HP 35s manual

HP 3 5s sc ie ntif i c calc ulator user's guide H Ed i t io n 1 HP part number F2 215AA-90001[...]

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Contents 1 Contents Part 1. Basic Operation 1. Getting Started ............... ...................... ....................... 1-1 Important Preliminaries .............. ................... .................... ........ 1-1 Turning the Calcula tor On and Off ..................... .................. 1-1 Adjusting Display Contrast .............. .....[...]

2 Contents Complex number display format (  ,  ,  ·‚) ... ................. 1-24 SHOWing Full 12–Digit Precisio n ......... ...................... ........ 1-25 Fractions ............. ................ .................... ................... ........... 1-26 Entering Fractions ............ .................... ..............[...]

Contents 3 Using the MEM Catalog .................. ................. ................... ..... 3-4 The VAR cata log..... ................ .................... ................ ........ 3-4 Arithmetic with Stored Variables .... .................... ................... ..... 3-6 Storage Arithmetic ..... .................... ................ ........[...]

4 Contents 5. Fractions ....... .......................... ...................... .............. 5-1 Entering Fractions ... .................... ................... .................... ...... 5-1 Fractions in the Display ... ................... .................... ................... 5- 2 Display Rules ............ ................... ...........[...]

Contents 5 Operator Precedenc e . .................... ................ ................... 6-1 4 Equation Functions ........ .................... ................ ................ 6-1 6 Syntax Errors....... ................... ................ .................... ...... 6-19 Verifying Equations ................ ................... ...............[...]

6 Contents Dot product .......... ................. ................... .................... .... 10-4 Angle between vecto rs ..... .................... ................ .............. 10-5 Vectors in Equations ... .................... ................... .................... . 10-6 Vector s in Programs.................. ...........................[...]

Contents 7 Part 2. Programming 13.Simple Programming ...... ........................................... 13-1 Designing a Pro gram ...... .................... ................ ................... 1 3-3 Selecting a Mode ... ................ .................... ................... ... 1 3-3 Program Boundaries (L BL and RTN) ........ .................[...]

8 Contents Clearing One or More Prog rams .............. ................... ...... 1 3-23 The Checksum .......................... ................... ................... 13-2 3 Nonprogrammable Functions ... .................... ................... ...... 13-24 Programming with BASE .............. ................ ................... ...... 1 3-24 [...]

Contents 9 15.Solving and Integrating Programs ............. ................. 15-1 Solving a Program .... ................... .................... ................... ... 15-1 Using SOLVE in a Program ..................... ................... ............. 15-6 Integrating a Program ........ ................. ................... ................ 1[...]

10 Contents B. User Memory and the Stac k ....................... .................. B-1 Managing Calculator M emory ...................... ................... .......... B -1 Resetting the C alculator ............................ ................ ................ B-2 Clearing Memo ry .................... ................. ................... .....[...]

Contents 11 How SOLVE Finds a Root ............. .................... ................ ........ D-1 Interpreting Results ............. ................. ................... .................. D-3 When SOLVE Cannot Find a Root ........................... .................. D-8 Round–Off Error ... .................... ................ .............[...]

12 Contents[...]

Pa r t 1 Basic Op er ation[...]

[...]

Getting Star ted 1-1 1 Gett ing Star ted Important Preliminaries T urning th e Calculator On and Of f T o turn the calculat or on , pr es s  . ON is pr inted on the bottom of the  key . T o turn the calculat or off , press  . That is, pr es s and r elease the  shift ke y , then pres s  (w hic h has OFF pr inted in ye llo w abo [...]

1-2 Getting Star ted Highlights of the K ey b oar d and Di spl ay Shifted Ke y s E ach ke y has three functi ons: one pr in te d o n i ts fa c e , a le f t –s hi ft ed f u n c t i on (yello w) , and a righ t–shifted functi on (blue). The shifted f uncti on names ar e prin ted in ye llo w abo ve and in blue on the bottom of eac h k e y . Pr es s[...]

Getting Star ted 1-3 Pr essi ng  or  turns on the cor re sponding or  ann unc iato r sy mbol at the top of the displa y . The ann unc iato r r emains on until y ou pr es s the next k ey . T o cancel a shift ke y (and tur n off its annunc iato r), pr ess the same shift k ey again . Alpha K e y s Most k ey s  display a letter in the ir bo[...]

1-4 Getting Star ted Backspac ing and Clearing Among the f irs t things y ou need to kno w are ho w to c lear an entry , corr ect a number , and clear the entire display to start over . Keys fo r C l e ar in g Key D es c r ip t i on  Backspace . If an e xpr essio n is in the proce ss of be ing enter ed,  erases the char acter to the left of t[...]

Getting Star ted 1-5 Ke ys for Clearing (continued) Key D e s c ri p t io n  Th e C LE AR m enu (       ) contains options f or c learing x (the n umber in the X-r egister ), all dire ct v ari ables, all o f memory , a ll statistical data, all stacks and indirect v ari ables. If you pr ess ?[...]

1-6 Getting Star ted Using Men us The re is a lo t mor e po w er to the HP 3 5s than w hat y ou s ee on the k e yboar d. This is because 16 of the k e y s ar e menu k e ys . T her e ar e 16 menus in all , w hic h pro vide many mo r e functi ons, or mo r e options f or mor e f unctions . HP 35s Menus Men u Name Men u Description Chapter Numeric F un[...]

Getting Star ted 1-7 T o use a menu function: 1. Pre ss a menu k e y to displa y a set of menu items. 2. Pr ess Õ Ö × Ø to mov e the under line to the item y ou w ant to select . 3. Press  while the item is under lined. With n umber ed menu items, y ou can either pr ess  while the ite m is underlined, or just enter the number of the item.[...]

1-8 Getting Star ted Some men us, lik e the CONS T and S UM S , hav e mor e than one page . Ente ring the se menus turns on the  or  annunc iator . In these menus , use the Õ and Ö c ursor k ey s to na v igate to an item on the c urr ent menu page; us e the Ø and × k e ys t o access the ne xt and pr ev ious pages in the menu . Ex ample: I[...]

Getting Star ted 1-9  Pr es sing  backs out of the 2–le v el CLEAR or MEM me nu , one le v el at a time . Re fe r to  in the table on page 1–5.  Pr es sing  or  cancels an y other menu .  Pr essing an other menu k e y r eplaces the old men u w ith the ne w one . RPN and AL G M odes The calc ulator can be set to perf orm ar [...]

1-10 Getting Star ted T o s elect ALG mode: Pre ss 9{  (  ) t o set the calc ulato r to AL G mode. When the calc ulator is in AL G mode, the AL G annunc iator is on . Ex ample: Suppose y ou w ant to calculate 1 + 2 = 3 . In RPN mode, y ou enter the first n umber , pre ss the  ke y , enter the second number , and finall y pr ess[...]

Getting Star ted 1-11 Undo ke y The Un do Ke y The operation of the Undo k e y depends on t he calculator context , but serves largel y to r ecov er from the deleti on of an e ntry rather than to undo an y arbitr ary operati on . See T he Last X Register in Chapt er 2 fo r details o n r ecalling the entry in line 2 o f the displa y after a numer ic[...]

1-12 Getting Star ted The Displa y and Annunciators The dis play com pr ises tw o lines and ann unc iato rs . Entr ies w ith more than 14 c har acter s w ill sc r oll to the left . Dur ing input , the entry is display ed in the f irst line in AL G mode and the second line in RPN mode. E v ery calculati on is display ed in up to 14 digits , includin[...]

Getting Star ted 1-13 HP 35s Annunciators Annunciator Meaning Chapter  The "  (Bus y)" annunci ator appears while an operati on , equation , or pr ogr am is execu t in g.   When in Fr action–display mode (press   ) , only one of t he "  " or "  " halv es of the "  "' ann u[...]

1-14 Getting Star ted HP 35s Annunciators (continu ed) Annunciator Meaning Chapter  ,  The re ar e more char act ers to the left or r ight in the display o f the entry in line 1 or line 2 . Both of th ese an nunciat ors may ap pe ar simultaneously , indic  ting that ther e ar e char acters to the le ft and ri ght in the disp lay o f an ent[...]

Getting Star ted 1-15 Keyi n g i n N u m b e r s The minimum and max imum v alues that the calc ulato r can handle are ± 9 . 99999999999 499 . If the result of a calc ulation is bey ond this r ange , the err or message “  ” appears momentarily along w ith the  annunc i ator . The o verflo w message is then r eplaced [...]

1-16 Getting Star ted Ke ying in P owers o f T en The  key i s us e d to e n t er p owe r s of t e n qu i ck ly. Fo r exa m p l e, i n s t e ad o f e nt e ri n g one million as 1000000 y ou can simply enter  . T he f ollo w ing e xam ple illustrates the process as w ell as how the calculator di splay s the result . Ex ample: Suppose y o[...]

Getting Star ted 1-17 Other Exponent Functions T o calculate an e xponent o f ten (the base 10 antilogar ithm) , use   . T o calculate the r esult of any n umber raised to a pow er (e xponentiation), use  (see chap ter 4) . Understanding Entry Cursor As yo u k ey in a number , the cur sor (_) appears and blinks in the display . The c urs o[...]

1-18 Getting Star ted P erforming Ar ithmetic Calculations The HP 3 5s c an operat e in either RPN mode or in Algebr aic mode (AL G). These modes affect ho w e xpres sions ar e enter ed.  The f ollo w i ng secti ons illus tr ate the entry differences for single ar gument (or unar y) an d two argument ( or binar y) operations. Single Argument or [...]

