn to the stack. Entering comple x numbers Com plex numbe rs in the calculat or can be enter ed in e ither of the tw o Carte sian representations, na mely , x+iy , or (x,y) . The re su lts in the calculat or will be sho wn in the or der ed-pair for mat, i .e ., (x,y) . F or e xample , with the calc ulator[...]

Page 4-3 P olar repr esentation of a complex number The polar r epres entation of the comple x number 3. 5-1.2i, enter ed abov e, is obta ined by changing th e coor di nate sy stem to cylindrical or pol ar (using func tion CYLIN). Y ou can find this f unction in the catalog ( ‚N ). Y ou can also change the coordinat e to polar using H . Changing [...]

Page 4-4 Sim ple o per ati ons w ith comp le x nu mber s Com plex number s can be combined using the f our fundamental oper ations ( +-*/ ). The r esults f ollow the rules of algebr a w ith the cav eat that i2= -1 . Oper ations w ith complex number s are similar to tho se with r eal numbers . For e x ample, w ith the calc ulator in AL G mode and th[...]

Page 4-5 The f irst men u (options 1 thr ough 6) sho ws the f ollow ing f unctions: Example s of appli cations o f these f unctio ns are sho wn next in RECT coor dinates. R ecall that, f or AL G mode , the function mu st pr ecede the argumen t, w hile in RPN mode, y ou enter the ar gument f irst , and then select the func tion. A lso , recall that [...]

Page 4-6 CMP LX m enu in k ey board A second CMP LX menu is accessible by u sing the righ t -shift option assoc iat ed with the 1 k ey , i .e., ‚ß . With s y stem f lag 117 set to CHOO SE box es, the ke yboar d CMP LX menu sho w s up as the f ollo wing scr e ens: The r esulting men u include some of the f unctions alr eady intr oduced in the pr [...]

Page 4-7 Function DROITE: equation o f a straight line F unction DROITE tak es as ar gument t w o complex number s, say , x 1 + iy 1 and x 2 +iy 2 , and r eturns the equati on of the strai ght line, sa y , y = a + bx, that contains the po ints (x 1 , y 1 ) and (x 2 , y 2 ) . For exa mp le, th e l i ne between po ints A(5, -3) and B(6, 2) can be fou[...]

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Page 5-1 Chapter 5 Algebraic and arithmetic oper ations An algebr aic object , or simply , algebr aic , is an y number , var iable name or algebrai c expr essi on that can be oper ated upon , manip ulat ed, and combined accor ding to the ru les of algebr a. Ex amples of algebr aic obj ects ar e the follo wing: Entering algebr aic objec ts Algebr ai[...]

Page 5-2 Simple operations w it h algebr aic objec ts Algebr aic ob jects can be added , subtrac ted, m ultiplied, div ided (e xcept b y z er o) , r aised to a po wer , us ed as arguments f or a var iety of standar d functi ons (exponenti al, logarithmi c, tr igonometry , h yperboli c, etc .) , as y ou w ould any r eal or complex n umber . T o demo[...]

Page 5-3 @@A1@@ * @@A 2@@ ` @@A1@@ / @@A2@@ ` ‚¹ @@A1@@ „¸ @@A2@@ The same re sults are obtai ned in RPN mode if using the f ollo wing keyst rokes : Functions in the AL G menu The A L G (Alg ebrai c) menu is a vailable b y using the k e ystr oke s equence ‚× (ass oci ated w ith the 4 ke y). W ith sy stem f lag 117 set to CHOOSE bo x es , t[...]

Page 5-4 T o complete the oper ation pr ess @@OK@ @ . Here i s t he h elp screen for fun ctio n COL LECT : W e noti ce that, at the bottom of the sc reen , the line See: EXP AND F A CT OR suggests links t o other help fac ility entri es, the f unctions E XP AND and F A CT OR. T o mov e dire ctly to thos e entri es, pr ess the so f t men u ke y @SEE[...]

Page 5-5 F or ex ample , for f unction S UBS T , w e find the f ollow ing CA S help fac ility entry: Operations wi t h tr anscende ntal functions The calc ulator off ers a number of fu nctions that can be used to r eplace e xpressi ons containing logar ithmic and e xponential func tions ( „Ð ), as well as trigonometric functions ( ‚Ñ ). Expan[...]

Page 5-6 Info rmation and e xample s on these commands ar e a vailable in the help fac ility of the calc ulator . F or e xample , the desc ri ption of E XPLN is sho wn in the left-hand side , and the exam ple fr om the help fac ility is show n to the rig ht : Expansion and factoring using tr igonometric functions The TRIG me nu, tr igger ed by usin[...]

Page 5-7 Functions in the ARITH M E TIC menu The ARI THMETIC menu is tr igger ed thr ough the ke ystr oke comb ination „Þ (assoc iated with the 1 k ey). With sys tem flag 117 set to CHOOSE bo xes , „Þ sho ws the f ollo wing men u: Out of this menu list , opti ons 5 thro ugh 9 ( D IVI S, F A CT OR S, L GCD, PR OPFRAC, SIMP2 ) corr espond to co[...]

Page 5-8 Po l y n o m i a l s P oly nomials ar e algebr aic expr es sions consisting of one or mor e terms containing dec rea sing po wers of a gi ven v ari able. For ex ample , ‘X^3+2*X^2 -3*X+2’ is a thir d-order pol y nomi al in X, while ‘S IN(X)^2 - 2’ is a second-or der poly nomial in S IN(X) . F uncti ons COLLECT and E XP AND, sho wn [...]

