HP HP 50g manuale d’uso

HP 5 0g gr aphing calc ulat or user ’s manual H Ed it io n 1 HP part number F2 2 2 9AA-90 001[...]

Notice REG I STER Y OUR PROD UC T A T: www .register .hp .com THI S MANUAL AND ANY EX AMPLES CONT AI NED HEREI N ARE PRO VIDED “ AS I S” AND ARE SUBJECT T O CHANGE WITHOUT NO TICE. HEWLETT-P A CKARD COMP ANY MAKE S NO 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 , IN CLUDI NG, B UT NO T LIMITED T O, THE IMPLIED [...]

Pr ef ace Y ou hav e in y our hands a compact s y mbolic and n umer ical comput er that w ill f acilit ate calc ulation and mathe matical analy sis of pr oblems in a var iety of disc iplines, f r om elementary mathematics to ad vanced engineer ing and sc ie nce subjec ts . T his manual contains e xamples that illus tr ate the us e of the basi c cal[...]

Page TOC-1 T able of Contents Chapter 1 - Getting started Basic Operat ions , 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 Select ing calc ulato r modes ,[...]

Page TOC-2 Editing expressions i n the stack , 2-1 Creating arithmetic expressions, 2-1 Creating algebraic expressions, 2-4 Using the Equation Write r (EQW) to create expres sions , 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 Variab[...]

Page TOC-3 Available units, 3-9 Attaching units to numbers, 3-9 Unit prefixes, 3-10 Operations with uni ts, 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 Enterin[...]

Page TOC-4 The PROOT fu nction, 5-9 The QUOT and R EMAINDER functions, 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 function, 5-11 Step-by-step operations with polynomials and fractions , 5-11 Reference , 5-12 Chapter 6 - Solution to[...]

Page TOC-5 Addition, subtraction, multiplication, di vision, 7-2 Functions applied to lists, 7-4 Lists of complex number s , 7-4 Lists of algebraic objects , 7-5 The MTH/LIST menu , 7-5 The SEQ functi on , 7-7 The MAP function , 7-7 Reference , 7-7 Chapter 8 - Vectors Entering v ectors , 8-1 Typing vectors in the stack, 8-1 Storing vectors into var[...]

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 NO RM 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 deriv atives , 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 Ge tti ng s ta rte d T his chapt er pr ov ides basi c inf ormatio n about the oper ation of y our calc ulator . It is designed to f amili ar i z e y ou w ith the basic oper ations and settings be fo r e y ou perf orm a calc ulation . Basic Ope r ations Ba tte ri es T he calc ulator u ses 4 AAA (LR0 3) batter ie s as main po wer a[...]

Page 1-2 b . Insert a new CR203 2 lithium bat tery . Mak e sur e its positi v e (+) side is facing up. c. Replace the plate and push it to the or iginal place . After installi ng the batteri es , pr ess $ to tur n the po w er on . Wa r n i n g : When the lo w bat tery icon is displa y ed , y ou need to r e place the batteri es as soon as pos sible [...]

Page 1-3 Contents of the calculator ’s displa y T ur n y ou r c alc ul at or on on ce mor e . A t the to p o f the di spl ay y ou w il l h a v e two lines of inf ormati on that des cr ibe the settings of the calc ulator . T he f irst line sho w s the ch ar act er s: RAD XYZ HEX R = 'X' F or details on the meani ng of thes e s ymbols see[...]

Page 1-4 The se si x functi ons for m the fir st page of the T OOL menu . This menu has actuall y ei ght entr ies arr anged in t wo pages . The second page is av ailable b y pr essing the L (N eXT menu) k e y . T his k e y is the thir d ke y fr om the lef t in the thir d r o w of k ey s in the k e yboar d. In this case , only the fir st tw o soft m[...]

Page 1-5 F or e x ample , the P key , key (4,4 ) , has the f ollo w ing six f unctio ns associ ated with it: P Main func tio n , to acti vate the S YMBolic menu „´ L eft -shift functi on, to ac ti v ate the MTH (Math) menu …N R ight -shift functi on, to acti vat e the CA T alog func tion ~p ALPHA f uncti on, to ente r the upper -case letter P [...]

Page 1-6 Of the si x functi ons assoc iated w ith a k ey onl y the fir st f our ar e show n in the k e y boar d itself . The f igur e in next page sho ws these f our labels for the P k e y . Notice that the color and the position of the labels in the k ey , namely , SY M B , MTH , CA T and P , indicate w hic h is the main functi on ( SY M B ) , and[...]

Page 1-7 Operating Mode T he calc ulator off ers tw o operating modes: the Alge b raic mode, and the Revers e P ol i s h N ot a t io n ( RPN ) mode . T he 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 famil iar w ith the [...]

Page 1-8 Y ou could also type the e xpr essi on direc tly into the dis pla y w ithout using the equation w riter , as follo ws: R!Ü3.*!Ü5.- 1/3.*3.™ /23.Q3+!¸2.5` to obta in th e same r esult . Change the oper ating mode to RPN b y fir st pr es sing the H butt on . Select the RPN operating mode b y e ither usin g the k e y , o r p r e s s i [...]

Page 1-9 Le t's try some other simple oper ations bef or e trying the mor e compli cated e xpr essi on used earlie r for the algebr aic oper ating mo de: Note the po sition o f the y and x in the las t two oper atio ns. T he base in the e xponenti al oper atio n is y (stac k le v el 2) w hile the e xponent is x (stac k le v el 1) be f or e the[...]

Page 1-10 T o se lect between the AL G vs . RPN operating mode , y ou can also set/ c lear s y stem f lag 9 5 thr ough the follo w ing k e ys tr oke s equence: H @FLAGS! 9˜˜˜˜ ` Number F o rmat and decimal dot or comma Changing the n umber f ormat allo ws y ou to c usto mi z e the wa y real number s ar e display ed by the calc ulator . Y ou w i[...]

Page 1-11 Pr es s the r ight ar ro w k e y , ™ , to highlight the z er o in fr ont of the option Fix . Pr es s the @CHOOS so ft menu k ey and , using the up and do wn ar r ow keys, —˜ , select , say , 3 decimals . Pr es s the !!@@OK#@ soft menu k e y to comple te the select ion: Pr es s the !!@@OK#@ s o ft me nu k e y r e tur n t o th e ca lc [...]

Page 1-12 K eep the number 3 in fr ont of the Sc i . ( This number can be c hanged in the same f ashio n that w e c hanged the Fix e d number of dec imals in the e x ample abo ve). Pr es s the !!@@OK#@ s o ft me nu k e y r e tu rn to t he c alc u la to r di s p la y . T he n um ber no w is sho wn as: T his r esult , 1.2 3E2 , is the calc ulator’s[...]

Page 1-13 Pr es s the !!@@OK#@ s o ft me nu k e y r e tur n t o th e ca lc ula to r d is p la y . T he n um ber no w is s ho w n as: Becau se this n umber has thr ee f igur es in the int eger part , it is sh o wn w ith fo ur signif icati ve f igur es and a z er o po w er of ten , w hile using the Engineer ing for mat . F or ex ample , the number 0.[...]

Page 1-14 Angle M easure T r igonometr ic f unctions , f or e xample , r equir e ar guments r e pr esenting plane angles . The calc ulator pr ov ides thr ee differ ent A ngle Measur e modes f or wo rk i n g wi t h a n g l e s, n a m e l y: • Degr ees : Th er e ar e 360 degr ees ( 360 ° ) i n a c om p l e t e ci rcu m fe re n c e. • R adians : [...]

Page 1-15 soft men u k ey to complet e the oper ation . F or e x ample , in the fo llo w ing sc r een, the P olar coor dinate mode is selected: Selec ting CAS setting s CA S st ands f or C omputer A lgebr aic S y ste m. T his is the mathemati cal cor e of the calc ulator whe r e the s ymbo lic mathematical oper ations and fu ncti ons ar e pr ogramm[...]

Page 1-16 Non-Rati onal options abo v e) . Unselected options w ill sho w no chec k mark in the underline pr eceding the option of inte r est (e .g., the _Numer ic , _Appr o x , _Comple x , _V erbo se , _Step/St ep , _Incr P ow options abov e) . • Afte r hav ing selec ted and uns elec ted all the options that y ou w ant in the CA S MODE S input f[...]

Page 1-17 Selec ting Displa y modes T he calc ulator displa y can be cu stomi z ed to y our pr efer ence b y selec ting diffe r ent displa y modes. T o see the optional dis pla y settings u se the fo llo wing: •F i r s t , p r e s s t h e H button to acti vat e the CAL CULA T OR MODE S input f or m. W ithin the CAL CUL A T OR MODE S input f orm ,[...]