Getting Star ted 1-19 Example: Calculate 3.4 2 , fir st in RPN mode and then in AL G mode. In the ex ample, the sq uar e oper ator is sho wn on the ke y as  but display s as S Q() . Ther e are se v er al single ar gument operators that display differentl y in AL G mode than they a ppear on the ke y boar d (and differ ently than the y appear in R[...]

1-20 Getting Star ted Ex ample Calc ulate 2+3 and 6 C 4 , fir st in RPN mode and then in AL G mode. In AL G mode, the inf i x oper ator s ar e  ,  ,  ,  , and  . The other tw o argumen t oper ations us e func tion not ation o f the for m f(x ,y), where x and y ar e the fir st and second operands in or der . In RPN mode, the operands [...]

Getting Star ted 1-21 F or commutati ve operati ons such as  and  , the order of the operands does not affect the calculated result . If you mistak enly enter the operand fo r a noncommut ativ e tw o ar gument operati on in the w r ong or der in RPN mode , simply pr ess the  ke y to ex c hange the conte nts in the x - and y -r egisters . T[...]

1-2 2 Getting Star ted Scientific F ormat (  ) S CI for mat displa y s a number in sc ie ntifi c notati on (one digit be fo r e the "  " o r "  " ra dix mar k) w ith up to 11 dec imal places and up to thr ee di gits in the expo nent . Aft er th e prom pt,  _ , t ype in the number of dec imal places to be [...]

Getting Star ted 1-23 Example: This e x ample illu str ate s the behav ior of the Engineer ing f ormat us ing the number 12 .3 46E4. It als o sho w s the use o f the  @ and  2 functi ons. This e xample uses RPN mode . ALL Format (  ) The All f or mat is the defa ult for mat , display ing numbers w ith up to 12 di git pr ec ision . If[...]

1-24 Gett ing Started Ex ample Enter the n umber 12 , 3 4 5, 6 7 8.90 and c hange the dec imal po int to the co mma. Then c hoos e to hav e no thou sand separ ator . Finall y , r eturn t o the defa ult settings . This e x ample u ses RPN mode . Complex number displa y format (  ,  ,   ) Co mple x numb ers ca n be displa y ed[...]

Getting Star ted 1-25 Example Display the complex number 3+4i in each of the differ ent for mats. SHO W ing Full 12–Digit Pr ecision Changing the number of display ed dec imal places affects what y ou see , but it does not affect the inte rnal r epr esent ation o f numbers. A n y number stor ed inte rnall y alw a y s has 12 digits . F or e x ampl[...]

1-2 6 Getting Star ted Frac t i on s The HP 3 5 s allow s y ou to enter and operate on fr actions , display ing them as either dec imals or fr acti ons. T he HP 3 5s displ ay s fracti ons in the fo rm a b/c , wher e a is an integer and both b and c ar e counting n umbers. In additi on , b is such that 0 ≤ b<c and c is such that 1<c ≤ 409 [...]

Getting Star ted 1-2 7 Example Enter the mix ed numer al 12 3/8 and di spla y it in frac tion and decimal f orms . Then ente r ¾ and add it to 12 3/ 8. Th is ex ample uses RPN mod e . Re fer to c hapter 5, "Fr actions," for m o re in fo rma t io n a b o u t u s i n g fract ion s. Mes sa ge s The calc ulator r espo nds to err or conditi o[...]

1-28 Gett ing Started  An y other k e y also c lears the message , though the k e y func tion is not en ter ed If no message is dis play ed, but the  annunciator appears, then y ou hav e pr essed an inactiv e or in vali d ke y . F or ex ample , pres sing  will dis play  beca use the second dec imal point ha s no meaning in this co[...]

Getting Star ted 1-2 9 Clearing All of Memor y Clea ring a l l of me mory erase s all numbers , equations , and pr ograms you' ve stor ed . It does not aff ect mode and fo rmat settings. (T o clear set tings as well as data , see "Clear ing Memory" in appendi x B .) To c l e a r a ll o f m e m o r y : 1. Pre ss  (  [...]

1-30 Getting Star ted[...]

RPN: The Automatic Memory Stac k 2- 1 2 RPN: T he Automatic Me m o ry St ack This c hapter e xplains ho w calculati ons tak e place in the automatic memory stack in RPN mode. Y ou do not need to r ead and unders tand this mater ial to use the calculator , but understanding the mater ial w ill gr eatl y enhance yo ur use of the calculator , especi a[...]

2- 2 RPN: The Automatic Me mory Stack The mo st "r ecent" number is in the X–r egister : this is the numbe r y ou see in the second line of the displa y . Ev ery register is separated into three par ts:  A r eal number or a 1-D vector w ill oc c up y part 1; part 2 and part 3 will be null in this case   A comple x number or a 2[...]

RPN: The Automatic Memory Stac k 2- 3 The X and Y–Registers ar e in the Displa y The X and Y–Registers are what y ou see exc ep t when a menu , a message, an equation line ,or a pr ogr am line is being displa y ed. Y ou might hav e noticed that sev er al func tion names include an x or y . This is no coinc idence: these letters r efe r to the X[...]

2- 4 RPN: The Automatic Me mory Stack What w as in the X–r egiste r rotates into the T–regis ter , the contents of the T–r egist er r otate int o the Z–r egister , etc. Noti ce that onl y the contents of the r egister s ar e r olled — the r egister s themsel v es maintain the ir positi ons, and onl y the X– and Y–r egister's cont[...]

RPN: The Automatic Memory Stac k 2- 5 Arithmetic – Ho w the Stac k Does It The contents o f the stac k mov e up and do wn automati cally as ne w n umbers enter the X–r egister ( lifting the stac k) and as oper ators combine two numbers in the X – and Y–registers to produce one new number in the X–register ( dr opp ing the stac k ). Suppos[...]

2- 6 RPN: The Automatic Me mory Stack Ho w ENTER W orks Y ou kno w that  separ ate s two n umber s k ey ed in one after the other . In terms of the st ack , ho w doe s it do this ? Suppos e the s tac k is again f illed w ith 1, 2 , 3, and 4. Now en ter and add two ne w numbers: 1. Lifts the stack. 2. Lifts the stack and replicates the X–regist[...]

RPN: The Automatic Memory Stac k 2- 7 Filling the stack with a constant The r eplicating effec t of  together w ith the r eplicating e ffec t of stac k dr op (fr om T int o Z) allow s y ou to f ill the stac k w ith a numer ic cons tant f or calculati ons . Example: G i v en bacter ial c ultur e w i th a constant gr o wth rate of 5 0% per day , h[...]

2- 8 RPN: The Automatic Me mory Stack 1. Lifts the stack 2. Lifts the stack and replicates the X–register . 3. Overwr ites the X–register . 4. Cl ears x by ov erwr iting it w ith z er o . 5. Ov erwr ites x (r eplaces the z ero .) Th e L AST X Register The LAS T X register is a companion to the st ack: it ho lds the number that w as in the X–r[...]

RPN: The Automatic Memory Stac k 2- 9 Corr ecting Mistakes with LAS T X W rong Single Argument F unction If you e xec ute th e w r o n g single ar gument function , use  to r etr ie v e the number so y ou can ex ec ute the correct funct io n. ( P res s  firs t if you w ant to clear the incor r ect r esult fr om the stac k .) Since  a[...]

2- 1 0 RPN: The Automatic M emor y Stack Ex ample: Suppose y ou made a mistak e w hile calc ulating 16 × 19 = 304 The r e are thr ee kinds of mistak es y ou could ha ve m ad e : Reusing Numbers with LAST X Y ou can use  to r eus e a number (such a s a constant) in a calc ulati on. Remember to ent er the constant second, j ust bef or e ex ec [...]

RPN: The Automatic Memory Stac k 2- 1 1 Example: T w o clo se s tellar nei ghbor s of E a rth are R igel Cent auru s ( 4. 3 light–y ears aw a y) and Siriu s (8.7 ligh t–y ears a w ay). Use c , the sp eed of li ght (9 . 5 × 10 15 meter s per y ear) to conv ert th e distances from the E arth to these stars i nto meters: T o R igel Centau rus: 4.[...]

2- 1 2 RPN: The Automatic M emor y Stack Chain Calculations in RPN M ode In RPN mode, the a utomati c lifting and dropp ing of the stac k's conten ts let y ou re tain inter mediate r esults witho ut stor ing or r eentering them , and w ithout u sing par entheses . W ork from the P arentheses Out For exam pl e, ev al u at e (1 2 + 3 ) × 7. If [...]

RPN: The Automatic Memory Stac k 2- 1 3 Now study the f ollo wing e xam ples. R emember that y ou need to pr ess  only to separ ate sequentiall y-enter ed numbers , such a s at the beginning of an expr essi on. T he operations themsel ve s (  ,  , et c.) separ ate sub seque nt number s and sav e inte rmedi ate r esults . The las t r esult [...]

2- 1 4 RPN: The Automatic M emor y Stack Ex ercises Calculate: Solution:   Calculate: Solution:   Calculate: (10 – 5) ÷ [(17 – 12) × 4] = 0.2 500 Solution:    or ?[...]