Page 5-9 Th e PROOT f unc t io n Gi ven an ar ra y containing the coeffi c i ents of a pol ynomial , in decr easing or der , the functi on PROO T pro vi des the r oots of the poly nomial . Example , from X 2 +5X+6 =0, P ROO T([1, –5, 6]) = [2 . 3 .]. Th e Q UO T and RE MA IN DE R f un ct io ns The f unctions QUO T and REMAINDER pro vi de, r espec[...]

Page 5-10 F A CT OR(‘(X^3-9*X)/(X^2 -5*X+6)’ )=‘X*(X+3)/(X- 2)’ The SIMP2 function F unction S IMP2 , in the ARITHME TIC men u, t akes as ar guments two number s or polyn omials, r epre senting the numer ator and denominator of a r ational fr action , and retur ns the simplified n umerator and de nominator . F or ex ample: SIMP2( ‘X^3-1?[...]

Page 5-11 FCOEF([2 ,1,0, 3,–5,2 ,1,–2 ,–3 ,–5])=‘(X--5 )^2*X^3 *(X- 2)/(X-+3)^5*(X-1)^2’ If y ou pres s µ„î` (or , si mpl y µ , in RPN mode) yo u will get: ‘(X^6+8*X^5+5*X^4-50*X^3 )/(X^7+13*X^6+61*X^5+10 5*X^4 - 4 5*X^3- 2 9 7*X6 2 -81*X+2 4 3)’ Th e F ROOTS fu n c ti on The f uncti on FROO T S, in the ARI THMET IC/P OL YNOMIA[...]

Page 5-12 Refe renc e Additi onal informati on, def initions , and ex amples of algebr aic and arithme tic oper a ti ons are pr esent ed in Chapter 5 of the calc ulator’s us er’s guide . SG49A.book Page 12 Friday, September 16, 20 05 1:31 PM[...]

Page 6-1 Chapter 6 Solution to equations Assoc iated w ith the 7 ke y there ar e two menu s of equation -sol ving functi ons, the S ymboli c SOL V er ( „Î ) , and the NUMer ical S oL V er ( ‚Ï ). Fo llow ing, w e pr esent some o f the functi ons contained in these men us. S y mbolic solution of algebr aic equations H e r e w e d e s c r i b e[...]

Page 6-2 the fi gure to the le ft. A fter apply ing IS OL, the r esult is show n in the fi gure to the ri ght: The f irst ar gument in IS OL can be an e xpre ssion , as show n abov e , or an equation . For e xample , in AL G mode, try: The same pr oblem can be sol ved in RPN mode as illus trate d be low (f igur es sho w the RPN stac k befor e and a[...]

Page 6-3 The f ollo wing e xamples sh ow the us e of functi on SOL VE in AL G and RPN modes (Us e Comple x mode in the CA S): The scr e en shot s ho wn above displays two solut ions. In the f irst one , β 4 -5 β = 1 2 5 , S O L V E p r o d u c e s n o s o l u t i o n s { } . I n t h e s e c o n d o n e , β 4 - 5 β = 6, S OL VE p r odu ce s f ou[...]

Page 6-4 Fun c tio n SOL VEV X The f unction S OL VEVX solv es an equati on for the defa ult CAS var iable co nta in ed in th e rese r ved variab le na me VX . By d efau lt, th is va riab le is set to ‘X’ . Ex amples, using the AL G mode with VX = ‘X’ , a r e show n below : In the fir st case S OL VEVX could not find a solu tion. In the sec[...]

Page 6-5 sc reen shots sh ow the RPN st ack bef ore and afte r the applicatio n of ZERO S to the tw o ex amples abov e (Use Complex mode in the CAS): The S ymbolic S olve r functions pr esen ted abov e produ ce solutions to rati onal equations (mainl y , polynomi al equations). If the equation to be sol ved f or has all numer ical coeffi c ients, a[...]

Page 6-6 w ith ex amples for the numeri cal sol ver appli cations. It em 6. MSL V (Multiple equation SoL V er) w i ll be prese nted later in page 6 -10 . P oly nomial Equations Using the So lv e poly… opti on in the calculator’s SOL V E en vironment you can: (1) find the s olutions to a pol ynomi al equation; (2) obtain the coeffi ci ents of th[...]

Page 6-7 Pr ess ` to retur n to stack . The s tack w ill show the f ollo wing r esults in AL G mode (the s ame result w ould be sho wn in RPN mode): All the soluti ons are comple x numbers: (0.4 3 2 , -0.3 8 9) , (0.4 3 2 , 0.3 8 9) , (- 0.7 66 , 0.6 3 2) , (-0.7 6 6, -0.6 3 2) . Generating pol ynomial coeffic ients given the polynomial's roo [...]

Page 6-8 Generating an algebraic e xpression f or th e pol ynomial Y ou can us e the calculator to ge nerate an algebr aic e xpre ssion f or a poly nomial gi ven the coeff ic ients or the r oots of the pol ynomial . The r esulting expr essi on will be gi v en in terms of the de fault CA S vari able X. T o generate the algebr aic e xpres sion using [...]

Page 6-9 Solv ing equations with one unknow n through NUM.SL V The calculator's NUM .SL V menu pr ov ides item 1. Sol ve equation .. so lve diffe rent ty pes of equati ons in a single vari able , including non-linear algebrai c and transcende ntal equations . F or ex ample , let's solv e the equati on: ex- si n ( π x/3) = 0. Simply en te[...]

Page 6-10 T he e qu ati on we st or ed i n v ar ia bl e E Q i s al r ead y l oad ed i n th e Eq fiel d i n the SO L VE E QU A TION in put for m. Also , a fiel d labeled x is pr ov ided . T o solv e the equation all y ou need to do is highlight the fi eld in front o f X: b y using ˜ , and pres s @SOLVE@ . The s olution show n is X: 4.5 006E- 2 : Th[...]