Page 1-18 Selec ting the display f ont Fi r s t , p re s s t h e H button to activ ate the C AL CUL A T OR MO D E S i nput f orm . Within the CAL CULA T OR MODE S input f orm , pr ess the @@DIS P@ soft menu k e y to displa y the D ISP LA Y MODE S input f orm . The Fon t : fie l d i s highlighted , an d the option F t8_0: sy stem 8 is selected . Thi[...]

Page 1-19 Selec ting pr operties of the Stac k Fi r s t , p re s s t h e H but ton to a cti vate the CAL CUL A T OR MOD E S i nput fo rm . Within the CAL CUL A T OR MODE S input for m, pr ess the @ @DISP@ soft menu k e y ( D ) to displa y the D ISP L A Y MODE S input fo rm . Pre ss the do w n arr o w k e y , ˜ , twi ce , to get to the Sta ck line [...]

Page 1-20 Selec ting pr oper ties of the equation writer (E QW ) Fi r s t , p re s s t h e H button to activ ate the C AL CUL A T OR MO D E S i nput f orm . Within the CAL CULA T OR MODE S input f orm , pr ess the @@DIS P@ soft menu k e y to dis play the DISP L A Y MODE S input f orm . Pre ss the do wn arr o w k ey , ˜ , thr e e times , to get t o[...]

Page 2-1 Chapter 2 Intr oduc ing t he calc ulator In this cha pter w e pre sent a n umber of basi c operati ons of the calc ulator inc luding the use of the E quati on W riter and the manipulati on of data obj ects in the calc ulator . Stud y the e xamples in this c hapter to get a good gr asp of the capab ilities o f the calc ulator f or f utur e [...]

Page 2-2 Notice that , if y our CA S is set to E X A CT (see Appendi x C in user ’s guide) and y ou enter y our expr essi on using integer number s fo r integer v alues, the r esult is a s ymboli c quantity , e. g ., 5*„Ü1+1/7.5™/ „ÜR3-2Q3 Bef or e pr oduc ing a r esult , y ou w ill be ask ed to c hange to Appr o x imate mode . Accept the[...]

Page 2-3 If the CA S is set to Ex act , yo u w ill be ask ed to appr ov e changing the CA S sett in g to Appr ox . Once this is done , y ou w ill get the same r esult as bef ore . An alte rnati ve w ay t o e valuat e the e xpr essi on enter ed earli er between quot es is by u sing the opti on …ï . W e w ill no w ente r the expr essi on used a bo[...]

Page 2-4 Creating algebr aic e xpressions Algebr aic e xpre ssi ons inc lude not onl y number s , but also v ari able names . As an e x ample , w e will ent er the fo llo w ing algebrai c e xpr ession: W e s et the calc ulator oper ating mode to A lgebrai c, the CA S to Exac t , and the displa y to Te x t b o o k . T o ente r this algebr aic e xpr [...]

Page 2-5 Using the Equation W riter (E QW ) to c reate ex p r e s s i o n s T he equation w rite r is an extr emel y po w erful t ool that not only le t y ou ent er or see an eq uation , but also allo ws y ou to modify and w ork/appl y func tions o n all or part of the equati on . T he E quation W r iter is la unched by pr essing the k e y str ok e[...]

Page 2-6 Suppos e that y ou w ant to r eplace the quantity between par enthese s in the denominator (i .e ., 5+1/ 3) with (5+ π 2 /2) . F irs t , w e use the delet e k ey ( ƒ ) delete the c urr ent 1/3 expr essi on, and then w e r ep lace that fr action wi t h π 2 /2 , as f ollo ws: ƒƒƒ„ìQ2 When hit this po int the sc r e en looks as f oll[...]

Page 2-7 F irst , w e need to hi ghlight the entir e fir st ter m b y using eithe r the ri ght arr o w ( ™ ) or the upper ar ro w ( — ) k ey s, r epeatedly , until the entir e e xpr essi on is highli ghte d , i .e. , se ven time s, pr oduc ing: Once the e xpr ession is hi ghlighted as sho w n abo v e , t ype +1/ 3 to add the fr action 1/3 . R e[...]

Page 2-8 ~„y———/~‚tQ1/3 T his r esults in the output: In this e x ample w e us ed se ver al lo w er -case English letter s, e .g ., x ( ~„x ), se v er a l G r e ek le tt e rs , e .g ., λ ( ~‚n ) , and e v en a combinati on of Gr eek and English letter s, name ly , ∆ 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[...]

Page 2-9 Subdirectories T o s tor e your dat a in a w ell or gani z ed dir e ctory tr ee yo u ma y w ant to c r eate subdir ector ies under the HOME dir ectory , and mor e subdir ector ie s w ithin subdir ector ies , in a hier ar ch y of dir ector ie s similar to f olders in modern co mput ers . The su bdir ect or ies w ill be giv en names that ma [...]

Page 2-10 T o unloc k the upper -case lock ed k e y board , pre ss ~ . T ry the f ollo wing e xe r c ises: ~~math` ~~m„a„t„h` ~~m„~at„h` T he calc ulator displa y w ill sho w the f ollo w ing (left-hand side is Algebr aic mode , r ight-hand side is RPN mode) : Creating v ariables Th e s i m p l es t way t o cre a t e a va ria b l e is by [...]

Page 2-11 The f ollo w ing are the k e ys tr oke s for ente r ing the r emaining var iables: A12: 3V5K~a12` Q: ~„r /„Ü ~„m+~„r™ ™K~q` R: „Ô3‚í2‚í1™ K~r` z1: 3+5*„¥K~„z1` (Acce p t cha n ge to Co mp l ex mode if ask ed ) . p1: å‚é~„r³„ì* ~„rQ2™™ ™K~„p1` . The sc r een , at this po int , w ill loo k as[...]

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 ocedur e: 3V5³~a12`K Her e is a wa y to enter the contents of Q: Q: ~„r/„Ü ~„m+~„r™™³~q`K T o ent er the value of R , we can us e an e ve n shor ter v ersio n of the pr ocedur e: R: „Ô3#2#1™ ³~rK Notice that t o se[...]

Page 2-13 Chec king var iables contents Th e s i m p l es t way to che ck a va ria b l e c o nt e n t i s by p res s i n g t h e so f t m en u k e y label fo r the var iable . F or e x ample , for the v ari ables listed abo ve , pr ess the foll o w ing k ey s to see the contents o f the var iables: Algebraic mode T ype the se k ey str ok es: J @@z1[...]

Page 2-14 T his pr oduces the f ollo wing s cr een (A lgebr aic mode in the left , RPN in the rig h t ) Notice that this time the co ntents of pr ogr am p1 are listed in the s c r een. T o see the r emaining var iables in this dir ectory , pr es s L . L isting t he contents of all va riables in th e sc reen Use the k ey str ok e combinati on ‚˜ [...]

Page 2-15 Y ou can use the P URGE command to er ase mor e than one var iable b y plac ing their names in a list in the ar gument of P URGE . F or e x ample , if n ow we wa n t e d t o p u rg e va ri a b l es R and Q , simultaneousl y , w e can try the follo w ing ex erc ise . Pr ess : I @PURGE @ „ä³J @@@R!@@ ™‚í³J @@@Q!@@ At this po int ,[...]

Page 2-16 UNDO and CMD functions F unctions UNDO and CMD are u sef u l f or r ecov er ing r ecent commands, or to r ev er t an oper ation if a mist ak e was made . T hese f unctions ar e as soc iat ed w ith the HI S T k ey : UNDO re sults fr om the k e y st r ok e seq uence ‚¯ , w hile CMD r esult s fr om the k e y str ok e sequ ence „® . CHO[...]

Page 2-17 T her e is an alte rnati ve w ay to acces s thes e menu s as sof t ME N U keys, by set tin g sy stem flag 117 . (F or infor mation on F lags see Cha pter s 2 and 2 4 in the calc ulator ’s user ’s guide) . T o set this f lag tr y the f ollo wing: H @FLAGS! ——————— T he sc re en sho w s fl ag 117 not s et ( CHOO SE bo x es[...]

Page 2-18 Pr ess B to sel ect the M EMOR Y sof t m enu ( ) @@MEM@ @ ). T he di s p la y n o w sho w s: Pr ess E to se lect th e D I RECT O R Y soft me nu ( ) @@DIR@ @ ) T he ORDER command is not sho wn in this sc reen . T o f ind it w e use the L key t o fi n d i t : T o ac ti v ate the ORDE R command w e pr es s the C ( @O RDER ) soft m enu k e y [...]