RPN: The Automatic Memory Stac k 2- 1 5 4 ÷ [14 + (7 × 3) – 2 ] by s tarting w ith the inner mos t par enthe ses ( 7 × 3) and w orking o u t w ar d , j u s t as yo u wo uld w ith penc il and paper . The k e ys tr ok es w er e    . If y o u w o r k t h e p r ob l e m f r om left–to–ri ght , p r es s ?[...]

2- 1 6 RPN: The Automatic M emor y Stack Mor e E x erci ses Pr acti ce using RPN b y w orking thr ough the follo w ing pr oblems: Calculate: (14 + 12) × (18 – 12) ÷ (9 – 7) = 7 8.000 0 A Solution:   Calculate: 23 2 – (13 × 9) + 1/7 = 412 .14 29 A Solution: [...]

RPN: The Automatic Memory Stac k 2- 1 7 A Solution:      [...]

2- 1 8 RPN: The Automatic M emor y Stack[...]

Storing Data into V ariables 3-1 3 Storing Dat a in to V ar i a b le s The HP 3 5 s has 3 0 KB of memory , in whi ch y ou can stor e numbers , equations , and pr ogr ams. Numbers ar e st or ed in locations called var iables , each named w ith a letter fr om A thr ough Z . (Y ou can c hoose the letter to re mind you o f what is s tor ed ther e , suc[...]

3-2 Storing Data into V ariables In AL G mode, y ou can st or e an e xpr essi on into a v ar iable; in this case , the value of the expr ession is stor ed in the vari able rather than the expressi on itself . Ex ample: E ach p ink letter is assoc iat ed with a k ey and a unique v ar ia ble. (T he A. .Z annunc iator in the dis pla y confir ms this.)[...]

Storing Data into V ariables 3-3 T o recall the v alue st or ed in a v ari able , use the Recall command . T he displa y of this command differs sli ghtl y fr om RPN to AL G mode , as the follo wing e xam ple illustr ates . Example: In this e xam ple , w e r ecall the value o f 1.7 5 that we s tor ed in the v ar iable G in the last e x ample . This[...]

3-4 Storing Data into V ariables Vie w ing a V ariable The VIE W command (  ) displa y s the value of a v ar iable w ithout recalling that value t o the x -r egist er . T he displa y tak es the for m V aria ble=V alue. If the numbe r has too man y digits to f it into the displa y , use  Õ or  Ö to v ie w the missing digits. T o cancel[...]

Storing Data into V ariables 3-5 Example: In this ex ample , we stor e 3 in C, 4 in D , and 5 in E. T hen w e vi e w these v ar iables vi a the V AR Catalog and clear them as well . This e x ample uses RPN mode . Note the  and  annunc iator s indicating that the Ø and × ke y s ar e acti v e to help y ou scr oll through the catalog; ho w e v[...]

3-6 Storing Data into V ariables T o leave the V AR catalog at any time , press e ither  or  . An alternate me t ho d to cl e a ri ng a va ria bl e i s s i mp ly t o s t ore t he va l ue zero i n i t. Fin a ll y , yo u c a n clear all dir ect var iable s by pr essing   (  ). If all direct var ia bles ha ve the value z [...]

Storing Data into V ariables 3-7 Recall Arithmetic Recall ar ithmeti c uses  ,  ,  , or  to do arithmeti c in the X–regis ter using a r ecalled number and to leav e the r esult in the dis play . Only the X–r egiste r is affec ted . T he value in the v ar iable r emains the same and the resu lt r eplaces the value in the [...]

3-8 Storing Data into V ariables Ex ample: Suppose the variables D , E , and F contain the values 1, 2 , and 3 . Use stor age arithmeti c to add 1 to each of th ose v ar iables . Suppose the variables D , E , and F contain the values 2 , 3, and 4 from the las t ex ample . Div ide 3 by D , multipl y it by E , and add F to the r esult . Ex changing x[...]

Storing Data into V ariables 3-9 Example: The V a riables "I" and "J" Ther e ar e two v ar iables that y ou can acc ess dir ectl y: the var iables I and J. A lthough they stor e v alues as other var i ables do , I and J ar e spec ial in that the y can be us ed to r ef er to other v a r iable s, inc luding the st atistical r egis[...]

3-10 Storing Data into V ariables[...]

Rea l–Nu mb er Fu nc tio ns 4- 1 4 Real–Number F u nctions This c hapter co ver s most o f the calculat or's functi ons that perfo rm computati ons on real n umbers, inc luding some n umeri c functi ons used in pr ograms (such as AB S , the absolu te–value functi on). These f uncti ons ar e addr ess ed in gro ups , as f ollo ws :  Exp[...]

4- 2 Real–Number Functions Quotient and Remainder of Div ision Y ou can use  (   )and  (  ) to pr oduce the integer qu otient and int eger r emainder , r espec tiv ely , fr om the di v isio n of two integer s. 1. K e y in the f irst int eger . 2. Pres s  to separ ate the fir st number f r om the [...]

Rea l–Nu mb er Fu nc tio ns 4- 3 In RPN mode, to calc ulate a r oot x of a number y (the x th root of y ), k e y i n y  x , then pres s  . F or y < 0, x must be an i nteger . T rigonometry Entering π Pr es s   to place the fi rst 12 digits o f π into the X–r egister . (The number display ed depends on the display for mat .) [...]

4- 4 Real–Number Functions Setting th e Angular Mode The angular mode spec ifies w hic h unit of measur e to assume f or angles u sed in trigonometric functions. The mode does not convert numbers alread y present (see "Con v ersi on F uncti ons" later in this c hapter ). 3 60 degr ees = 2 π radians = 400 grads T o set an angular mode ,[...]

Rea l–Nu mb er Fu nc tio ns 4- 5 Example: Sho w that cosine (5/7) π r adians and cosine 1 2 8 . 5 7° a r e equal (to four significant digits). Progra mming Note: E quati ons using in verse tr igonometr ic f uncti ons to det ermine an angle θ , often look something lik e this: θ = arc tan ( y / x ). If x = 0, then y / x is undefined , r esulti[...]

4- 6 Real–Number Functions Hy perbolic Functions With x in the display : Pe r c e n t a g e F u n c t i o n s The pe r centage f uncti ons ar e speci al (compar ed w ith  and  ) because the y pres erve the value of the b ase number (in the Y– r egister) when the y r eturn the result of the per centage calculati on (in the X–r egiste r )[...]

Rea l–Nu mb er Fu nc tio ns 4- 7 Suppos e that the $15.7 6 item co st $16.12 last y ear . What is the percent age change fr om last year's pri ce to this year's ? Ke ys: Dis pla y: Description:  8  (  )  Rounds dis play to tw o decimal places .     Calculates 6% [...]

4- 8 Real–Number Functions Ph y sics Constants Ther e ar e 41 ph y sics const ants in the CONS T menu. Y ou can pre ss   to v ie w the follo w ing items . CONST Menu Items Description V alue  Speed of li ght in va c uum 29 979 24 58 m s –1  Standar d acceler ati on of gr av it y 9. 8 0 6 6 5 m s –2  Newtonian constant of gra[...]

Rea l–Nu mb er Fu nc tio ns 4- 9 T o insert a consta nt: 1. P osition y our cursor w her e y ou w ant the const ant inserted. 2. Pr ess   to displa y the ph ys ics cons tants menu . 3. Press ÕÖ×Ø (or , y ou can pre ss   to acces s the next page , one page at a time) to sc roll thr ough the men u until the const ant y ou want is[...]

4- 10 Real–Number Functions Conv ersion F unctions The HP 3 5s support s four types of conv ersions . Y ou can convert between:  r ectangular and polar for mats for comple x numbers  degr ees , r adia ns, and gr adients fo r angle measur es  dec imal and he x agesimal fo rmats f or time (and degree angle s)  v ariou s supported units [...]

Rea l–Nu mb er Fu nc tio ns 4- 1 1 T o conv ert between rectangular and polar coordinates: The fo rmat fo r repr esen ting complex number s is a mode setting. Y ou may ente r a complex number in an y for mat; upon entry , th e complex number is con verted to the for mat determined b y the mode setting . Here ar e the steps r equired to set a comp[...]

4- 12 Real–Number Functions Ex ample: Conv ersion w i th V e ctors. Engineer P .C. Bor d has det ermined that in the R C c irc uit sho w n , the tot al impedance is 77 .8 ohms and voltage lags curr ent b y 36 . 5º. What are the values of resistance R and capaciti v e r eactance X C in the c ir cuit ? Use a v ec tor diagr am as sho wn, w ith im p[...]

Rea l–Nu mb er Fu nc tio ns 4- 1 3 Time Con versions The HP 3 5s can con v ert between dec imal and hex a gesimal f ormats f or numbers . This is es peci all y use ful f or time and angles measur ed in degrees . F or e x ample , in deci mal for mat an angle measured in degr ees is e xpr ess ed as D .ddd…, while in hex agesimal the same angle is[...]

4- 14 Real–Number Functions T o c onv ert an angl e between degrees and radians: Ex ample In this ex ample, w e con vert an angle measur e of 30 ° to π /6 r adians . Unit Conv ersions The HP 3 5s has ten unit–conv er sion f uncti ons on the k e yboar d:  kg,  lb,  ºC ,  ºF ,  cm,  in ,  l,  gal,  MILE ,  KM K e[...]

Rea l–Nu mb er Fu nc tio ns 4- 1 5 Probability F unc tions Fac to ria l T o calculate the factorial of a displa ye d non-negativ e integer x (0 ≤ x ≤ 2 53), press  * (the ri ght–shifted  key ) . Gamma T o calculate the gamma f unction o f a noninteger x , Γ ( x ), k e y in ( x – 1) and press  * . The x ! fu nctio n calculat es ?[...]