Page 6-11 In AL G mode, pr ess @ECHO t o copy the e xample to the stack , pre ss ` to run the e x a m ple. T o see all the ele ments in the solution y ou need to acti vate the line edito r by pr essing the do wn arr o w ke y ( ˜ ): In RPN mode , the solutio n f or this ex ample is pr oduced by u sing: Acti vating f unction M SL V resul ts in the f[...]

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Page 7-1 Chapter 7 Ope r atio ns w ith l ist s L ists are a type o f calculator ’s object that can be us eful f or data pr ocessing. This c hapter pr esents e xamples of operatio ns with list s. T o get started w ith the e xamples in this C hapter , w e use the Appr o ximate mode (S ee Chapter 1). Creating and stor ing lists T o c reat e a list i[...]

Page 7-2 Addition, subtr action, multiplication, div ision Multiplicati on and div ision of a list b y a single number is distr ibuted acr oss the list , for e xample: Subtr action of a single n umber from a list w ill subtr act the s ame number fr om each element in the list , for e xample: Additi on of a single number to a list pr oduces a list a[...]

Page 7-3 The di v ision L4/L3 w ill produce an inf inity e ntr y becau se one of the elements in L3 is z er o, and an e rr or message is r eturned . If the lists in vol ved in the operati on hav e differ ent lengths , an err or mess age (Inv alid Dimensions) is pr oduced. T ry , for e xampl e, L1-L4. The pl us s ig n ( + ), when appli ed to lists, [...]

Page 7-4 Functions applied to lists Real n u mber f unctions fr om the ke yboar d (ABS , e x , LN, 10 x , L OG, S IN, x 2 , √ , CO S, T AN, A SIN, A COS , A T AN, y x ) as well as those fr om the MTH / HYPERB OLIC menu (SINH, CO SH, T ANH, A SINH, A CO SH, A T ANH) , and MTH/REAL menu (%, etc .), can be applied t o lists, e .g., L ists of complex[...]

Page 7-5 Lists o f alg ebr aic objec ts The f ollo wing ar e e xamples of lis ts of algebrai c objec ts with the fun ction SIN appli ed to them (selec t Exact mode f or these e xampl es -- See Chapter 1): Th e M T H/ LI ST m e nu The MTH men u pro vi des a number of func tions that ex clu siv ely to lis ts. W i t h s y s t e m f l a g 1 1 7 s e t t[...]

Page 7-6 Example s of applicati on of these f unctions in AL G mode are sh ow n next: S ORT and REVLI ST can be combined t o sort a list in decr easing or der: If y ou are w orking in RPN mode , enter the list on to the stac k and then select the ope ratio n you w ant. F or ex ample , to calculate the inc remen t between consec utiv e elements in l[...]

Page 7-7 Th e S EQ fu n c ti on The SE Q functi on, a vailable thr ough the command catalog ( ‚N ), tak es as argume nts an expr ession in te rms of an index , the name of the inde x, and starting , ending, and incr ement v alues for the inde x, and r eturns a list consisting of the e valuation o f the e xpre ssion for all pos sible values o f th[...]

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Page 8-1 Chapter 8 Ve c t o r s This Ch apter pr ov ides e xamples o f enteri ng and operating w ith vec tors, both mathematical v ectors o f many e lements, as w ell as ph ysical v ector s of 2 and 3 components . Entering v ec tors In the calculat or , vect ors ar e repr esent ed by a sequence o f numbers enclo sed betwee n brac kets , and t y pic[...]

Page 8-2 Stor ing vectors into v ariables in the stack V e c t o r s c a n b e s t o r e d i n t o v a r i a b l e s . T h e s c r e e n s h o t s b e l o w s h o w t h e ve cto rs u 2 = [1, 2] , u 3 = [-3, 2, -2] , v 2 = [3,-1] , v 3 = [1, -5, 2] Stored in to variables @@@u2@@ , @@@u3@@ , @@@v2@@ , and @@@v3@@ , respec tiv ely . F irst , in AL G m[...]

Page 8-3 Using the M atri x W riter (MTR W ) to enter v ec tors V ectors can also be e ntered b y using the Matr ix W r iter „² (thir d ke y in the fo ur th r ow o f ke y s fro m the top of the k ey board). This command gener ates a spec ies of spr eadsheet corr esponding t o ro ws and columns of a matri x (Details on using the Matr ix W rit er [...]

Page 8-4 @+ROW@ @- ROW @+COL@ @-COL@ @GOTO@ The @+ROW@ ke y will add a r ow f ull of z ero s at the location of the se lected cell of th e spr eadsheet. The @-ROW k ey will dele te the ro w corr esponding t o the selected cell o f the spr eadsheet. The @+COL@ k ey w ill add a column full of z er os at the location of the selec ted cell of the spre [...]

Page 8-5 Simple operations w it h v ec tors T o illustr ate operati ons wi th vect ors we w ill use the v ector s u2 , u3, v2 , and v3, sto r ed in an earlier e xerc ise. Also , stor e vector A =[-1,- 2 ,- 3,- 4,-5] to b e used in the f ollow i ng e xe rc ises. Changing sign T o c hange the sign of a v ector use the k ey , e .g., Addition, subtr [...]

Page 8-6 Multiplication by a s calar , and div ision b y a scalar Multiplicati on by a scalar or di vi sion by a scalar is s traigh tforwar d: Absolute v alue func tion The ab solute value f unction ( ABS), when appli ed to a vector , produ ces the magnitude of the ve ctor . F or ex ample: ABS( [1,-2,6]) , ABS(A) , ABS(u3) , w ill sho w in the s cr[...]

Page 8-7 Magnitud e The magnitude of a v ector , as discus sed earlier , can be found w ith functi on A B S . T h i s f u n c t i o n i s a l s o a v a i l a b l e f r o m t h e k e y b o a r d ( „Ê ). Example s of applicati on of functi on ABS w ere sho wn a bov e. Dot pr oduc t F unction DO T (option 2 in CHOO SE box abov e) is used t o calcul[...]