Page 3-1 Chapter 3 Calculations with re al numbers T his chapt er demons tr ates the use o f the calc ulator for oper ations and func tions r elated to r eal numbers . The us er sho uld be acquainted w ith the k e ybo ar d to i dentify certain f uncti ons a v ailable in the k e y boar d (e .g ., SIN , CO S, T AN, e tc.). Also , it is assumed that t[...]

Page 3-2 6.3#8.5- 4.2#2.5* 2.3#4.5/ • P arentheses ( „Ü ) can be used to gr oup ope r ations , as well as to enclose a rgument s of function s. In AL G mode: „Ü5+3.2™/„Ü7- 2.2` In RPN mode , y ou do not need the par enthesis , calc ulatio n is done dir ectl y on the stac k: 5`3.2+7`2.2-/ In RPN mode , typ ing the e xpre ssi on betw een[...]

Page 3-3 • T he po w er func tion, ^, is a vailable thr ough the Q key . W h e n calc ulating in the stac k in AL G mode , enter the ba se ( y ) f ollo w ed by the Q k ey , and then the e xponent ( x ), e .g ., 5.2Q1.25` In RPN mode, ent er the number f irst , then the functi on, e .g., 5.2`1.25Q • The r oot functi on, XR OO T (y ,x) , is av ai[...]

Page 3-4 2.45`‚¹ 2.3`„¸ • T hr ee tr igonome tr ic func tions ar e r ead ily a vailable in the k e yboar d: sine ( S ), c os i n e ( T ) , and tangent ( U ). Ar guments of the se f uncti ons ar e a ngles in either degr ees, r adians, gr ades . T he fo llo wing e xample s us e angles in degr ees (DE G): In AL G mode: S30` T45` U135` In RPN [...]

Page 3-5 Real number functions in t he MTH menu Th e M T H ( „´ ) me nu inc lude a number of mathemati c al f uncti ons mostl y applicable t o r eal number s. W ith the def ault setting of CHOO SE bo x es for sy ste m fla g 1 1 7 (se e Ch ap te r 2) , t he M TH m e nu s h ow s th e fol l ow in g fu n ctio n s : T he func tions ar e gr ouped b y [...]

Page 3-6 F or e xample , in AL G mode , the k e ys tr ok e sequence t o calc ulate, sa y , tanh( 2 .5 ) , is the f ollo w ing: „´4 @@OK @@ 5 @@OK@@ 2.5` In the RPN mode , the ke ys tr ok es to perf or m this calc ulatio n ar e the f ollo wing: 2.5`„´4 @@OK@@ 5 @@OK@@ T he oper ations sh o w n abo ve as sume that y ou ar e using the def ault s[...]

Page 3-7 F inally , in or der to selec t , f or e x ample , the hy perboli c tangent (tanh) functi on, simpl y pr ess @@TANH@ . F or e x ample , to calc ulate ta nh(2 .5 ) , in the AL G mode , w hen using SO F T menus ove r CHOOSE bo xe s , f ollow this pr ocedur e: „´ @@HYP@ @@ TANH@ 2.5` In RPN mode , the same v alue is calc ulated us ing: 2.5[...]

Page 3-8 Optio n 1. T ools.. cont ains f uncti ons u sed t o oper ate on units (disc uss ed later ) . Options 2. L e n g t h . . t h r o u g h 17 .V iscosity .. conta in menus w ith a number o f units fo r each of the quantiti es desc r ibed . F or e x ample , selec ting option 8. F or c e .. sho ws the f ollo wing units menu: T he user w ill r eco[...]

Page 3-9 Pr es sing on the appr opri a te so ft menu k e y will open the sub-menu of units fo r that partic ular selec ti on . F or e x ample , for the @) SPEED su b-menu , the fo llo wing units ar e av ailable: Pr essing the so ft men u k ey @ ) UNITS w ill tak e you back to the UNIT S menu . R ecall that y ou can alw ay s list the full men u labe[...]

Page 3-10 5‚Û8 @@OK@ @ @@ OK@@ Notice that the unders cor e is enter e d au tomati call y w hen the RPN mode is acti ve . The k e y str oke s equences to enter units w hen the SO F T m e n u option is selec ted , in both AL G and RPN modes , ar e illustr ated next . F or e xample , in AL G mode , to enter the quan tity 5_N use: 5‚Ý‚ÛL @ ) [...]

Page 3-11 123‚Ý~„p~„m Using UB ASE (type the name) to conv ert to the def ault unit (1 m) r esults in: Operations w ith units Her e ar e some calc ulation e xamples u sing the AL G operatin g mode . Be w arned that , when multipl y ing or di vi ding quantitie s w ith units, y ou must enc los ed each quan tity w ith its units betw een par en [...]

Page 3-12 Additi on and subtr a cti on can be perfo rmed , in AL G mode, w ithout u sing par enthese s, e .g., 5 m + 3 200 mm, can be enter ed simply as 5_m + 3 200_mm ` . Mor e complicated e xpre ssion r equir e the use of par entheses , e . g ., (12_mm)*(1_cm^2)/( 2_s) ` : St ack calc ulations in the RPN mode do not r equir e y ou to encl os e th[...]

Page 3-13 Ph ysical constants in the calculator T he calc ulator ’s ph ysi cal cons tants ar e contained in a cons tants libr ar y acti vated w ith the command CONLIB. T o launc h this command y ou could simpl y t y pe it in the s tac k: ~~conlib` , or , you can s elect the command CONLIB f ro m the co mmand catalog , as fo llo ws: F ir st , laun[...]

Page 3-14 If w e de -select the UNI T S option (pr es s @UNITS ) onl y the values ar e sho w n (English units selec ted in this case): T o cop y the value o f Vm to the stac k, s elect the v ari able name , and pr ess @²STK , then, press @QUIT@ . F or the calc ulator se t to the AL G , the s cr een w ill look lik e this: T he displa y sho w s w ha[...]

Page 3-15 Defining and using func tions User s can def ine thei r o w n functi ons b y using the DEFIN E command av ailable thought the ke ystr ok e sequence „à (assoc iat ed with the 2 k e y) . The func tion mu st be enter ed in the follo w ing for mat: F unction_name(ar guments) = expr ession_con taining_ar guments F or ex ample , w e could de[...]

Page 3- 16 r elativ ely simple and consists o f two parts, contai ned between the pr ogram container s This is t o be inter pr eted as say ing: enter a v alue that is tempor aril y assigned to the name x (r efer r ed to as a local v ar iable), ev aluate the e xpr essi on betw een quotes that contain that local v ar ia ble , and sho w the eval u a t[...]

Page 4-1 Chapter 4 Calculations with compl e x numbers T his cha pter sho ws e xample s of calc ulation s and applicati on of fu ncti ons to comp le x number s. Definitions A comple x number z is a number z = x + iy , wher e x and y ar e real number s , and i is the imaginary unit def ined by i ² = –1. The comple x num ber x + iy ha s a r eal pa[...]

Page 4-2 Pr ess @@O K@@ , t wi ce, to r e turn to the sta ck . Entering comple x numbers Com p le x numbers in the calc ulator can be e nter ed in e ither of the tw o Car tesia n representations, nam ely , x+iy , or (x,y) . T he re sults in the calc ulator w ill be sho wn in the or dered-pair f ormat , i . e ., (x ,y) . F or e x ample , with the ca[...]

Page 4-3 P olar r epresentation o f a comple x number The polar r epr esentati on of the complex number 3 . 5-1.2i, enter e d abo v e , is ob tain ed by changing the c oor din ate sy stem to cylindri cal or pol ar (using f uncti on C YLIN) . Y ou can find this f unction in the catalog ( ‚N ) . Y ou can also c hange the coordinate t o polar using [...]

Page 4-4 Si mp le o per at io ns w ith co mple x nu mb er s Com ple x numbers can be comb ined using the f our fundament al oper ations ( +-*/ ) . T he re sults f ollo w the rule s of algebr a w ith the cav eat that i2= -1 . Oper atio ns w ith comple x numbers ar e similar to tho se w ith r e al number s . F or e x ample , with the cal c ulator in [...]