4- 16 Real–Number Functions The RANDOM f uncti on uses a seed t o generat e a random n umber . E ach r andom number gener ated becomes the seed f or the ne xt r andom number . Theref or e , a sequence of r a ndom number s can be repeat ed by s tarting with the same seed . Y ou can stor e a new seed w ith the SEED functi on . If memory is clear ed[...]

Rea l–Nu mb er Fu nc tio ns 4- 1 7 Pa r t s o f N u m b e r s These f uncti ons ar e pr imaril y us ed in progr amming. Integer part T o remo v e the fr ac tional part of x and r eplace it with z er os , pres s  (  ) . (F or e x ample , the integer part of 14.2 300 is 14.0000.) Fr actional part T o remo v e the integer part of x[...]

4- 18 Real–Number Functions Greatest integer T o obtain the greatest int eger equal to or less than gi v en number , pr ess  (  ). Ex ample: This e x ample summar i z es many of the oper ations that e xtr act parts of numbers. The RND f uncti on (   ) r ounds x internall y to the n umber of digits spec ifi ed by the [...]

Frac ti ons 5-1 5 Frac ti on s In Ch apter 1, the section Fr actio ns intr oduced the basic s of enter i ng , display ing, and calculating w ith frac tions . T his cha pter giv es mor e info rmati on on these topi cs . Here is a sho rt re v ie w of ent eri ng and display ing frac tions:  T o enter a fr action , pres s  twice: once after the i[...]

5-2 Frac ti ons If y ou didn't get the same r esults as the ex ample , y ou may ha v e acc identall y change d ho w fr acti ons ar e displa y ed . (See "C hanging the F r acti on Displa y" late r in this chapter .) The ne xt topic inc ludes mor e ex amples of v alid and inv alid input fr actions . Frac t i on s i n t he D is pl ay In[...]

Frac ti ons 5-3 Accuracy Indicators The acc ur acy of a displa y ed fr ac tion is indi cated b y the  and  annunc iators at the ri ght of the dis play . The calcu lator compar es the value of the fr actional part of the intern al 12–digit n umber w ith the va lue of the displa y ed fr ac tion:  If no indicat or is lit , the fr acti onal [...]

5-4 Frac ti ons This is espec ially important if y ou c hange the r ules abo ut ho w f rac ti ons are display ed . (See "C hanging the F r actio n Display" later .) Fo r ex ample , if y ou f or ce all fr acti ons to ha v e 5 as the den ominator , then 2 / 3 is displa y ed as    becau se the ex act fr acti on is appro ximate[...]

Frac ti ons 5-5  T o set th e max imum denominator value, enter the value and then press  . F r actio n-display mode w ill be auto maticall y enabled . T he value y ou ent er canno t e x ceed 4 09 5 .  T o recall the /c v alue to the X– r egister , press  .  T o re stor e the default value t o 40 9 5, press  or en[...]

5-6 Frac ti ons 2 . In AL G mode, y ou can use the r esult of a calculati on as the ar gument f or the /c functi on . With the v alue in line 2 , simply pres s  . The v alue in line 2 is display ed in F r action f ormat and the integer part is used to determine the max imum denominator . 3 . Y ou may not us e either a co mple x number or a v [...]

Frac ti ons 5-7 Y ou can c hange flag s 8 and 9 to set the f r acti on fo rmat u sing the steps lis ted her e . (Because f lags ar e es pec iall y usef ul in pr ogr ams, the ir use is co v er ed in detail in chapter 14.) 1. Pre ss  to get the flag menu. 2. T o set a flag, pr ess  (  ) and type the flag number , such a s 8. T o cle[...]

5-8 Frac ti ons Ex amples of Fr action Display s The f ollo wing table sh o ws h o w the number 2 .7 7 is displa y ed in the thr ee fr acti on form at s f or t wo /c val u es. The fo llow ing table show s ho w differ ent numbers ar e display ed in the three fr action fo rmats f or a /c val ue of 16. R ounding Fr actions If F r acti on–display mod[...]

Frac ti ons 5-9 Example: Suppos e y ou ha ve a 5 6 3 / 4 –inch space that y ou w ant to di v ide in to si x equal sections. Ho w w ide is each section , assuming you can conv eniently measur e 1 / 16 – inch incr ements ? What's the cum ulati v e r oundo ff err or ? Fr actions in Equations Y ou can use a fr acti on in an equation . When an [...]

5-10 Frac ti ons Fr actions in Progr ams Y ou can u se a fr acti on in a pr ogr am ju st as yo u can in an equation; n umer ical values ar e show n in their en ter ed fo rm . When y ou'r e running a pr ogr am , display ed v alues ar e sho wn using F r actio n– display mode if it's acti v e . If yo u're pr ompted for v alues by INP [...]

Entering and E valuating Equations 6- 1 6 Entering and E valuating Equations How Y ou Can Use Equations Y ou can us e equati ons on the HP 3 5s in s ev eral wa y s:  F or s pecify ing an equation to e v aluate (this cha pter ).  F or spec if ying an equati on to sol v e fo r unkno w n values (c hapter 7).  F or spec if ying a f uncti on to[...]

6- 2 Entering and Ev aluating Equations By co mpar ing the chec ksum and length of y our equation w ith tho se in the e x ample , yo u can verify that you'v e entered the equation properl y . (See "V er ifying E quations" at the end of this chapter fo r mor e infor mation .) Ev aluate the equati on ( to calc ulate V ): K ey s: Displa[...]

Entering and E valuating Equations 6- 3 Summary of Equation Operations All equat ions y ou c r eate ar e sa v ed in the equati on list . This list is v isible whenev er y ou acti v ate E quatio n mode. Y ou use certain k e ys to perform operati ons in vol v ing equations . The y'r e desc ribed in more detail later . When display ing equations [...]

6- 4 Entering and Ev aluating Equations Entering Equations into the Equation List The equati on list is a collection of equations you enter . The list is sav ed in the calculat or's memory . E ach eq uatio n yo u ente r is automati call y sa ved in the eq uation list . T o enter an equation: Y o u ca n m ake a n eq u at i on a s l o n g a s yo[...]

Entering and E valuating Equations 6- 5 Numbers in Equations Y ou can enter an y v alid number in an eq uation , including bas e 2 , 8 and 16 , real , comple x, and f r actio nal numbers . Numbers ar e al w ay s sho w n using ALL displa y for mat , whi ch displa y s up to 12 c harac ters . T o enter a number in an equation , y ou can use the standa[...]

6- 6 Entering and Ev aluating Equations P arentheses in Equations Y ou can inc lude par enthese s in equations to contr ol the or der in whi ch oper ations are perf ormed . Pres s 4 to insert parenthe ses . (F or mor e info rmati on, s ee "Operator Pr eced ence" later in this chapter .) Ex ample: Entering an Equation. Enter the eq uation [...]

Entering and E valuating Equations 6- 7 T o displ ay equa tions: 1. Pre ss  . T his acti vates E quati on mode and tur ns on the EQN annunc iator . The dis pla y sho w s an entry fr om the eq uation list:     if the equation poin ter is at the top of the lis t .  The curr ent equation (the last equation yo u v[...]

6- 8 Entering and Ev aluating Equations Editing and Cl earing Equations Y ou can edit or c lear an equatio n that y ou're ty ping . Y ou can also edit or clear equations sa v ed in the equation lis t . Ho we ver , y ou cannot edit or c lear the two built- in equations 2*2 lin . so lv e and 3*3 lin . sol v e . If y ou attemp t to insert a equat[...]

Entering and E valuating Equations 6- 9 T o clear a saved equati on: Scr oll the equation list up or dow n until the desi r ed equation is in line 2 of the displa y , and then pr es s  . T o clear all saved equations: In EQN mode , press  . Select  (  ). T he     menu is displayed . Select Ö (Y)  [...]

6- 10 Entering and Ev aluating Equations  Expr essions. The equati on does not cont ain an "=". F or e xample , x 3 + 1 is an exp res si on. When you' re calcula tin g w ith an equati on, y ou might use an y type of eq uatio n — although the type can aff ect ho w it's evaluated . Whe n yo u'r e sol v ing a pr oblem fo [...]

Entering and E valuating Equations 6- 11 T o e valuate an equation: 1. Display the desired equation. (See "Displaying and Selecting Equations" above .) 2. Pr ess  or  . T he equati on pr ompts f or a value for eac h v ari able needed. (If the base of a number i n the equation is different fr om the cur r ent base , the calc ulator a[...]

6- 12 Entering and Ev aluating Equations  If the equati on is an as signment , onl y the ri ght–hand si de is ev aluate d. T he re sult is r etur ned to the X–reg ister and st or ed in the left–hand va ri able , then the var iable is v iew ed in the displa y . Essen tiall y ,  finds the v alue o f the left–hand var ia ble .  If the[...]

Entering and E valuating Equations 6- 13 Example: Ev aluating an Equation w ith XEQ. Use the r esults fro m the pr ev ious e xam ple to f ind out ho w mu ch the v olume o f the pipe changes if the diameter is c hanged to 3 5 . 5 millimeters. The v alue o f the eq uation is the old v olume (fr om V) minu s the new v olume (calc ulated using the ne w[...]