Page 8-8 Examples of cr oss pr od ucts of on e 3-D vector w it h one 2-D vector , or v ice ve rsa, ar e pr esented ne xt: Attemp ts to ca lculate a c ross product of v e ctors of len gth oth er th an 2 or 3 , pr oduce an err or message: Refe renc e Additi onal informati on on operati ons with v ectors , including appli cations in the phy sical sc i[...]

Page 9-1 Chapter 9 M atr ices and linear alg ebr a This c hapter sho ws e xamples of cr eating matri ces and oper ations w ith matri ces, inc luding linear algebra appli cations. Entering matr ices in th e stack In this secti on we pr esent tw o differe nt methods to enter matri ces in the calc ulator stac k: (1) using the Matri x W rit er , and (2[...]

Page 9-2 If y ou hav e selected the t extbook displa y option (using H @) DISP! and che cki ng off  Textbook ), the matri x will loo k like the one sho wn abo ve . Other w ise, the display will sho w: The displa y in RPN mode w ill look very similar to these . T yping in the matrix dir ec tl y into the stac k T h e s a m e r e s u l t a s a b o [...]

Page 9-3 Ope r atio ns w ith m atr ic es Matri ces, lik e other mathematical obj ects, can be added and su btracted . The y can be multiplied by a scalar , or among themselv es, and r aised to a r eal pow er . An important operati on for linear algebr a applicati ons is the inv erse o f a matr ix . Details of these operati ons are pr esented ne xt.[...]

Page 9-4 Addition and subtr ac tion F our ex amples ar e show n below using the matr ices stor ed abov e (AL G mode). In RPN mode , tr y the f ollow ing ei ght ex amples: Mult ipl icat ion Ther e are a number o f multiplication oper ations that inv olv e ma tr ices . The se are des cribed ne xt. T he ex amples are sho wn in algebr aic mode . Multip[...]

Page 9-5 Matrix -vector multiplication Matri x -vector m ultiplication is po ssible only if the number of columns of the matri x is equal t o the length of the v ector . A couple o f ex amples of matr ix - vec tor multiplicati on follo w: V ector-matr i x multiplicatio n, on the other hand , is not def ined. T his multiplicati on can be performed ,[...]

Page 9-6 T erm-b y-term multiplication T erm-by- term mul tiplica tion of t wo matrices of th e same dimen sions is possib le through t he use of function HAD A MARD. T h e r esu lt is, of cou rse , another matri x of the same dime nsions. T his function is a vailable thr ough F unction catalog ( ‚N ) , or thr ough the MA TRICE S/OPERA TION S sub[...]

Page 9-7 The identity matri x The i dentity matri x has the pr opert y that A ⋅ I = I ⋅ A = A . T o ver if y this pr opert y w e prese nt the follo w ing exam ples using the matri ces stor ed earli er on. U se functi on IDN (find it in the MTH/MA TRI X/MAKE menu) to gener ate the identity matr ix as sho wn her e: The in verse matri x The inve r[...]

Page 9-8 Characteri zing a matri x (The matr ix NORM menu) The matr ix NORM (NORMALI ZE) menu is acces sed through the k ey strok e sequ ence „´ . This men u is descr ibed in detail in Chapter 10 of the calculator ’s user’s guide . Some of thes e functions ar e desc ribed ne xt. Fun c tio n D ET F unction DE T calculat es the deter minan t o[...]

Page 9-9 Solution of linear s ystems A s ys tem of n linear eq uations in m var iables can be wr itten as a 11 ⋅ x 1 + a 12 ⋅ x 2 + a 13 ⋅ x 3 + …+ a 1,m-1 ⋅ x m-1 + a 1,m ⋅ x m = b 1 , a 21 ⋅ x 1 + a 22 ⋅ x 2 + a 23 ⋅ x 3 + …+ a 2, m - 1 ⋅ x m-1 + a 2, m ⋅ x m = b 2 , a 31 ⋅ x 1 + a 32 ⋅ x 2 + a 33 ⋅ x 3 + …+ a 3,m-[...]

Page 9-10 2x 1 + 3x 2 –5x 3 = 13, x 1 – 3x 2 + 8x 3 = -13, 2x 1 – 2x 2 + 4x 3 = -6 , can be wr itten as the matri x equation A ⋅ x = b , if This s y stem has the same n umber of equations as of unkno wns, and w ill be r e f e r r e d t o a s a s q u a r e s y s t e m . I n g e n e r a l , t h e r e s h o u l d b e a u n i q u e soluti on to[...]

Page 9-11 A soluti on was f ound as show n next . Sol utio n wi th the in v erse matr i x The s olution to the s yste m A ⋅ x = b , w here A is a squar e matri x is x = A -1 ⋅ b . F or the ex ample used ear lier , w e can find the solu tion in the calculat or as follo ws (F irs t e nter matri x A and vector b once mor e): Solution b y “ divis[...]

Page 9-12 Refe renc es Additi onal informati on on cr eating matri ces, matr ix oper ations, and matr ix applicati ons in linear algebra is p r es ent ed in Chapters 10 and 11 of the calculator ’s user’s guide . SG49A.book Page 12 Friday, September 16, 20 05 1:31 PM[...]

Page 10-1 Chapter 10 Gr aph ics In this cha pter we intr oduce some of the gr aphics capa bilities of the calc ulator . W e w ill pre sent gr aphics o f functi ons in Cartesian coor dinates and polar coor dinates, par ametri c plots, gra phics of coni cs, bar plots, scatterplots , and fast 3D plots . Graphs options in the calc ulator T o access the[...]