Page 4-5 T he f irs t menu (opti ons 1 thr ough 6) sho ws the f ollo w ing f uncti ons: Ex amples of applic ations of these func tions are sho wn ne xt in RE CT coor dinates. R ecall that, f or AL G mode , the func tion mu st pr ecede the ar gument , while in RPN mode , y ou ente r the ar gument f irs t , and then select the fu ncti on . Also , r e[...]

Page 4-6 CMP LX menu in k e y boar d A second CMP L X menu is access ible by u sing the r ight- shift option ass oc iated w ith the 1 k e y , i .e ., ‚ß . With s y st em fl ag 117 set t o CHOO SE box es , the k ey boar d CMPLX me nu sh o ws u p as the f ollo w ing scr e ens : T he r esulting men u include s ome of the f unctions alr eady in tr o[...]

Page 4-7 F unc tion DROITE: equation o f a straight line F unction DROI TE tak es as ar gument two comple x numbers, sa y , x 1 + iy 1 and x 2 +iy 2 , and r etur ns the equati on of the str aight line , say , y = a + bx, that contains the po ints (x 1 , y 1 ) and (x 2 , y 2 ) . Fo r exa m p l e, t h e l i n e between po ints A(5, - 3) and B(6, 2) c[...]

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Page 5-1 Chapter 5 Algebraic and ar ithm etic oper ations An algebr aic objec t , or simply , algebrai c , is an y number , var iable name or algebr aic e xpr es sio n that can be oper ated upon , manipulated , and comb ined accor ding to the r ules o f algebr a. Ex amples o f algebr ai c obj ects ar e the f ollo wing: Enteri ng alge br aic objec t[...]

Page 5-2 Simple operations w it h alg ebr aic objects Algebr aic ob jec ts can be added, subtr acted , multipli ed , di vi ded (e x cept by z er o) , r aised to a po w er , used as ar guments f or a var iety of st andar d functi ons (exponen tial , logar ithmic , tr igonome tr y , h y perboli c, etc .) , as y ou w ould an y real o r comple x number[...]

Page 5-3 @@A1@ @ * @@A2@@ ` @@A1@ @ / @@A2@@ ` ‚¹ @@A1@@ „¸ @@A2@@ T he same r esults ar e obtained in RP N mode if u sing the f ollo wi ng keyst ro kes : Functions in the AL G menu T he AL G (Alg ebr aic) men u is a vail able b y using the k e y str ok e sequ ence ‚× (assoc iat ed w ith the 4 k e y) . W ith s y stem flag 117 set to CHOO S[...]

Page 5-4 T o complete the oper ation pr ess @@ OK@@ . H e re i s t h e h el p scre en for fu n ct io n COL L ECT : W e noti ce that , at the bottom of the sc r een, the line See: EXP AND F A CT OR suggests l inks to other help f ac ility entr ie s, the f unctio ns EXP AND and F A CT OR . T o mo ve dir ectl y to thos e entr ies , pr ess the soft men[...]

Page 5-5 F or e x ample , for f unction S UB S T , w e find the f ollo wing CA S help fac ility entry: Operations w ith transcendental func tions T he calc ulator off ers a number of f uncti ons that can be used t o r eplace e xpr essions con taining logar ithmic and e xponential f uncti ons ( „Ð ), as well as trigonometric f unctions ( ‚Ñ ).[...]

Page 5-6 Inf or mation and e x amples on the se commands ar e av ailable in the help fac ility of the calc ulator . F or ex ample , the de sc r ipti on of EXP LN is sh o w n in the left-hand side , and the ex ample fr om the help f ac ilit y is sho wn to the rig h t : Expansion and factoring using tr igonometric functions T he TRIG menu , tr igger [...]

Page 5-7 F unc tions in the ARITH MET I C menu The ARI TH MET IC menu is tr igger ed thr ough the k e y str oke co mbinati on „Þ (asso c iated w ith the 1 k e y) . With sy stem f lag 117 set t o CHOO SE bo xe s , „Þ sho ws the f ollo w ing men u: Out o f this men u list , opti ons 5 thr ough 9 ( DIVIS , F A CT ORS , L GCD , P ROP FR A C, S IM[...]

Page 5-8 Po l y n o m i a l s P oly nomi als ar e algebrai c e xpr essi ons consisting of one or more ter ms containi ng decr easing po w ers of a gi v en var iable . F or e xam ple , ‘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 COLLE CT and EXP AND , [...]

Page 5-9 Th e PRO O T f u n c t i o n Gi ven an ar ra y containing the coeff ic i ents of a pol ynomi al , in decr easing or der , the functi on PR OO T pr ov ides the r oots of the pol ynomi al . Ex ample , fr om X 2 +5X+6 =0, P RO O T([1, –5, 6]) = [2 . 3 .]. Th e Q U O T a n d R E M A I ND E R f u n c t i o n s T he func tio ns QUO T and REMAI[...]

Page 5-10 F A CT OR(‘(X^3-9*X)/(X^2 -5*X+6)’ )=‘X*(X+3)/(X- 2)’ T he SI MP2 func tion F unction SIMP2 , in the ARITHME TIC men u , tak es as argume nts tw o number s or pol y nomi als, r epr esen ting the numer ator and denominator o f a r a tio nal fr action , and retur ns the simplified n umerato r and denominat or . F or e x ample: S IMP[...]

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 pre ss µ„î` (or , si mply µ , in RPN mode) y ou w ill 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 R O O TS f u n c t i o n T he f unct io n FR OO T S, in the A RI THMET IC[...]

Page 5-12 Refe re n c e Additi onal infor mation , def initions , and e xamples o f algebr aic and ar ithmeti c oper ation s ar e pr esented in C hapter 5 of the calc ulator’s u ser ’s guide . SG49A.book Page 12 Friday, September 16 , 2005 1:31 PM[...]

Page 6-1 Chapter 6 Solution to equations Ass oc iated w ith the 7 k e y there ar e t wo me nus of equati on -sol v ing func tions , the S y mbolic S OL V er ( „Î ) , and the NUMeri cal SoL V er ( ‚Ï ) . F ollo wing , w e pr ese nt some o f the f u ncti ons contained in thes e menu s. S y mbolic solution o f algebraic equation s H e r e w e d [...]

Page 6-2 the f igur e to the left . After a pply ing IS OL, the r esult is sho w n in the f igur e to the ri ght: T he fir st ar gument in IS OL can be an expr essi on, as sho wn a bov e , or an equation . F or ex ample , in AL G mode , tr y : T he same pr oblem can be sol ved in RPN mode as illus tr ated belo w (fi gur es sho w the RPN stac k bef [...]

Page 6-3 T he fo llo wing e xample s sho w the use of f unction S OL VE in AL G and RPN modes (U se C omple x mode in the CA S): The scr een s hot show n above displ ay s t wo solution s. In t he first on e , 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 [...]

Page 6-4 Fun c t i on SO L V EV X T he functi on S OL VEVX sol v es an eq uation f or the def ault CA S v ari able co n t a i n e d i n t h e re se r ved va ria b l e n a me V X . By d efa u l t, t h i s va ria b l e i s s e t to ‘X’ . Example s, u sing the AL G mo de w ith VX = ‘X’ , a r e sho w n below : In the fi rst cas e S O L V EVX co[...]

Page 6-5 sc reen sh ots sho w the RPN stac k bef or e and after the appli cation of ZERO S to the two e xamples abo ve (Use C omple x mode in the CAS): T he S ymboli c Solv er functi ons pre sente d abo v e pr oduce solutions t o r ational equations (mainl y , poly nomi al equations). If the equation to be sol ved f or has all numer ical coeff ic i[...]

Page 6-6 w ith e xamples fo r the n umer ical sol v er applicatio ns. Item 6. MS L V (Multiple equation SoL V er ) w i ll be pr esen ted later in page 6 -10 . P oly nomial Equations Using the Solve p oly… option in the calc u lator’s SOL V E env ironment you can: (1) f ind the soluti ons to a pol y nomi al equati on; (2) obtain the coeff ic ien[...]

Page 6-7 Pr ess ` to r eturn to st ack . The st ac k w ill sho w the follo w ing r esults in AL G mode (the same r esult w ould be sho w n in RPN mode) : All the solu tions ar e complex number s: (0. 4 3 2 , -0. 3 8 9) , (0.4 3 2 , 0.3 89 ) , (- 0.7 66 , 0.6 3 2), (-0.7 66 , -0.6 3 2) . Generating pol y nomial coeffic ients giv en t h e poly nomial[...]