6- 14 Entering and Ev aluating Equations  T o c hange th e number , type the ne w number and pr es s  . This ne w number writes o v er the old value in the X–register . Y ou ca n enter a number as a fr acti on if y ou w ant . If y ou need to calc ulate a number , us e normal k ey boar d calc ulations , then pre ss  . F or e xam ple , y o[...]

Entering and E valuating Equations 6- 15 So , f or e x ample , all operat ions insi de par ent hese s ar e perf orme d bef ore oper ations outside the par entheses . Examples: Order Operation Ex ample 1 P arentheses  2F u n c t i o n s  3P o w e r (  )  4 Unary Minus (  )  5 Multipl y and [...]

6- 16 Entering and Ev aluating Equations Equation Functions The f ollo wing table lis ts the func tions that ar e v alid in eq uation s. Appe ndi x G , "Oper ation Inde x" also giv es this inf or mation . F or con v enience , pr ef i x–type f unctio ns, w hic h r equir e one o r two ar guments , displa y a left parenthe sis when y ou en[...]

Entering and E valuating Equations 6- 17       E ight o f the equati on func tions ha v e names that diff er fr om their equi vale nt operati ons: Example: P erimeter of a T r apez oid. The f ollo w ing equati on calc ulates the per imeter of a tr apez oid . T his is ho w the equa[...]

6- 18 Entering and Ev aluating Equations Th e ne xt equation als o obe y s the s ynt ax rules . T his equati on use s the inv er se functi on ,  , instead of the fractional fo rm ,    . Noti ce that the SIN f uncti on is "nested" insi de the INV functi on . (INV is typed b y  .) [...]

Entering and E valuating Equations 6- 19 Y ou can ent er the equatio n into the equati on list using the f ollo wing k ey strok es:   Õ  S y ntax Err ors The calculator doesn't c heck the s y ntax of an equation until you e v aluate the equation . If [...]

6- 20 Entering and Ev aluating Equations K ey s: Displa y: Desc ription:  ( ×  as required)  π  Displa ys the desir ed equation .   (hold)   Displa y equati on's chec ksum and length. (release)  π  Redis pla ys the e[...]

Solving Equations 7- 1 7 Solv ing Equations In chapt er 6 y ou sa w ho w y ou can us e  to f ind the value o f the left–hand variab le in a n assignment –type equati on . W ell, y ou can use S OL VE to find the v alue of any vari ab le in any type of equati on . For exa m p l e, c o n s id e r t h e e qu a t io n x 2 – 3 y = 10 If y ou kno[...]

7- 2 Sol ving Equations 2. Pres s  then pr ess the ke y fo r the unknow n var iable . F or e xample , press  X to sol v e f or x. The equatio n then pr ompts f or a v alue f or ev ery other v ar iable in the equati on . 3. F or each pr ompt, enter the desired v alue:  If the display ed v alue is the one y ou w ant , pr ess  .  [...]

Solving Equations 7- 3 g (accelerati on due to gr av ity) is included as a var i able so y ou can c hange it f or differ ent units (9 .8 m/s 2 o r 32. 2 f t / s 2 ). Calc ulate ho w man y meters an obj ect falls in 5 seconds , starting fr om r est . Since E quation mode is tur ned on and the desir ed equati on is alr eady in the displa y , y ou can[...]

7- 4 Sol ving Equations Ex ample: Sol ving the Ideal Gas L aw Equati on. The Ideal Gas L aw de sc ri bes the r elatio nship betwee n pr essur e, v olume , tempe ratu r e , and the amount (mole s) of an ide al gas: P × V = N × R × T whe re P is pr essur e (in atmospher es o r N/m 2 ), V is volume (in liters), N is the number of moles of gas , R i[...]

Solving Equations 7- 5 A 2–liter bottle contains 0.00 5 moles of car bon dio xide gas at 2 4°C. Assuming that the gas beha v es as an i deal gas, calc ulate its pres sur e . Since E quati on mode is turned on and the desir ed eq uation is alr e ady in t he d ispl ay , you ca n sta rt solving for P : A 5–liter fla sk contains nitr ogen gas. The[...]

7- 6 Sol ving Equations Solv ing built-in Equation The bu ilt-in equations ar e: “2*2 lin. sol v e ” ( Ax+B y=C, Dx+E y=F ) and “3*3 lin . Sol v e ”(Ax+B y+Cz=D , Ex+Fy+Gz=H , Ix+Jy+Kz=L). If you se lect one of the m, the  ,  and  ke y will hav e no e ffect . Pressing the  w ill re quest 6 var ia bles (A to F) f or the 2*2 ca[...]

Solving Equations 7- 7 Understanding and Contr olling SOL VE S OL VE f irst atte mpts to so lv e the eq uation dir ectly f or the unkno wn var iable. If the attempt f ails, S O L VE c hanges to an it er ati ve (r epetitiv e) pr ocedur e . Th e procedu r e starts b y ev aluating the eq uation using tw o initial gue sse s for the unkno w n var iable.[...]

7- 8 Sol ving Equations  T he Y–register (press  ) cont ains the pr ev ious estimat e for the r oot or equals to z er o . This nu mber should be the same as the value in the X–regist er . If it is not , then the r oot r etur ned wa s only an appro x imation , and the value s in the X– and Y–registers brac ket the r oot . These br ack [...]

Solving Equations 7- 9 These sour ces ar e used for guesses w hether you enter guesses or not . If y ou enter only one guess and st ore it in the v ar iable , the second guess w ill be the same value since the displa y also holds the number y ou just s tor ed in the vari able . (If suc h is the case, th e cal culator changes one g uess sl ightly so[...]

7- 1 0 Solving Equations Ex ample: Using Guesses to Find a Root . Using a r ectangular pi ece of sheet metal 40 cm b y 80 cm , f orm an open–top bo x hav ing a v olume o f 7 5 00 cm 3 . Y ou need to find the he ight of the bo x (that is, the amount to be f olded up along eac h of the f our sides) that gi ves the spec if ied vo lume . A taller bo [...]

Solving Equations 7- 1 1 It seems reasonable that either a ta ll , narro w b o x or a short, flat box could be for med hav ing the desired v olume . Becaus e the taller bo x is pr ef err ed , lar ger initial estimate s of the hei ght ar e r easonable . Ho w e ve r , hei ghts gr eater than 20 cm ar e not ph y sicall y pos sible becaus e the metal sh[...]

7- 1 2 Solving Equations The dimensi ons of the desir ed box ar e 5 0 × 10 × 15 cm . If yo u ignor ed the upper limit on the heigh t (20 cm) and used initial es timates of 30 and 4 0 cm, y ou would obta in a h eight of 4 2 .0 2 56 cm — a root th at is phy sical ly mean ing less. If you used small initial estimates suc h as 0 and 10 cm, y ou wou[...]

Integrating Equations 8-1 8 Integr ating Equations Many pr oblems in mathematic s, sc ience, and engineer ing r equir e calc ulating the def inite integr al of a f uncti on. If the f uncti on is denoted b y f(x) and the interval of integrati on is a to b , then the int egr al can be expr es sed mathematicall y as The q uantity I can be in terp r et[...]

8-2 Integrating Equations Integrating Equations ( ∫ FN) T o integrate an equation: 1. If the equation that de fines the integr and's func tion isn't st or ed in the equatio n list, k ey it in (see "Enter ing E quati ons into the E quati on L ist" in c hapter 6) and leav e E quation mode . The equati on usually contains j ust a[...]

Integrating Equations 8-3 Example: Bes sel Fu nction . The Bessel functi on of the first kind of order 0 can be expr essed as F ind the Bess el functi on fo r x– val ues o f 2 a nd 3 . Enter the e xpr ession that de fi nes the integ rand's f uncti on: cos ( x sin t ) No w integr ate this f unctio n w ith r espec t to t fr om zer o to π ; x [...]

8-4 Integrating Equations No w calc ulate J 0 (3) w ith the same limits o f integr ation. Y ou mus t r e -spec if y the limits of i nte gration (0 , π ) since they w ere pushed o ff the stac k b y the sub sequent di visio n by π . Ex ample: Sine Integral. Certain pr oblems in comm unications theory (f or ex ample , pulse transmis sion thr ough id[...]

Integrating Equations 8-5 Enter the e xpr ession that de fine s the integ rand's f uncti on: If the calculator attempted to ev aluate this func tion at x = 0, the lo w er limit o f integr atio n, an e rr or (    ) wo uld result . How ev er , the integrati on algor ithm normall y does no t ev aluate func tions at e it[...]

8-6 Integrating Equations Accuracy of Integr ation Since the calc ulator cannot com pute the v alue of an integ ral e xactly , it appro ximates it. T he acc ur acy of t his appr o x imation depends on the acc ur acy o f the integrand's f uncti on itself , as calc ulated b y y our equation . T his is affected b y r ound– off err or in the cal[...]

Integrating Equations 8-7 Example: Specifying Accuracy . With the displa y f ormat s et to S CI 2 , calculate the int egr al in the e xpre ssi on fo r Si(2) (f rom t he p revio us exa mp l e) . The integr al is 1.61±0.0161. Since the uncertainty wo uld not affec t the appro ximation until its thir d dec imal place , y ou can consider all the displ[...]

8-8 Integrating Equations This unce rtainty indicates that the r esult might be corr ec t to onl y thr ee dec imal places. In r ealit y , this r esult is acc ur ate to seven dec imal places when com par ed w ith the actual v alue of this integr al . Since the uncertaint y of a r esult is calc ulated conservati ve ly , the calculato r's appr o [...]