Page 10-2 P lot ting an e xpression of the for m y = f(x) As an e xample , let's plot the f unction , • First , enter the PL O T SETUP env ironment by pressing, „ô . Mak e sur e that the option F unction is select ed as the TYPE , and that ‘X’ is selec ted as the independent var iable ( INDEP ). Pr es s L @@@OK@@@ to r eturn to nor ma[...]

Page 10-3 •P r e s s ` to retur n to the PL O T - FUNCTION w indow . The expr essi on ‘Y 1(X) = EXP(-X^2/2)/ √ (2* π ) ’ w ill be highlighted. Pr ess L @@@OK@@@ to r eturn to normal calc ulator display . • Enter the PL O T WINDO W env ironmen t by enter ing „ò (pres s them simultaneou sly if in RPN mode) . Us e a range of –4 to 4 f [...]

Page 10-4 Gen er ating a table of v alues for a function The com bin at ions „õ ( E ) and „ö ( F ), pr esse d simultaneousl y if in RPN mode, let ’s the user pr oduce a table of va lues of func tions. F or ex ample, w e w ill produce a t able of the fu nction Y(X) = X/ (X+10), in the range -5 < X < 5 f ollo wing thes e instruc tions: [...]

Page 10-5 • With the option In hi ghlight ed, pr ess @@@OK@@@ . The ta ble is expanded so that the x -incr ement is no w 0.2 5 rather than 0. 5 . Simpl y , what the calc ulator does is to m ultiply the or iginal inc reme nt, 0. 5, b y the z oom fac tor , 0.5, to pr oduce the ne w incr ement of 0.2 5 . Th us, the zo o m i n option is useful w hen [...]

Page 10-6 • K eep the def ault plot windo w r anges to read: •P r e s s @ERASE @DRAW to dr aw the thr ee -dimensional surface . The r esult is a w iref rame pic ture of the surface with the r efer ence coor dina te s yst em sho wn at the lo wer le f t co rner of the sc reen . By u sing the arr ow k ey s ( š™—˜ ) y ou can cha nge th e orie[...]

Page 10-7 • When done , pr ess @EXIT . •P r e s s @CANCL to r eturn to P L O T WINDO W . •P r e s s $ , or L @@@OK@@@ , to re turn to normal calculat or display . T r y also a F ast 3D plot f or the surface z = f(x,y) = sin (x 2 +y 2 ) •P r e s s „ô , simultaneousl y if in RPN mode, to access the P L O T SETUP w indo w . •P r e s s ˜ [...]

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Page 11-1 Chapter 11 Calculus Applications In this Chapt er we dis cuss a pplications o f the calculator ’s functio ns to oper ations r elated to Calc ulus , e.g ., limits, der i vati ves , integrals , po wer series, etc. T h e CAL C (Calc ulus) menu Many o f the functions pr esent ed in this C hapter are co ntained in the calculat or’s CAL C m[...]

Page 11-2 Fu nc t io n lim is enter ed in AL G mode as lim(f (x),x=a) to calculate the limit . In RPN mode , enter the functi on fir st, then the e xpres sion ‘ x=a’ , and finally f unction lim . Example s in AL G mode ar e sho wn ne xt, including some limits t o infinity , and one -si ded limits. T he infi nit y s ymbol is as soci ated with th[...]

Page 11-3 Functions DERI V and DERVX The function D ERIV is used to tak e d er ivativ es in terms of any indep endent var iable , while the functi on DERVX tak es deri vati ve s with r espect to the CAS defau lt variabl e V X (t ypic ally ‘X’ ) . Wh il e fun ctio n D ERVX is ava il abl e dir ectly in the CAL C menu , both functi ons are a vaila[...]

Page 11-4 P lease notice that f unctions S IGMA VX and SIGMA ar e designed f or integr ands that inv olv e some s ort of integer functi on like the f actor ial (!) functi on sho wn abo ve . Their r esult is the so -called discr ete der iv ativ e, i . e ., one def ined for intege r n umbers only . Definite integr als In a def inite integr al of a fu[...]

Page 11-5 Infinite series A func tion f(x) can be expanded in to an infinite se rie s around a poin t x=x 0 by u sing a T ay lor’s ser ies, namel y , , wher e f (n) (x) r epre sents the n- th der iv ativ e of f(x) w ith re spect to x , f (0) (x) = f(x). If the value x 0 = 0, th e se ries is refer red to a s a Ma cla uri n’s serie s. Functions T[...]

Page 11-6 ser ies) or an e xpres sion of the fo rm ‘ var iable = va lue’ indicating the po int of e xpansion of a T aylor se ries , and the order of the s eri es to be produced . F unction SER I E S retur ns two output it ems: a list w ith four items , and an expr ession for h = x - a, if the second ar gum ent in the function call i s ‘ x=a?[...]

Page 12-1 Chapter 12 Multi-variate Calculus Applications Multi-var iate calc ulus r ef ers to func tions o f two or mor e var iables . In this Chapte r we disc uss basi c concep ts o f multi- v ari ate calculus: partial deri vati v es and multiple integr als. Pa r t i a l d e r i v a t i v e s T o q uickl y calculate partial der iv ative s of multi[...]

Page 12-2 T o d e fine the func tions f(x,y) and g(x ,y ,z) , in AL G mode, us e: DEF(f(x,y)=x*C OS(y)) ` DEF(g(x,y ,z)= √ (x^2+y^2)*SIN(z) ` T o t y pe the deri vati ve s ymbol us e ‚¿ . The de rivative , fo r ex ample, w ill be enter ed as ∂ x(f(x ,y)) ` in AL G mode in the scr een. Multipl e integr als A ph ysical in terpr etation of the [...]