Page 6-8 Generating an algebraic e xpression f or the poly nomial Y ou can use the calc ulator to gener ate an algebr aic e xpr essi on for a poly nomial gi ven the coe ffi ci ents or the r oots of the pol ynomi al . T he r esulting e xpr essi on wi ll be gi v en in ter ms of the de fa ult CA S v ar iable X. T o ge ner ate the algebr aic e xpr essi[...]

Page 6-9 Solv ing equations with one unkno wn thr ough NUM.SL V T he calc ulator's NUM. S L V menu pr ov ides it em 1. Sol ve eq uation .. solve diffe r ent t y pes o f equati ons in a single v ar iable , inc luding non-linear algebr aic and tr anscendent al equati ons . F or e x ample , let's solv e the equati on: ex- s i n ( π x/3) = 0[...]

Page 6-10 T he eq uat i on w e s t or ed i n v ar i ab le E Q i s al r ead y lo ade d in t he Eq fie l d i n the S OL VE E Q U A TION inpu t fo rm . Also , a f ield labeled x is pr ov ided. T o sol v e the equation all y ou need to do is highlight the f ield in fr ont of X: by using ˜ , and pre ss @SOLVE@ . The s oluti on sho wn is X: 4. 5006E - 2[...]

Page 6-11 In AL G mode, pr ess @ECHO to cop y the e x ample to the s tack , pr es s ` to run the e x ample . T o see all the ele ments in the soluti on y ou need to acti vate the line editor b y pr essing the do wn arr o w ke y ( ˜ ): In RPN mode , the soluti on fo r this e x ample is pr oduced b y using: Ac ti v ating func ti on MSL V r esults in[...]

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Page 7-1 Chapter 7 Ope r at i on s w ith li sts L ists ar e a t ype o f calc ulator ’s obj e ct that can be us ef ul for dat a pr oces sing. T his chapt er pr esents e xamples o f oper a tio ns w ith lists. T o get started w ith the e xamples in this Chapte r , we use the A ppr ox imate mode (See C hapter 1) . Creating and stor ing lists T o c r [...]

Page 7-2 Addition , subtr ac tion, multiplication, di vision Multipli cation and di visi on of a list b y a single number is distr ibuted acr os s the list , for e xample: Subtr action o f a single number fr om a list w i ll subtr act the s ame number fr om each element in the list , for e xample: Additi on of a single number to a lis t pr oduces a[...]

Page 7-3 T he di v isi on L4/L3 w i ll pr oduce an infinity entry becaus e one of the elements in L3 is z er o , and an err or mes sage is r eturned . If the lists in vol v ed in the oper atio n hav e differ ent lengths , an err or mess age (In valid Dime nsi ons) is pr oduced. T r y , for e xam ple , L1-L4. Th e p l us s ig n ( + ) , whe n applied[...]

Page 7-4 Functions applied to lists Real n umber functi ons fr om the k e yboar d (ABS , e x , LN , 10 x , L OG , SIN, x 2 , √ , CO S, T AN, A SIN , A CO S, A T AN, y x ) as well as those fr om the M TH/ HYP ERBOLIC menu (S INH, C O SH, T ANH, A SINH, A C OSH , A T ANH) , and MTH/REAL men u (%, etc .) , can be appli ed to lists , e .g., L ists of[...]

Page 7-5 L ists of algebraic objects T he f ollo wi ng ar e e xamples o f lists of algebr aic ob jec ts w ith the functi on SIN a pplied t o them (se lect Ex act mode fo r thes e e x amples -- See C hapter 1): Th e M T H / L I ST m e n u T he MTH menu pr ov ides a n umber of f uncti ons that e x c lusi vel y to lists . W i t h s y s t e m f l a g 1[...]

Page 7-6 Ex amples of applic ation o f thes e func tions in AL G mode ar e sho w n next: S ORT and REVLI S T can be combined to sort a list in dec rea sing or der : If y ou ar e w or king in RPN mode , enter the lis t onto the s tac k and then selec t the oper ation y ou want . F or e x ample , to calc ulate the inc r ement between cons ec uti v e [...]

Page 7-7 Th e S E Q f u n c t i o n T he SE Q functi on, a vailable thr ough the command catalog ( ‚N ), tak es as ar guments an e x pr ession in t erms o f an index , the name of the inde x , and st arting, ending , and incr ement v alues f or the inde x, and r etur ns a list consisting of the e valuation o f the e xpr essi on for all possible v[...]

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Page 8-1 Chapter 8 Ve c t o r s T his Chapte r pr ov ides e xample s of ent er ing and oper ating w ith v ector s, both mathematical v ector s of man y elements , as well as ph ysi cal ve ctor s of 2 and 3 componen ts. Enteri ng v ec tors In the calc ulator , ve ctor s are r epr esented b y a sequence of number s enc los ed betwee n br ack ets, and[...]

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 c to rs u 2 = [1, 2] , u 3 = [-3, 2, -2] , v 2 = [3,-1] , v 3 = [1, -5, 2] Stored i nto variable s @@@u 2@@ , @@@u3 @@ , @@@v2@@ , and @@@v3@@ , r especti ve ly . F irst , in A[...]

Page 8-3 Using th e Ma tri x W riter (MTR W ) to enter vec tors V e ctor s can also be enter ed b y using the Matri x W rite r „² (thir d k e y in the f ourth ro w of k e ys f r om the t op of the k ey board). This command gener ates a spec ies of spr eadsheet cor r esponding to r ow s and columns of a matr i x (Details on using the Matr ix W r [...]

Page 8-4 @+ROW@ @ -ROW @+COL@ @-COL@ @GOTO@ Th e @+ROW@ k ey w ill add a ro w full of z ero s at the location of the selec ted cell of the sp r eadsheet . Th e @- ROW ke y w ill delete the r o w corr esponding to the s elected cell o f the spr eadsheet . Th e @+COL@ k ey w ill add a column full of z er os at the loca tio n of the selec ted cell of [...]

Page 8-5 Simple operations w it h vectors T o illu str ate oper ations w ith vec tor s w e w ill us e the vect ors u2 , u3, v2 , and v3, stored in an ea rlier ex erc ise. Also , store v ector A =[ -1 ,- 2 ,-3 ,- 4,-5] to be used in the fo llo w ing ex er c ises . Changing sign T o c hange the sign o f a v ector us e the k e y , e .g., Addition , [...]

Page 8-6 Multiplication b y a scalar , and div ision b y a scalar Multipli cation b y a scalar or di vi sion b y a scalar is str aigh tfo rwar d: Absolute v alue function T he absolu te v alue func tio n (AB S) , when appli ed to a v ector , pr oduces the magnitude of the v ect or . F or ex ample: ABS([1,-2 ,6]) , ABS(A) , ABS(u3) , w ill sho w in [...]

Page 8-7 Ma gnitude T he magnitude of a v ector , as disc ussed ear lier , can be f ound w ith f uncti 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 ). Ex amples of applicati on of func tion AB S wer e sho w n abo ve . Dot pr oduc t F unction DO T (optio n 2 in CHOO SE bo x abov e) is us ed t[...]

Page 8-8 Exampl es of cross products of on e 3 -D vector with o ne 2 -D vector , or vice v ers a , ar e pr esented ne xt: Atte mpt s to c al culat e a cross product of vectors of l eng th oth er th an 2 or 3, pr od uce an er r or mes sage: Refe re n c e Additi onal infor mation on oper atio ns w ith vec tors, inc luding applicati ons in the ph y si[...]

Page 9-1 Chapter 9 M atrices and linear algebr a T his chapt er sho ws e xample s of c reating matr ice s and oper ations w ith matr ices , including linear algebr a applicati ons . Enteri ng matrices in the stac k In this secti on we pr esent tw o differ ent methods to enter matr ices in the calc ulator stac k: (1) using the Matr i x W rit er , an[...]

Page 9-2 If y ou hav e select ed the te xtbook display opti on (using H @) DISP! and ch e ck i n g of f  Textbook ) , the matri x wi ll look lik e the one show n abo v e . Other wise , th e display will sho w: T he displa y in RPN mode w ill look very similar to thes e . T yping in the matr ix dir ec tly int o th e stack T h e s a m e r e s u l [...]

Page 9-3 Ope r at i on s w ith ma tr ice s Matr ices , like other mathematical ob jec ts, can be added and su btr acted. T he y can be multipli ed b y a scalar , or among themsel ve s, and r aised to a r eal po wer . An important oper a tion f or linear algebr a appli cations is the in v erse o f a matr i x . Details of these oper atio ns ar e pr e[...]