Operations with Complex Numbers 9-1 9 Operations w ith Comple x Numbers The HP 3 5s can use complex numbers in the form     It has oper ations f or comple x ar ithmetic (+, –, × , ÷ ), complex tr igonometry (sin, cos, tan), an d the mathematic s func tions – z , 1/ z , , ln z , and e z . (w her e z 1 and z 2 are comple[...]

9-2 Operat ions with Comple x Numbers Th e C o m p l ex St a c k A complex number occ upie s part 1 and part 2 of a stack lev el. In RPN mode , the complex number occ up y ing part 1 and part 2 of the X-register is displa yed in line 2 , wh ile the comple x number occup ying part 1 and part 2 of the Y - r egiste r is display ed in line 1. Complex O[...]

Operations with Complex Numbers 9-3 Functions for One Complex Number , z T o do an arithmetic operation w ith two complex numbers: 1. Enter the f irs t comple x number , z 1 as descr ibed befor e . 2. Enter the second comp lex number z 2 as descr ibed befor e. 3. Select the ar ithmetic oper atio n: Arithmetic With T wo Complex Numbers, z 1 and z 2 [...]

9-4 Operat ions with Comple x Numbers Ex amples: Her e are so me e xam ples of tr igono metry and arithmetic w ith comple x number s: Ev aluate sin (2i3) Evalu ate t he exp ression z 1 ÷ (z 2 + z 3 ), whe re z 1 = 2 3 i 13, z 2 = –2i1 z 3 = 4 i – 3 P erform the calc ulation as Eval ua te (4 i –2/5)  (3 i –2/3) . K ey s : Display: Des cr[...]

Operations with Complex Numbers 9-5 Evalu ate , wher e z = (1 i 1). Using Comple x Numbers in P olar Notation Many appli cations us e r eal numbers in polar for m or polar notation . T hese fo rms use pair s of number s, as do com plex number s, so y ou can do arithmetic w ith these numbers b y using the comple x operations. Example: V ec tor Addit[...]

9-6 Operat ions with Comple x Numbers Y ou can do a complex operation w ith numbers who se complex for ms are differ ent; ho w ev er , the result f orm is depe ndent on the se tting in 8 menu . K ey s : Display: Description: 9  (  ) Sets Degr ee s mode .  8  (   ) Sets com ple x mode  ?  ?[...]

Operations with Complex Numbers 9-7 Evalu ate 1 i1 +3 θ 10+5 θ 30 Comple x Numbers in Equations Y ou can type comple x number s in equations . When an eq uation is displa y ed , all numer i c for ms ar e sho wn as the y w er e ent er ed , lik e x iy , or r θ a When y ou e valuate an equation and ar e pr ompted for v ari able value s, y ou may en[...]

9-8 Operat ions with Comple x Numbers Complex Number in Pr ogr am In a progr a m, y ou c an type a complex number . F or e xample , 1i2+3 θ 10+5 θ 30 in pr ogram is: When y ou are r unning a progr am and ar e prompted f or values b y INPU T instru ctions , y ou can ente r comple x number s. T he value s and for mat of the r esult are contr olled [...]

V ector Arithmetic 10 -1 10 V ec tor Arithmetic F r om a mathematical po int of v ie w , a vector is an ar r ay of 2 or mor e elements arr anged into a r ow or a column . Ph ysi cal vec tors that ha v e two or thr ee compo nents and can be used to r epr esent ph ysi cal quantiti es such a s positi on , veloc it y , accelerati on , for ces, moments,[...]

10 -2 V ec tor Arithmetic Calc ulate [1. 5,- 2 .2]+[ -1. 5,2 .2] Calc ulate [-3 .4, 4 . 5]-[2 .3,1.4] Multiplication and div isions b y a scalar: 1. Enter a vector 2 . Enter a scalar 3. Pre s s  for m ultiplication o r  for divi sio n K ey s: Display: Desc ription: 9  (  ) S w itc hes to RPN mode(if necessary)  3 ?[...]

V ector Arithmetic 10 -3 Calc ulate [3, 4]x5 Calc ulate [- 2 ,4]÷2 Absolute va lue of the vector The abs olute v alue functi on “ ABS” , when applied to a v ector , produces the magnitude of the v ecto r . F or a v ector A=( A1, A2 , …An) , the magnitude is defined as = . 1. Press  2. E n t e r a v e c t o r 3. Pr es s  F or e x amp[...]

10 -4 V ec tor Arithmetic Dot pr oduct F uncti on DO T is used to calc ulate the dot pr oduc t of tw o vec tors w ith the same length . Attempting to calculat e the dot pr oduc t of tw o vec tor s of diff er ent length cause s an err or mess age “   ”. F or 2 -D vecto rs: [ A, B], [C, D], dot pr oduct is defined[...]

V ector Arithmetic 10 -5 Angle bet w een vectors The angle between two v ect ors, A and B , can be found as  θ  = ACOS(A  B/ ) F ind the angle between tw o v ector s: A=[1, 0],B=[0,1] F ind the angle between tw o v ector s: A=[3,4],B=[0,5]   Presses  for dot produc t ,and the dot pr oduc t of tw o vec to rs i[...]

10 -6 V ec tor Arithmetic V ec tors in Equations V ectors can be us ed in equati ons and in equation v a r iable s ex actly lik e r eal numbers . A vec tor can be enter ed w hen pr ompted f or a va ri able . E quations con taining v ector s can be sol ved , ho wev er the s olv er has limited ability if the unkno w n is a vec tor . E quati ons conta[...]

V ector Arithmetic 10 -7 V ectors in Progr ams V ectors can be used in pr ogr am in the same w ay as r eal and comple x n umbers F or e x ample , [5, 6] +2 x [7 , 8] x [9 , 10] in a progr a m is: A vec tor can be enter ed when pro mpted f or a va lue for a v a r iable . Progr ams that contain v ector s can be used f or solv ing and integr ating . P[...]

10 -8 V ec tor Arithmetic Creating V ec tors from V ariables or Registers It is possible to c r eate v ector s containing the con tents of memory v ari ables , stac k re gisters, o r values fr om the indirect r egisters , in run or pr ogr am modes. In AL G mo de , begin enter ing the vec tor b y pre ssing  3 . RPN mode w or ks similarly to AL G [...]

Base Conversions and Ar ithmetic and Logic 11-1 11 Base Conv ersions and Arithm etic and Log ic The B A SE menu (   ) allo ws y ou to ent er numbers and f or ce the dis play o f numbers in dec imal , binary , octal and hex adec imal base . The LOGIC menu (  > ) pro v ide s access to logi c func tions . BAS E M e n u Menu label D e s cr [...]

11-2 Base Conversions and Ar ithmetic and Logic Ex amples: Converting the Base of a Number . The f ollo w ing k e y str okes do v ar ious bas e con ve rsi ons. Conver t 1 25 .99 10 to he xa dec imal , octal , and binary numbers. Note: When no n dec imal bases ar e us e , only the integer part of numbers ar e us ed fo r displa y . T he fr actional p[...]

Base Conversions and Ar ithmetic and Logic 11-3 yo u c a n us e  menu to enter base-n sign b/o/d/h follo w ing the operand to repr esent 2/8/10/16 base number in any base mode. A number w ithout a base sign is a dec imal number Note: In AL G mode: 1. The r esult’s base mode is dete rmined by the c urr ent base mode setting. 2 . If there is no [...]

11-4 Base Conversions and Ar ithmetic and Logic LO G I C M e n u The “ AND” , “OR” , “X OR” , “NO T” , “NAND” , “NOR” can be used as logic functions . Fr action , complex , vector ar guments will be seen as an "   " in logic f uncti on . Arithmetic in Bases 2, 8, and 16 Y ou can per[...]

Base Conversions and Ar ithmetic and Logic 11-5  The r esult of an operation is al w ay s an inte ger (any f rac tional portio n is truncated). Wher eas co n ve rsio ns change o nly the dis play o f the number but not the ac tual number in the X–r egist er , arithmeti c does alter the n umber in the X–r egister . If the re sult of an oper at[...]

11-6 Base Conversions and Ar ithmetic and Logic The Repr esentation of Numbers Although the displa y of a number is conv erted when the base is changed, its stor ed fo rm is not modif ied , so decimal nu mbers ar e not truncated — until the y ar e used in arithmeti c calc ulations . When a num ber app ears in h exadecima l, oct al, or bina ry bas[...]

Base Conversions and Ar ithmetic and Logic 11-7 Range of Numbers The 3 6-bit binar y number si z e determines the r ange of numbers that can be repr esented in hex adec imal (9 digits) , octal (12 di gits), and binary bas es (3 6 digits), and the range of dec imal number s (11 digits) that can be con v erted to thes e other bases. Range of Numbers [...]

11-8 Base Conversions and Ar ithmetic and Logic In BIN/OCT/HEX, If a number ent er ed in decimal ba se is outside the r ange gi ve n abov e , then it produces the message   . A n y operati on using   cause s an o v erflo w conditio n, w hi ch su bstitu tes the lar ges t positi v e or negati ve number possible f o[...]

Statistical Operations 12-1 12 Statistical Operations The s tatisti cs men us in the HP 3 5s pro v ide f uncti ons to s tatisti call y analyz e a set of one– or two–v ar iable data (real n umbers):  Mean , sample and population standar d dev iati ons.  L inear r egr essio n and linear estimation ( and ).  W eighted mean ( x weig ht e d[...]