Page 13-1 Chapter 13 V ec tor Anal ysis Applications This c hapter desc ribes the use of fu nctions HE S S, DIV , and CURL , for calc ulating operati ons of vec tor analy sis. The del operator The f ollo win g operato r , re ferr ed to as the ‘ del’ or ‘ nabla ’ operat or , is a vec tor-bas ed oper ator that can be applied to a scalar or v [...]

Page 13-2 Div ergence Th e div er genc e of a v ect or fu nctio n, F (x,y ,z) = f( x ,y ,z ) i + g(x,y ,z) j +h(x ,y ,z) k , is def ined by taking a “ dot-product ” of the del oper ator w ith the functi on, i .e ., . F unction DIV can be used to calc ulate the div erg ence of a vector f ield . F or ex ample, fo r F (X,Y ,Z) = [XY ,X 2 +Y 2 +Z 2[...]

Page 14-1 Chapter 14 Differential Equations In this Chapter w e pre sent ex amples of so lving or dinary differe ntial equati ons (OD E) us ing calculator f unctions . A differ ential equati on is an equati on inv olv ing deri vati ve s of the independent var iable . In most ca ses, w e seek the dependent functi on that satisfie s the diff eren tia[...]

Page 14-2 • the ri ght -hand side of the ODE • the char acter istic equation of the ODE Both of these inputs must be gi ven in ter ms of the def ault independent var iable for the calc ulator’s CA S (t y picall y X) . T he output f rom the funct ion is the general solu tion of the ODE . The ex amples belo w ar e show n in the RPN mode: Exampl[...]

Page 14-3 Fun c ti on DESO L VE The calc ulator pro vi des functi on D E SOL VE (Differ ential E quation S OL VEr) to solv e certain types of diff erential equati ons. The f unction r equires as input the differ ential eq uation and the unkno wn f u nc tion , and retur ns the solution to the equation if a vailable . Y ou can also pr o vide a v ecto[...]

Page 14-4 ‘ d1y(0 ) = -0. 5’ . Changing to these Ex act expr essions f acilitates the solution. Pr ess µµ to simplify the r esult. Use ˜ @EDIT to s ee this r esult: i. e. , ‘ y(t) = -((19* √ 5*SI N( √ 5*t) - (14 8*COS( √ 5*t)+8 0*CO S(t/2)))/190)’ . Pr ess ``J @ ODETY to get the string “ Linear w/ cst coeff ” fo r the ODE t y p[...]

Page 14-5 Compar e these e xpressi ons with the one gi ven earli er in the definition o f the La place transfo rm, i .e ., and yo u will noti ce that the CAS def ault var iable X in the equati on wr iter sc reen r eplaces the var iable s in this de finition . Ther ef ore , when u sing the functi on L AP y ou get bac k a functi on of X, whic h is th[...]

Page 14-6 Fo urier series f or a quadratic function Determine the coeff ic ients c 0 , c 1 , and c 2 for the f unction g(t) = (t-1) 2 +(t -1), w ith peri od T = 2 . Using the calc ulator in AL G mode , first w e def ine functi ons f(t) and g(t) : Ne xt, w e mov e to the CA SDI R su b-direct or y under HOME t o change the val ue of va riabl e PE RI [...]

Page 14-7 Th us, c 0 = 1/3, c 1 = ( π⋅ i+2)/ π 2 , c 2 = ( π⋅ i+1)/( 2 π 2 ). The F ou r ier series with three ele ments will be written as g(t) ≈ R e[(1/3) + ( π⋅ i+2)/ π 2 ⋅ ex p (i ⋅π⋅ t)+ ( π⋅ i+1)/(2 π 2 ) ⋅ exp (2 ⋅ i ⋅π⋅ t)]. Referenc e F or additional def initions, appli cations, and e xer c ises on solv in[...]

SG49A.book Page 8 Friday, September 16, 200 5 1:31 PM[...]

Page 15-1 Chapter 15 Pr obabilit y Distr ibutions In this Chapte r we pr ov ide e xamples o f applicatio ns of the pre-defined pr obability distributi ons in the calculator . T h e MTH/P ROB ABI LI TY .. sub-menu - par t 1 The MTH/P ROB ABILI T Y .. sub-men u is acces sible through the k ey str oke sequ ence „´ . W i t h s y s t e m f l a g 1 1 [...]

Page 15-2 • PERM(n ,r): Calc ulates the number o f permutati ons of n items tak en r at a time • n!: F actor ial of a positi ve integer . For a no n -integer , x! r eturns Γ (x+1), whe re Γ (x) is the Gamma functi on (see Chapter 3). The fact orial s ymbol (!) can be enter ed also as the ke ystr oke combinati on ~‚2 . Exam ple of applicati [...]

Page 15-3 T h e MTH/P ROB menu - part 2 In this secti on w e disc uss f our continuou s proba bility distri butions that ar e commonl y used f or proble ms relate d to statisti cal infer ence: the nor mal distr ibution, the S tudent’s t distr ibution , the Chi-s quare ( χ 2 ) dis tribution , and the F-dis tributi on. The f u nc tions pro v ided [...]

Page 15-4 The Chi-squar e distribution The Chi -s qua re ( χ 2 ) distributi on has one paramete r ν , kno wn as the degr ees of fr eedom. T he calculato r pr o vi des for v alues of the upper -tail (c umulativ e) distr ibution func tion f or the χ 2 -distributi on using UTPC gi ven the value o f x and the parameter ν . The def inition of this f[...]

Page 16-1 Chapter 16 Statistical Applications The calc ulator pr ov ides the follo wing pr e -progr ammed statisti cal features accessible thr ough the k ey str ok e combination ‚Ù (the 5 key) : Entering data Applicati ons numbered 1, 2 , and 4 in the list abov e requir e that the data be av ailable as columns of the matr ix Σ D A T . One wa y [...]