Page 9-4 Addition and subtr ac tion F our ex amples ar e show n below using the matr ices stor ed abo v e (AL G mode) . In RPN mode , tr y the follo w ing ei ght ex amples: Mul ti pl ica ti on T her e ar e a number of multipli cation oper ations that inv olv e matr ices . T hese ar e desc r ibed next . The e xamples ar e show n in algebrai c mode .[...]

Page 9-5 Matrix -v ector multiplication Matr i x - v ector m ultiplicati on is possible onl y if the number o f columns of the matr i x is equal to the length of the v ector . A couple o f ex amples o f matri x - ve ctor m ultiplicati on follo w: V e ctor -matr i x multiplicati on , on the other hand , is not def ined. T his multiplicati on can be [...]

Page 9-6 T erm-b y-term multiplica tion T erm- by- term mu lt ip lica tion of t wo mat rices of t he sam e d im ens ions is possi bl e th r oug h th e use of function H ADAMAR D . The result i s, of cou rse , another matri x of the same dime nsio ns. T his functi on is av ailable thr ough F unction catalog ( ‚N ) , or thr ough the MA TRICE S/OP E[...]

Page 9-7 T he identit y matri x T he ide ntity matri x has the pr oper ty that A ⋅ I = I ⋅ A = A . T o ve r ify this pr oper ty w e pr esent the f ollo w ing ex amples us ing the matri c es st or ed earli er o n. U se functi on ID N (f ind it in the MTH/MA TRIX/MAKE me nu) to gener ate the iden tity matri x as sho wn her e: T he inv erse matri [...]

Page 9-8 Char ac teri zing a matri x (The matr ix NORM menu) T he matri x NORM (NORMALI ZE) menu is acces sed thr ough the k ey str oke sequ enc e „´ . This men u is desc r ibed in de tail in Chapter 10 of the calc ulator’s us er’s gui de . Some o f these f uncti ons ar e des cr ibed next . Fu nc t i o n D ET F unction DET calc ulates th e d[...]

Page 9-9 Solution of linear s y stems A s ys tem of n linear equati ons in m var iab les can be w r 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[...]

Page 9-10 2x 1 + 3x 2 –5x 3 = 13, x 1 – 3x 2 + 8x 3 = -13, 2x 1 – 2x 2 + 4 x 3 = -6, can be wr it ten as the matr ix eq uation A ⋅ x = b , if T his s y stem has the same number o f equatio ns as of unkno w ns, 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 [...]

Page 9-11 A solu tion w as found as sho wn ne xt . Sol uti on w ith the in v erse ma tr i x T he soluti on to the s yst em A ⋅ x = b , wher e A is a squar e matri x is x = A -1 ⋅ b . F or the e x ample us ed earli er , we can f ind the soluti on in the calc ulator as f ollo ws (F irs t enter matr ix A and v ec tor b once more): Solution b y “[...]

Page 9-12 Refe re n c e s Additi onal informati on on cr eating matri ces, matr i x operati ons , and matri x appli cations in linear algebr a is pr es ented in Cha pter s 10 and 11 of the calculator ’s us er’s gui de . SG49A.book Page 12 Friday, September 16 , 2005 1:31 PM[...]

Page 10-1 Chapter 10 Gr aph ics In this cha pter w e intr oduce some of the gr aphic s capab ilitie s of the calc ulator . W e w ill pr es ent gr aphic s of f unctions in C artesian coor dinates and polar coor dinates , parametr ic plots , gr aphi cs of coni cs, bar plots, scatter plots, and fa st 3D plots . Graphs options in the calc ulator T o ac[...]

Page 10-2 P lot ting an e xpression o f the for m y = f(x) As an e xample , let's plot the f u ncti on , • F irst, enter th e PL O T S ETUP envir o nment by pressing, „ô . Mak e sur e that the option F uncti on is select ed as the TYPE , and that ‘X’ is selec ted as the independent v ar iable ( INDEP ). Pr e s s L @@@OK@@@ to r etur n[...]

Page 10-3 •P r e s s ` to r eturn t o the PL O T - FUNCTION w indo w . The e xpr essi on ‘ Y1(X) = EXP(- X^2/2)/ √ (2* π )’ will be highlig hted. Pr ess L @@@OK@@@ to r etur n to normal calc ulator display . • Enter the P L O T WINDO W en vir onment b y enter ing „ò (pre ss them simultaneou s l y if in RPN mode) . Use a r ange of –4[...]

Page 10-4 Gen er ating a table of v alues f or a func tion The c o m bi n a t ion s „õ ( E ) and „ö ( F ) , pressed simultaneousl y if in RPN mode , let’s the us er pr oduce a table o f value s of func tions . F or e x ample , w e w ill produ ce a ta ble of the f uncti on Y(X) = X/ (X+10) , in the r ange -5 < X < 5 follo w ing these i[...]

Page 10-5 • W ith the option In hi ghligh ted , pr ess @@@OK@@@ . The t able is e xpanded so that the x -incr ement is no w 0.2 5 rather than 0. 5 . Simply , what the calc ulator does is t o multipl y the or iginal incr ement , 0. 5, b y the z oom fa ctor , 0.5, t o pr oduce the ne w incr ement o f 0.2 5 . T hus , the zo o m i n option is us eful[...]

Page 10-6 • K eep the def ault plot w indo w r anges to r ead: •P r e s s @ERASE @ DRAW to dr aw the thr ee -dimensio nal surface . The r esult is a w i r ef r ame pic tur e of the surface w ith the re fer ence coor dinate sy stem sho wn at the lo we r left corne r of the sc r een . B y using the arr o w ke ys ( š™—˜ ) you c an cha ng e t[...]

Page 10-7 • When done , pr es s @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 r eturn to normal calc ulator displa y . T ry 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 C hapter w e disc uss appli catio ns of the calc ulator’s f uncti ons to oper ations r elated to C alc ulus , e.g ., limits, der i v ati v es, integr als, po w er series , etc. T he CAL C (Calc ulus) me nu Man y of the f uncti ons pr es ented in this Chapter ar e contained in the calc ulator’s [...]

Page 11-2 Fu n c t io n lim is enter ed in AL G mode as lim(f (x),x=a) to calculate the limit . In RPN mode , ente r the func tion f irst , then the e xpr ession ‘ x=a’ , and f inally func tion lim. Ex amples in AL G mode ar e sho wn ne xt , inc luding some limits to inf inity , and one -sided limits . The inf inity sy mbol is assoc iated w ith[...]

Page 11-3 F unc tions DERI V and DER VX The function D ERIV is used to take deri vati ve s i n terms of any ind epen dent var iable , while the functi on D ER VX tak es deri vati ve s w ith r espect to the C AS d efa ul t va ria bl e V X ( t ypic a l ly ‘ X’ ) . W hi l e fu n ct io n D E RVX i s ava i la b l e dir ectly in the CAL C menu , both[...]

Page 11-4 P leas e noti ce that func tions S I G MA VX and SIGMA ar e designed f or integr ands that in v ol v e some s ort of integer func tion lik e the fact or ial (!) func tion sh o w n abo ve . The ir r esult is the so -called disc r ete der i v ati v e , i.e ., one def i ned f or intege r numbers onl y . Definite integr als In a def inite int[...]

Page 11-5 Infinite ser ies A func tion f(x) can be e xpanded into an inf inite ser ies ar ound a point x=x 0 b y using a T a y lor’s se r ies , namely , , w here f (n) (x) r epr esen ts the n- th deri vati ve o f f(x) w ith r espec t to x , f (0) (x) = f(x) . If the value x 0 = 0 , t h e se ri es i s refe r red to a s a M a cl a u ri n’ s se ri[...]

Page 11-6 ser ies) or an e xpre ssi on of the f or m ‘ var iable = v alue ’ indicating the poin t of e xpansion of a T ay lor ser ies , and the or der of the ser ies to be pr oduced . F unction SERIE S r eturns two o utput it ems: a list w ith f our items , and an e xpression f o r h = x - a, if th e second argument in the function call is ‘ [...]

Page 12-1 Chapter 12 M ulti-v ari ate Calc ulus Applications Multi-var iate calc ulus r ef er s to f uncti ons o f tw o or mor e var iable s. In this Chapt er w e disc uss basi c concepts of multi-v ar iate calc ulus: partial der i v ati ves and m ultiple integr als. Pa r t i a l d e r i v a t i v e s T o qui c kly calc ulate partial deri vati ve s[...]