12 -2 Statistical Operations En teri ng On e– V ariab l e D ata 1. Pr ess  (  )to clear e x isting st atisti cal data. 2. Ke y i n e a ch x –value and pr ess  . 3. The display sho w s n , the number of st atistical data v alues no w accumulated . Pre ssing  actually enters two v ariables into the statistics register s because [...]

Statistical Operations 12-3 T o corr ect statistical data: 1. Reenter the incorr ect data, but instead of pr essing  , pres s   . This deletes the value(s) and dec r ements n . 2. Enter the cor r ect v alue(s) using  . If the incorr ect values w ere the ones j us t ent er ed, pr ess   to retr ieve them, then pre ss   to dele[...]

12 -4 Statistical Operations Statistical Calculations Once y ou hav e enter e d y our data , y ou can use the func tions in the statisti cs men us. Statistics M enus Mea n Mean is the arithmetic a ver age of a group of numbers .  Pr ess  ( ) for the mean of the x –valu es.  Pr ess  Õ ( ) fo r the mean of the y –v alues .  [...]

Statistical Operations 12-5 Example: Mean (One V ariable) . Pr oducti on supe rvis or Ma y K itt wants t o deter mine the a ve r age time that a certain pr oces s tak es . She ra ndomly p ic ks si x people , obse rves eac h one as he o r she carr ie s out the pr ocess , and r ecor ds the time r equir ed (in minut es): Calc ulate the me an of the ti[...]

12 -6 Statistical Operations Sample Standard De v iation Sample s tandar d dev i ation is a measur e of how dis persed the data v alues ar e about the mean sample s tandar d de vi ation a ssumes the data is a sampling of a larger , complete set of data , and is calc ulated using n – 1 as a di visor .  Pr ess  (  ) for the st andar [...]

Statistical Operations 12-7 P opulation Standar d Dev iation P opulation standard de vi ation is a measur e of ho w dispersed the data v alues are about the mean. P opulation st andard de v iation a ssumes the data constitutes the complete set of data, and is calc ulated using n as a div isor .  Pr es s   ÕÕ ( σ  ) for the population[...]

12 -8 Statistical Operations L.R. (Linear Regr ession) Menu  T o find an e stimated value f or x (or y ), ke y in a giv en h y potheti cal v alue fo r y (or x ), t hen pr ess  () ( o r  Õ () .  T o find the v alues that def ine the line that best f its y our data , pr ess   follo wed b y  ,  , or  . Ex ample: Cu[...]

Statistical Operations 12-9           Enters data; displ ay s n .     F iv e data pairs entered.   ÕÕ (  )     Display s li[...]

12 -10 Statistical Operations What if 7 0 kg of nitr ogen fertiliz er w er e applied to the r ice f ield ? Pr edict the gr ain y ield based on the a bov e s tatisti cs. Limitations on Pr ec ision of Data Since the calculat or uses f inite pr ecision , it f ollo w s that ther e ar e limitations to calc ulatio ns due to r ounding . Her e ar e tw o e [...]

Statistical Operations 12-11 Summation V alues and the Statistics Registers The statistics register s are si x unique loca tions in memor y that store the acc umulatio n of the si x summation v alues . Summation Statistics Pr essi ng   gi ve s y ou access to the conten ts of the st atisti cs r egist ers:  (  ) to r ecall the number o f [...]

12 -12 Statistical Operations Access to the Statistic s Registers The s tatistic s r egister a ssignme nts in the HP 3 5s are sho w n in the fo llow ing table. Summation r e gister s should be r ef err ed to by names and not b y numbers in expr essi on, equations and progr ams. Statistics Registers ×        V[...]

Statistical Operations 12-13 Y ou can load a statistics r egister w ith a summation b y sto ring the number (- 2 7 thr ough -3 2) of the r egister y ou want in I or J and then stor ing the summati on ( val ue  7 or A ). Similarly , you can pr ess   7 or A (or   7 or A ) to vi ew (or r ecall)a r egiste r value — the displa y is labe[...]

12 -14 Statistical Operations[...]

Pa r t 2 Pr ogr amming[...]

[...]

Simple Progr amming 13-1 13 Simple Progr amming P art 1 of this manual intr oduced you to func tions and oper atio ns that y ou can use manually , that i s, b y pr essing a k e y fo r each indiv i dual operation . And y ou sa w ho w y ou can us e equati ons to r epeat calc ulati ons w ithout do ing all o f the k ey strok es each time . In part 2 , [...]

13-2 Simple Programming This v ery si mple progr am assumes that the value for the radius is in the X– register (the display) w hen the pr ogr am starts to run . It comput es the ar ea and lea ves it in the X–reg ister . In RPN mode, t o enter this pr ogr am into pr ogr am memory , do the follo w ing: T r y running this pr ogram to f ind the ar[...]

Simple Progr amming 13-3 T r y running this pr ogr am to find the ar ea of a c ir c le w ith a radiu s of 5: W e will con tinue u sing the abo ve pr ogram fo r the ar ea of a c ir c le to illu str ate pr ogr amming concepts and methods. Designing a Progr am The f ollo w ing topi cs sho w what instruc tions y ou can put in a pr ogram. W hat y ou put[...]

13-4 Simple Programming Progr am Boundaries (LBL and R TN) If y ou wan t mor e than one progr am stored in pr ogr am memory , then a progr am needs a label to mark its beginning (suc h as    ) and a ret ur n to m ar k i ts end (such as   ). Notice that the line n umbers acquir e an  to match their lab[...]

Simple Progr amming 13-5  Using RPN oper ations ( w hic h w ork w ith the stack , as e xplained in c hapter 2).  Using AL G operati ons (as explained in appendi x C).  Using equati ons (as e xplained in chapter 6). The pr ev iou s ex ample used a ser ies of RPN oper atio ns to calculate the area of the c ir cle . Instead , y ou could ha ve[...]

13-6 Simple Programming F or outpu t , y ou can displa y a var ia ble w ith the VIEW instr ucti on, y ou can display a message der i v ed fr om an eq uation , y ou can displa y proces s in line 1, you can display the pr ogram r esult in line 2 , or you can lea v e unmark ed v alues on the stac k . The se ar e cov er ed later in this c hapt e r unde[...]

Simple Progr amming 13-7 5. End the progr am with a retu rn instructi on , w hic h sets the pr ogram point er bac k to   after the progr am runs . Pr ess  . 6. Pr ess  (or  ) to cancel progr a m entry . Numbers in progr am lines are stor ed pr ecisel y as you enter ed them, and they'r e displa y ed using ALL[...]

13-8 Simple Programming           No w , er ase line A00 2 , and line A004 changes to “ A003 G T O A002” Function Names in Progr ams The name o f a functi on that is used in a pr ogr am line is not nec es sar ily the same as the func tion's n[...]

Simple Progr amming 13-9 A different c hecksum means th e progr am was not enter ed ex actl y as given her e. Example: Enter ing a Progr am with an Equation . The f ollo w ing pr ogr am calc ulates the ar ea of a c ircle u sing an equation , r ather than using RPN operati ons lik e the pr ev i ous pr ogr am .  Cancels pr ogr am entry ( PRGM a[...]

13-10 Simpl e Programming Running a Pr ogr am To r u n o r execu te a progr am , pr ogr am entry cannot be acti ve (no pr ogr am–line numbers display ed; PRGM off). Pre ssing  w ill cancel Progr am–entry mode. Ex ecuting a Program (XEQ) Pre ss  label to ex ecute the pr ogram labeled w ith that let ter : T o ex ec ute a pr ogr am fr om it?[...]

Simple Progr amming 13-11 T esting a Program If you kno w there is an err or in a progr am, but are not sur e wher e the error is , then a good wa y to tes t the pr ogram is b y step w ise e x ec ution . It is also a good idea to test a lo ng or complicated pr ogram bef or e r el y ing on it . By s tepping thr ough its ex ecution , one line at a ti[...]

13-12 Simpl e Programming Entering and Displa y ing Data The c al cul a to r' s va ria bl es ar e used to s tor e data input , intermediat e r esults, and final r esults . (V ariables, as e xplained in chapter 3, ar e identif ied b y a letter fr om A thr ough Z , but the v ar iable names ha ve noth ing to do w ith pr ogr am labels .) In a pr o[...]

Simple Progr amming 13-13 Using INPUT f or Entering Data The INPUT instruction (   V ari able ) stops a running pr ogr am and displa ys a pr ompt for the gi v en va ri able . This dis pla y includes the e xisting v alue f or the var ia ble , suc h as   whe re "R" is the var iable's name, " ? " [...]

13-14 Simpl e Programming 2. In the beginning of the progr am , inse rt an INPUT ins tructi on f or eac h var iable whose v alue you w ill need. Later in the progr am, w hen you w r ite the par t of the calc ulation that needs a gi v en v alue , insert a  v ari able instr uc tio n to br ing that value bac k into the s tac k. Sin ce t he I NPUT i[...]

Simple Progr amming 13-15  T o cancel the INPUT prompt, pr ess  . T he curr ent value for the var iable remains in the X–register . I f y ou press  to r esume the pr ogr am , the canceled INPUT pr ompt is repeated . If y ou pr es s  during di git entry , it clear s the number to z ero . Pres s  again to cancel the INPUT pr om pt . [...]