Page 16-2 Calculating singl e-variable statistics After entering the column v ector into Σ DA T, p re s s ‚Ù @@@OK@@ to sel ect 1. Singl e-var .. The fo llow ing input f orm w ill be pr o vided: The f orm lists the dat a in Σ DA T , sho ws that column 1 is s elected (ther e is only one column in the c urr ent Σ D A T) . Mo ve a b o ut the for[...]

Page 16-3 Obtaining frequenc y distributions The app lic at ion 2. Frequenci es.. i n t h e S T A T m e n u c a n b e u s e d t o obtain fr equency dis tribution s for a set o f data. T he data must be pr esent i n t h e f o r m o f a c o l u m n v e c t o r s t o r e d i n v a r i a b l e Σ DA T. To g e t s ta r te d, pr ess ‚Ù˜ @@@OK@@@ . Th[...]

Page 16-4 Σ D A T , b y usi ng f unction S T O Σ (see e xample abo ve). Next , obtain single - var iable inf ormati on using: ‚Ù @@@OK@@@ . The r esults are: This information i ndicates tha t our data ranges fr om -9 to 9 . T o produce a f r e qu e nc y d is t r ib u ti on w e w il l us e t he i nt e rv a l ( -8 , 8) di v i di n g i t i n to 8[...]

Page 16-5 F it ting data to a function y = f(x) The pr ogram 3. F it da ta.. , a vailable as opti on number 3 in the S T A T menu , can be used to f it linear , logar ithmic, e xponential , and po w er func tions to data sets (x , y), stored in column s of the Σ D A T matri x. F or this applicati on, y ou need to ha ve at least tw o columns in you[...]

Page 16-6 Le vel 3 sh ow s the form o f the equation . Lev el 2 sho ws the sample corr elation coeff ic ient , and lev el 1 show s the cov ariance of x -y . F or def initions of these paramete rs see Chapter 18 in the user’s guide . F or additional inf ormatio n on the data -f it featur e of the calculator s ee Chapt er 18 in the user ’s guide [...]

Page 16-7 •P r e s s @@@OK@@@ to obtain the follo wing r esults: Confidence inter v als The a pplication 6. Conf Inter val can be acces sed by u sing ‚Ù— @@@OK@@@ . The a ppl ica tion offe rs th e fol lowing op tion s: These options are to be interpre te d as follo ws: 1. Z -INT : 1 µ .: Single sample confi dence interval f or the populatio[...]

Page 16-8 4. Z -INT : p 1− p 2 .: Confi dence inter v al for the diff erence of tw o pr opor tions , p 1 -p 2 , for lar ge samples w ith unkno wn populatio n varia nc es. 5. T- I N T: 1 µ .: Single sample confi dence interval fo r the population mean, µ , f or small samples with unkno wn populati on var iance. 6. T-I NT: µ1−µ2 .: C onfidenc[...]

Page 16-9 The gr aph sho ws the st anda r d normal dis tribution pdf (probability density functi on) , the locatio n of the cr itical points ± z α/2 , the mean value ( 2 3 .3) and the corr esponding interval limits ( 21.98 4 2 4 and 2 4.615 7 6) . Pr ess @TEXT to r eturn to the pr ev iou s results s cr een, and/or pr ess @@@OK@@@ to ex it th e co[...]

Page 16-10 2. Z - Te s t : µ1−µ2 .: Hy pothesis testing f or the differ ence of the population means, µ 1 - µ 2 , with either kno wn populati on var iances, or f or large samples w ith unkno wn populati on var iances . 3 . Z -T est: 1 p.: Single sample hy pothesis testing for the pr oportion, p , for lar ge samples with unkno wn populatio n v[...]

Page 16-11 Then , we r ejec t H 0 : µ = 150 , against H 1 : µ ≠ 150. The test z v alue is z 0 = 5 .6 5 68 54. The P -value is 1. 54 × 10 -8 . The cr itical v alues of ± z α /2 = ± 1.9 5 9 9 64, cor r esponding to c riti cal ⎯ x range of {14 7 .2 15 2 .8}. This inf ormati on can be observed gr aphicall y by pr essing the so ft -menu k ey @[...]

SG49A.book Page 12 Friday, September 16, 20 05 1:31 PM[...]

Page 17-1 Chapter 17 Numbers in Differ ent Bases Beside s our dec imal (base 10, digits = 0 -9) number s y stem, y ou can w ork w ith a binary s yste m (base 2 , digits = 0,1), an octal s y stem (bas e 8, digits = 0 - 7) , or a hex adec imal sy stem (base 16, di gits =0 -9 ,A-F) , among others . The s ame wa y that the dec imal integer 3 21 means 3[...]

Page 17-2 W riting non-dec imal numbers Numbers in non-decimal s yst ems, r eferr ed to as bin ar y i nteg ers , are w ritt en pr eced ed b y the # s ymbol ( „â ) in the calc ulator . T o select the cur rent base to be us ed for binary integer s, c hoose eithe r HEX (adec ima l), DEC (imal), OCT (al) , or BIN (ary) in the B ASE me nu . F or ex a[...]

Page 18-1 Chapter 18 Using SD car ds The calc ulator has a memor y car d slot into whic h you can insert an SD flash car d for backing up calc ulator objects , or for do wnloading objects fr om other source s. The SD car d in the calculator w ill appear as port numbe r 3 . Inserting and remo ving an SD car d The SD slot is located on the bottom e d[...]

Page 18-2 4. When the for m atting is finished , the HP 50g display s the message "FORMA T FINISHED . PRE SS ANY KEY T O EXIT". T o ex it the sy stem menu , hold dow n the ‡ key , press and r elease the C ke y and then r elease the ‡ key . The SD car d is now r eady f or use . It will ha ve been for mat ted in F A T3 2 forma t . Acces[...]