Page 12-2 T o de f ine the functi ons f(x ,y) and g(x ,y , z) , in AL G mode , use: DEF(f(x,y )=x*CO S(y)) ` D EF(g(x,y ,z)= √ (x^2+y^2)*SIN(z) ` T o t ype the der iv ativ e sy mbol use ‚¿ . Th e d e riva t ive , f or e xample , w ill be ente r ed as ∂ x(f(x ,y)) ` in A L G mode in the scr een. M ultiple integrals A ph ysi cal inter pret ati[...]

Page 13-1 Chapter 13 V ec tor Anal y sis Applications T his chapt er desc ribes the us e of f uncti ons HE S S, DIV , and CURL , f or calc ulating oper ations of v ector anal y sis . T he d el operator T he f ollo w ing oper ator , r ef er r ed to as the ‘ del’ or ‘ nabla ’ oper ator , is a ve ctor -based oper ator that can be applied to a [...]

Page 13-2 Di ve rgence T he di v er ge nce o f a v ect or f unc ti on , F (x ,y ,z) = f(x,y ,z ) i + g(x,y ,z ) j +h(x ,y ,z) k , is de f ined by t aking a “ dot -produc t” o f the del oper ator w i th the func tion , i .e . , . F unction DIV can be used to calc ulate the di ve r gence of a v ecto r fi eld . F or ex ample , for F (X,Y ,Z) = [XY[...]

Page 14-1 Chapter 14 Differential Equations In this Chapte r we pr esen t e x amples of so l v ing or dinar y differ ential equati ons (ODE) using calc ulator functi ons. A diff er ential equati on is an equati on inv olv ing deri vati ve s of the independent var iable . In mos t case s, w e seek the dependent f uncti on that satisf ie s the differ[...]

Page 14-2 • the ri ght-hand side of the OD E • the char acter isti c equation of the ODE Both of these inputs mus t be giv en in terms of the defa ult independent var iable f or the calc ulator ’s CAS (ty pi cally X). The output f r om the functi on is the general soluti on of the ODE . The e x amples belo w ar e sho w n in the RPN mode: Ex a[...]

Page 14-3 Fu n c ti o n DE SO L V E T he calculator pr o v ides f uncti on DE S OL VE (Differ ential E quation S OL VEr ) to sol v e certain t ype s of diff er enti al equations . The f unction r e quir es as input the differ enti al equatio n and the unkno wn f uncti on , and retur ns the soluti on to the equati on if av ailable . Y ou can also pr[...]

Page 14-4 ‘ d1y(0 ) = -0. 5’ . Changing to these Ex act e xpres s ions f ac i litates the solut ion. Pr es s µµ to simplif y the re sult . Use ˜ @EDIT to see this r esult: i. e . , ‘ y(t) = -((19* √ 5*S IN( √ 5*t) -(148*CO S( √ 5*t)+8 0*C OS(t/2) ))/19 0)’ . Pr es s ``J @ODETY to get the str ing “ Linear w/ cst coeff ” f or the[...]

Page 14-5 Compar e these e xpr essions w ith the one gi v en earli er in the def initi on of the L aplace tr ansf orm , i .e ., and y ou w ill notice that the CA S defa ult v ar iable X in the equati on wr iter sc r e en r epla ces the v aria ble s in this de f inition . Ther efor e , when us ing the func tion LAP y ou get bac k a functi on of X, w[...]

Page 14-6 F our ier series f o r a quadr atic func tion Deter mine the co eff ic ients c 0 , c 1 , and c 2 f or the f uncti on g(t) = (t-1) 2 +(t - 1) , w ith per iod T = 2 . Using the calc ulator in AL G mode , firs t w e def ine functi ons f(t) and g(t) : Ne xt , w e mo v e to the CA SD IR sub-dir ectory under HOME to c hange the va l ue of va 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 o urier seri es with three el ement s will be wr it ten as g(t) ≈ R e[(1/3) + ( π⋅ i+2)/ π 2 ⋅ ex p ( i ⋅π⋅ t)+ ( π⋅ i+1)/( 2 π 2 ) ⋅ ex p (2 ⋅ i ⋅π⋅ t)]. Referen ce F or additional def initi ons, a pplicati ons, and e xer c i ses [...]

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Page 15-1 Chapter 15 Pr obabilit y Distributions In this Chapt er w e pr o v ide e x amples of appli cati ons of the pr e -defined pr obab ility distribu tions in the calc ulator . T he MTH/P R OB ABI LI TY .. sub-menu - par t 1 T he MTH/PR OB ABILI TY .. sub-men u is accessible thr ough the k ey str oke sequ enc e „´ . W i t h s y s t e m f l a[...]

Page 15-2 • PERM(n ,r ) : Calc ulates the number o f perm utati ons of n items tak en r at a time • n!: F actor ial o f a positi ve inte ger . F or a non -integer , x! r etur ns Γ (x+1) , wh ere Γ (x) is the Gamma functi on (see C hapter 3). The f actor ial s ymbol (!) can be enter ed also as the ke ys tr ok e combinati on ~‚2 . Ex ample of[...]

Page 15-3 T he MTH/P ROB menu - part 2 In this sec tio n w e dis c us s f our cont inuou s pr obabil ity distr ibuti ons that ar e commonl y us ed f or pr oblems r elated to s tatisti cal infer ence: the nor mal distr ibution , the Student ’s t distr i buti on , the Chi-squar e ( χ 2 ) distr ibuti on , and the F-dis tributi on . The f uncti ons [...]

Page 15-4 T he C hi-squar e distribution Th e C h i - sq u a re ( χ 2 ) distribu tion has one par ameter ν , know n as the degr ees of fr eedom. The calc ulator pr ov ides f or values o f the upper - tail (c umulati v e) distr ibution f uncti on f or the χ 2 -distr ibution using UTPC gi ven the value o f x and the par ameter ν . The def inition[...]

Page 16-1 Chapter 16 Statistical Applications T he calc ulator pr ov ides the f ollo wing pr e -pr ogr ammed statis tical f eatur es access ible thr ough the k e y str ok e combinati on ‚Ù (the 5 key ) : Enteri ng data Appli cations number ed 1, 2 , and 4 in the list abo v e r equir e that the data be a vaila ble as columns of the matr ix Σ D A[...]

Page 16-2 Calculating singl e -v ar iable statistic s After enter ing the col umn vector into Σ DA T , p re s s ‚Ù @@@OK@@ to sele ct 1. Singl e - v ar .. The fo llo w ing input f or m w ill be pr ov ided: T he for m lists the data in Σ D A T , sho ws that column 1 is s elec ted (ther e is onl y one column in the c urr ent Σ D A T) . Mov e ab[...]

Page 16-3 Obtaining frequenc y distr ibutions The ap p l ic a tio n 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 f r equenc y distr ibuti ons f or a set of data . The data mu st 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 . T o g e t st a r t e d , pr ess ‚Ù˜ @@[...]

Page 16-4 Σ D A T , b y usi ng functi on ST O Σ (see e x ample abo ve) . Ne xt, obtain single - v ar ia ble infor mation us ing: ‚Ù @@@OK@@@ . The r esults are: This informat ion ind icates tha t our da ta ranges from -9 to 9 . T o p roduce a f r e q u e nc y d is t r i b ut i o n w e w i ll u s e th e i n t e rv a l (- 8 , 8) d i v i di n g i[...]

Page 16-5 F itting data to a func tion y = f(x) T he pr ogram 3. F it da ta.. , av ailable as option n umber 3 in the S T A T menu , can be used to f it linear , logar ithmic , exponenti al, and po w er func tions t o data sets (x , y) , stor ed in columns of the Σ D A T matr i x. F or this appli cation , yo u need to hav e at least tw o columns i[...]

Page 16-6 Le ve l 3 sho ws the f or m of the equati on. L e v el 2 sho ws the sample corr elation coeff ic ient , and lev el 1 sho ws the co var iance of x -y . F or def initions of the se par ameters se e Chapter 18 in the user ’s guide . F or additional inf ormatio n on the data-fit f eatur e of the calculat or see Cha pter 18 in the u ser ’s[...]

Page 16-7 •P r e s s @@@OK@@@ to obtain the fo llo wing r esults: Confidence inter vals T he applicati on 6. Con f In ter val can be acces sed b y using ‚Ù— @@@OK@@@ . Th e ap p l ic at io n of fe rs t h e fol l ow in g o p t io ns : These opt ions ar e to b e i nterpre ted as follo ws: 1. Z -INT : 1 µ .: Single sample conf idence in terval[...]