Page 18-3 N o t e t h a t i f t h e n a m e o f t h e o b j e c t y o u i n t e n d t o s t o r e o n a n S D c a r d i s longer than eigh t charac ters, it w ill appear in 8.3 DOS f ormat in port 3 in the F iler once i t is stor ed on the card . Recalling an object from the SD car d T o r ecall an obj ect from the SD car d onto the scr een, use fu[...]

Page 18-4 P urging all objects on t he SD card (b y refo rm at t in g) Y ou can pur ge all objec ts fr om the SD card b y re formatting it . When an SD car d is inserted, @FORMA a ppears an additional menu it em in File Manager . Selecting this opti on r efor mats the entire card , a proces s whic h also delete s ev ery object on the card . Specif [...]

Page 19-1 Chapter 19 Equation L ibrary The E quati on Libr ar y is a collecti on of equati ons and commands that enable y ou to solv e simple sc ience and engineer ing pr oblems. The libr ary consists o f more than 3 00 equations gr ouped into 15 t echnical sub jects containing mo re than 100 pr oblem titl es. E ach pr oblem title contains o ne or [...]

Page 19-2 No w use this equation s et to answ er the questi ons in the follo w ing ex ample . Step 4: Vi ew the fi ve eq uations in the Pr ojectile Moti on set . All fi ve ar e used inter changeably in or der to solv e for missing v ariables (see the ne xt ex ample) . #EQN# #NX EQ# #NXEQ# #NXEQ# #NXEQ# Step 5: Examine the v ariables used b y the eq[...]

Page 19-3 0 *!!!!!!X0!!!!!+ 0 *!!!!!!Y0!!!!!+ 50 *!!!!!!Ô0!!!!!+ L 65 *!!!!!!R!!!!!+ Step 3: Sol ve f or the ve locity , v 0 . (Y ou solv e for a v ariable b y pres sing ! and then the var iable ’s menu k ey .) ! *!!!!!!V0!!!!!+ Step 4: Recall the range , R , di v ide by 2 t o get the halfwa y distance , and enter that as the x- c o or di n a t [...]

Page 19-4 Refe renc e F or additional details on the E quation Libr ary , see Chapter 2 7 in the calculator’s u ser’s guide . SG49A.book Page 4 Friday, September 16, 200 5 1:31 PM[...]

Pa g e W - 1 Limited W arr ant y HP 50g gr aphing calculator ; W arr anty period: 12 months 1. HP warr ants to y ou, the end-user customer , that HP har dw are , accessor ies and supplie s will be f ree fr om defects i n materials and wor kmanship after the date of purc hase , for the per iod spec ified abo ve . If HP recei v es notice of such def [...]

Pa g e W - 2 REMEDIES . EX CEPT A S IND ICA TED ABO VE , IN NO EVENT WILL HP OR IT S S UPPLIER S BE LIABLE FOR L OS S OF DA T A OR FOR DIRE CT , SPE C IAL , INCIDENT AL, CO NSEQUENT IAL (INCL UDING L OS T PROFI T OR D A T A), OR O THER DAMA GE , WHE THER BA SED IN CONTRACT , T OR T , OR O THER WISE . Some countries , States or pr ov inces do not al[...]

Pa g e W - 3 Ser v ice Euro pe Count ry : Te l e p h o n e n u m b e r s Au stri a +4 3-1-3 60 2 7 71203 B e l g i u m + 32-2-7 1 262 1 9 Denmar k +4 5-8- 2 33 2 844 Eas te rn Eu rop e c ou nt rie s + 4 2 0 - 5 - 4 1422 52 3 F inland +35 8-9 -64 0009 F rance +3 3-1- 4 99 39 006 G e r m a ny + 49 - 69 - 953 0 7 1 0 3 Greece +4 20 -5- 414 22 5 2 3 Ho[...]

Pa g e W - 4 L.A me ri ca Co untry : Te l e p h o n e n u m b e r s Argentina 0- 81 0-5 5 5- 5 5 20 Br azil S a o Pa u l o 37 47-7 79 9 ; RO T C 0 -80 0 -15 77 51 Mex ico Mx C i t y 5 258 - 9922; RO T C 01-800- 4 7 2 -66 8 4 Ve n e z u e l a 0 80 0 - 4 7 4 6 - 8368 Chile 800 - 36 099 9 Colu mbia 9-800 -114 7 2 6 Pe r u 0-8 00- 10 11 1 Central Ameri[...]

Pa g e W - 5 Regulat or y inf ormation Feder al Communications Commission N otice This equipme nt has been tested and found t o comply with the limits fo r a Clas s B digital de v ice , pursua nt to P art 15 of the FC C Rule s. The se limits ar e designed to pr ov ide r easonable pr otecti on against harmf ul interf erence in a r esidenti al instal[...]

Pa g e W - 6 Or , call 1 -8 0 0 - 4 7 4 - 6836 F or questi ons regar ding this FC C declar ation , contact: Hew lett -P ack ard C ompany P . O . Bo x 6 9 2000, Mail Sto p 510101 Houston , T ex as 77 2 6 9- 20 00 Or , call 1 - 28 1 - 5 1 4 - 3333 T o identify this produc t, r efer t o the par t , ser ies, or model n umber found on the product. Canad[...]

Pa g e W - 7 Japane se Notice こ の装置は、 情報 処理装置等電波障害自主規制協議会 （VCCI） の基準に 基づ く ク ラ ス B 情報技術装置 で す 。 こ の装置は、 家庭環境 で 使用す る こ と を 目的 と し て い ま す が、 こ の装 置が ラ ジ オや テ レ ビ ジ ョ ン 受信[...]