Page 16-8 4. Z -INT : p 1− p 2 .: C onf idence interval f or the differ ence of tw o pr oportions, p 1 -p 2 , for lar ge samples w ith unkno w n populatio n va rian c es. 5. T- I N T: 1 µ .: Single sample confi dence int erval f or the population mean , µ , f or small samples with unkno w n population v ariance . 6. T- I N T: µ1−µ2 .: Conf [...]

Page 16-9 T he gr aph sho ws the s tandar d nor mal distr ibution pdf (pr o babi lity densit y func tion), the location of the c riti cal po ints ± z α/2 , the mean value ( 2 3 . 3) and the corr esponding interval limits ( 21.9 84 2 4 and 2 4.615 7 6 ) . Pres s @TEXT to r eturn to the pr e v io us r esults sc r e en , and/or pr es s @@@OK@@@ to e[...]

Page 16-10 2. Z - Te s t : µ1−µ2 .: Hy pothesis testing f or the differ ence of the populati on means, µ 1 - µ 2 , w ith either kno wn populati on v ari ances , or fo r lar ge samples w ith unkno wn populati on var iances . 3 . Z - T es t: 1 p.: Single sample h ypo thesis testing f or the pr oportion , p , for lar ge samples w ith unknow n po[...]

Page 16-11 Then , we r ej ect H 0 : µ = 15 0, against H 1 : µ ≠ 15 0. The tes t z value is z 0 = 5 .6 5 6 8 54. T he P -v alue is 1. 54 × 10 -8 . T he cr iti cal v alues of ± z α /2 = ± 1.9 5 9 9 64 , cor r esponding t o cr itical ⎯ x r ange of {14 7 .2 15 2 .8}. T his info rmati on can be obs erved gr aphi call y b y pr essing the s oft-[...]

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Page 17-1 Chapter 17 Numbers in Differ ent Bases Besi des our dec imal (base 10, di gits = 0 -9) number s y ste m , y ou can w ork w ith a b inary s yst em (bas e 2 , digits = 0,1) , an octal s yst em (base 8 , digits = 0 - 7) , or a he x adec imal s y ste m (base 16, di gits=0 -9 ,A -F), among others . T he same w ay that the dec imal int eger 3 2[...]

Page 17-2 W r iting non -dec imal numbers Numbers in non-de c imal sy stems , r ef err ed to as bi n ar y i nte g e rs , ar e w r itten pr eceded by the # s y mbol ( „â ) in the calculator . T o select the c urr ent base to be u sed f or binary integers , choo se e ither HEX (adec imal) , D E C (imal) , OCT (al), or BIN (ary) in the BA SE menu .[...]

Page 18-1 Chapter 18 Using SD car ds The calc ulator has a mem ory car d slot into w hic h y ou can insert an SD flash car d for backin g up calculat or objec ts, or f or do wnl oading objects fr om other sour ces . The SD car d in the calculat or w ill appear as port numb er 3. Inserting and remo ving an SD car d The SD slot is located on the bot [...]

Page 18-2 4. When the for matting is fin ished, the HP 5 0g display s the m essage "FORMA T FINISHED . PRE S S ANY KEY T O EXI T". T o ex it the sy stem menu , hold dow n the ‡ k e y , pr ess and r elease the C k e y and then r elease the ‡ key . The SD car d is no w r eady for u se . It w ill ha v e been for matted in F A T3 2 form a[...]

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 ei ght c har act ers , it w ill appear in 8.3 DO S for mat in port 3 in the F iler once it is stor ed on the card . Recalling an object fr om the SD card T o r eca ll an object f r om the SD card onto the sc r een, u[...]

Page 18-4 P urging all objects on t h e SD card (b y re fo rm at t i n g ) Y ou can pur ge all ob jects f r om the SD card b y r ef ormatting it . When an SD car d is inserted, @FO RMA appears an additi onal menu item in F ile Manager . Selec ting this optio n r ef ormats the entir e car d, a pr ocess w hic h also delete s e very obje ct on the car[...]

Page 19-1 Chapter 19 Equation L ibr ar y T he E quation L ibrary is a collectio n of equati ons and commands that enable y ou to sol v e simple sc ience and engineer ing pr oblems . T he libr ary consis ts of mor e than 300 equati ons grou ped into 15 tec hnical sub jects cont aining mor e than 100 pr oblem titl es . E ach pr oblem title contains o[...]

Page 19-2 No w us e this equati on set to ans w er the questi ons in the follo w ing e x ample . Step 4: Vi e w the f i v e equati ons in the Pr oj ectile Moti on set . All f iv e ar e used inter changeabl y in order to s olv e for missing v ariable s (see the ne xt e xample). #EQN# # NXEQ# #N XEQ# # NXEQ# #NXE Q# Step 5 : Ex amine the var iable s [...]

Page 19-3 0 *!!!!!!X0!!!!!+ 0 *!!!!!!Y0!!!!!+ 50 *!!!!!!Ô 0!!!!!+ L 65 *!!!!!!R!!!!!+ Step 3 : S olv e for the v eloc ity , v 0 . (Y ou solv e for a v ar iable b y pre ssing ! and then the var iable ’s menu k ey .) ! *!!!!!!V0!!!!!+ Step 4: Re call the r ange, R , di v ide b y 2 to get the halfwa y distance , and enter that as the x- c o o rd i [...]

Page 19-4 Refe re n c e F or additional det ails on the E quation L ibrary , see C hapter 2 7 in the calculator ’s us er’s gui de . SG49A.book Page 4 Friday, S eptember 16, 2005 1:31 P M[...]

Pa g e W - 1 L imited W arr ant y HP 50g gr aphing calculator ; W arr ant y per iod: 12 months 1. HP war r ants to y ou , the end-user c ustomer , that HP hard war e, accessor ies and suppli es w ill be fr ee fr om defects i n mater i als and w orkmanship after the date of pur c hase , for the per iod spec if ied a bov e. If HP rece i ves noti ce o[...]

Pa g e W - 2 REMEDIE S . EX CEPT A S INDICA TED ABO VE , IN NO EVENT WILL HP OR I T S S UPP LIERS BE LIABLE F OR L OS S OF D A T A OR FOR DIRE CT , SP E CIAL, INCIDENT AL , CO NSE QUENTIAL (INCL UD ING L O S T PR OFIT OR D A T A ) , OR O THER D AM A GE , WHETHER B ASED IN C ONT RA CT , T OR T , OR O THER WISE . Some countr ies , States or pr o v in[...]

Pa g e W - 3 Ser vice Eur ope Co untry : Te l e p h o n e n u m b e r s A us tr ia + 4 3-1-3 6 0 2 7 71203 B e l g i u m + 32-2-7 1 262 1 9 Denm ark + 4 5-8- 2 3 3 2 844 Ea s t e r n Eu ro p e c o u n t ri e s + 420 - 5 - 4 1 4 22 5 2 3 F inland +3 5 8-9 -64000 9 F rance +3 3-1- 4 99 3 9006 G e r m a n y + 49 - 69 - 953 07 1 0 3 Gr eece +4 20 -5- 4[...]

Pa g e W - 4 L.A me ri ca Co un try : Te l e p h o n e n u m b e r s Ar genti na 0- 8 1 0- 5 5 5 - 5 5 2 0 Br azil S a o Pa u l o 37 47-7 79 9 ; R O T C 0 -800 -15 77 51 Me x ico M x C i t y 5 258 - 9 922; R O T C 01-8 00 - 4 7 2 -66 84 Ve n e z u e l a 0 80 0 - 4 7 46 - 8368 Chile 80 0 - 3 609 99 Col um bia 9-800 -114 7 2 6 Pe r u 0- 8 0 0- 1 0 11[...]

Pa g e W - 5 Regulat or y inf ormation F ederal Communications Commission Notice T his equipment has been tes ted and fo und to comply w ith the limits f or a C las s B di gital de v ice , pursu ant t o P art 15 of the FCC R ules . Th ese limits ar e designed to pr o v ide r easona ble pr otec tion agains t harmf ul inte rfer ence in a re si dentia[...]

Pa g e W - 6 Or , call 1 - 8 0 0 - 4 7 4 - 6836 F or questi ons r e gar ding this FCC dec larati on, contac t: Hew lett -P ac k ar d Compan y P . O . Bo x 6 9 2000, Mail S top 510101 Houston , T ex as 77 2 6 9- 2000 Or , call 1 -28 1 - 5 1 4 - 3333 T o identify this pr oduct , r ef er to the part , ser ies , or model number f ound on the pr oduct. [...]

Pa g e W - 7 Japane se Not ice 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 ?[...]