13-16 Simpl e Programming Using Equations to Displa y Messag es E quations ar en't c heck ed for valid s yntax until the y'r e ev aluated . T his means yo u can enter almost any sequ en ce of ch ara cte rs in to a p rog ram as a n e qu at io n — you enter it just as you enter an y equation . On an y pr ogram line , pre ss  to start t[...]

Simple Progr amming 13-17 Keys : (In RPN mode) Display: Desc ription:     R    H   π  Calc ulates the v olume .     Chec ksum and length of equation .  V    Stor e the volume in V .    R  4 [...]

13-18 Simpl e Programming No w find the volume and surf ace ar ea–o f a cy linder w ith a r adius o f 2 1 / 2 cm and a height o f 8 cm. Display ing Inf ormation w ithout Stopp ing Normally , a program stop s when it displa y s a var iable w ith VIEW or display s an equation mes sage . Y ou nor mally ha v e to pr ess  to r esume e xec ution . I[...]

Simple Progr amming 13-19 Stopping or Inter rupting a Pr ogr am Progr amming a St op or P ause (ST OP , PSE)  Pr es sing  ( ru n / stop ) during pr ogram entry ins erts a S TO P inst ruc ti on . T his w ill display the con tents o f the X-r egister and halt a r unning pr ogr am until y ou r esume it b y pr es sing  fr om the k eyboar d. Y [...]

13-20 Simpl e Programming Editing a Progr am Y ou can modify a pr ogr am in pr ogram memo ry by inserting, deleting , and editing progr am lines. If a pr ogr am line contains an equation , y ou can edit the equati on . T o d elete a progr am line: 1. Select the r elevan t pr ogr am or r outine and pr ess Ø or × to locate the pr ogr am line that m[...]

Simple Progr amming 13-21 3. Mov ing the c ursor ”_” and pr es s  repeatedl y to delete the unw anted number or func tion , then r etype the r est of the pr ogr am line . (A fter pr essing  , Undo functi on is acti v e)  Notice: 1. When the c urso r is acti ve in the pr ogr am line , Ø or × ke y w ill be disabled. 2. When y ou are ed[...]

13-2 2 Simpl e Programming  Pr ess   to mo v e the pr ogra m pointe r to   .  Pr ess   label nnn to mov e to a spec i f ic line . If Progr am–entr y mode is not acti v e (if no pr ogr am lines ar e display ed), you can also mov e the pr ogr am pointer b y pressing  label line n umber . Canceling Pr ogr[...]

Simple Progr amming 13-23    wher e 6 7 is the number of by tes us ed b y the pr ogr am. C le arin g O n e or M ore P rogra ms T o clear a specific program fr om memory 1. Pre ss   (2  )  and displa y (using Ø and × ) the label o f the pr ogram . 2. Pr ess  . 3. Press  to cancel the catalog or[...]

13-2 4 Simpl e Programming F or e x ample , to see the c hecksum f or the c urr ent pr ogram (the "cylinder" pr o gr am): If y our ch ecks um does not matc h this number , then y ou hav e not entered this progr am correc tly . Y ou w i ll see that all of the a pplicati on pr ograms pro vided in c hapter s 16 and 17 include c hec ksum va l[...]

Simple Progr amming 13-25 This allo w s y ou to wr ite pr ograms that accept numbers in an y of the f our bases , do arithmetic in an y base , and display r esults in an y base . When w riting pr ograms that use n umbers in a base other than 10, set the base mode both as the c urr en t setting for the calc ulator and in the progr am (as an instruct[...]

13-2 6 Simpl e Programming P ol ynomial Expr essions and Horner's M ethod Some e xpr e ssions , suc h as pol yno mials , use the same var i able se v er al times f or their soluti on. F or ex ample , the expre ssion Ax 4 + Bx 3 + Cx 2 + Dx + E use s the var ia ble x fo ur differ ent times . A pr ogr am to calc ulate such an e xpr essi on using[...]

Simple Progr amming 13-2 7 No w ev aluate this po ly nomi al for x = 7 . Keys : (In RPN mode) Display: Description:         A      X       5  X           x 4  ?[...]

13-28 Simpl e Programming A more gener al form of this pr ogr am fo r any equati on Ax 4 + Bx 3 + Cx 2 + Dx + E wou l d be :                     ?[...]

Progr amming T ec hniques 14 -1 14 Pr ogr amming T ec hniques Chapter 13 co v er ed the basic s of pr ogr amming. T his cha pter e xplor es mor e soph istic ated but u seful te chniqu es:  Using subr outines t o simplify pr ogr ams by separ ating and labeling portions of the pr ogr am that ar e dedi cated to partic ular tasks. T he use o f subr [...]

14 -2 Progr amming T ec hniques  If y ou plan to ha v e only o ne pr ogr am in the calculato r memory , you can separate the r outine in vari ous labels . If y ou plan to ha v e mor e than one pr ogram in the calc ulator memory , it is better to hav e r outines part of the main pr ogram label , st arting at a specif ic line number .  A subr o[...]

Progr amming T ec hniques 14 -3 MAIN progr am (T op leve l) End of pr ogr am Attempting to ex ec ute a su br outine ne sted mor e than 20 le v els deep cau ses an   error . Example: A Nested Subroutine . The f ollo w ing subr outine , labeled S, calc ulates the v alue of the ex pre ssi on as part of a larger calc ul[...]

14 -4 Progr amming T ec hniques In RPN mode, Branching (G T O) As we hav e seen w ith subroutines, it is often desirable to transfer e x ecuti on to a par t of the pr ogram other than the ne xt li ne . This is called br anching . Unconditi onal br anching u ses the G T O ( go to ) instr ucti on to br anch t o a spec if ic progr am line (label and l[...]

Progr amming T ec hniques 14 -5 A Progr ammed G T O Instruction The GT O label  instruction (pr ess  label line n umber ) transfer s the exec ution of a running pr ogr am to the spec i f ied pr ogr am line . The pr ogram continues r unning fr om the ne w locati on , and nev er automatically retur ns to its point of origination, so G T O is no[...]

14 -6 Progr amming T ec hniques  To   :   .  T o a specif ic line nu mber:  label line number ( line n umber < 1000) . F or ex ample ,  A  . F or exa mple , pr es s  A   . The dis play w ill show ”   ” .  If y ou w ant to go to the fir st line of a l[...]

Progr amming T ec hniques 14 -7  Compar ison tests. T hese compare the X–and Y– r egisters, or the X–register and z er o .  F lag tes ts. T hese c hec k the statu s of flag s, w hic h can be either set or c lear .  L oop counters . T hese ar e usuall y used t o loop a spec if ied n umber of times. T ests of Comparison (x ? y, x ? 0) [...]

14 -8 Progr amming T ec hniques Ex ample: The "N ormal and Inv erse–Normal Distr ibuti ons" pr ogr am in chapt er 16 uses the x < y ? conditio nal in r outine T : Line T00 9 calculates the correcti on for X gues s . Line T013 comp are s the abs olute value of the calc ulated cor rec tion w ith 0 . 0001. If the value is les s than 0.0[...]

Progr amming T ec hniques 14 -9 Flags A flag is an indicator of status . It is either set ( tru e ) or clear ( false ). T estin g a fl ag is another conditional te st that f ollo ws the "Do if true" r ule: pr ogr am ex ec ution pr oceeds direc tly if the test ed flag is set , an d skips one line if the flag is clear . Mea ni n gs of F la [...]

14-10 Programming T echniques Fla g Stat us Fr action–Contr ol Fl ags 789 Clear (Defa ult) Fra c t io n d i s p l a y off ; di spl ay rea l number s in the cur r ent display form at. F r actio n denominator s not greater than t he /c val u e. Reduce fr ac tions to sma ll est form. Set Fra c t io n d i s p l a y on; display r eal numb ers as fract[...]

Progr amming T ec hniques 14-11  F lag 1 0 contr ols pr ogram ex ec uti on of equati ons: When flag 10 is c lear (the defa ult state), equations in running pr ogr ams ar e ev aluated and the result put on the stac k. When flag 10 is s et , equatio ns in running pr ogr ams ar e displa ye d as messages, cau sing them to behave lik e a VIEW stateme[...]

14-12 Programming T echniques Annunciators for Set F lags F lags 0, 1, 2 , 3 and 4 have annunc iators in the display that turn on w hen the corr esponding flag is set . The pr esence or absence of 0 , 1 , 2 , 3 or 4 lets you kn o w at an y time whether an y of these fi v e flags is s et or not . Ho w e ver , there is no suc h indicati on fo r the s[...]

Progr amming T ec hniques 14-13 It is good pr ac tice in a pr ogr am to mak e sure that any conditi ons y ou w ill be t esting start out in a know n stat e . Cur r ent flag settings depend on ho w the y hav e been left by ear lier pr o gr ams that ha ve been r un. Y ou should not assume that an y gi ven f lag is clear , fo r instance , and that it [...]

14 -14 Programming T echniques If y ou r eplace lines S00 2 and S003 b y SF0 and SF1, then f lags 0 and 1 ar e set so lines S006 and S010 tak e the natur al logar ithms of the X- and Y -inputs . Use abo ve progr am to see ho w to use flags Y ou can try other three case s. R emember to pr ess   (  )  and   (  )[...]

Progr amming T ec hniques 14 -15 Progr am Lines: (In RPN mode) Description:    Begins the fr acti on pr ogram .    Clear s thr ee fr acti on f lags.          Displays messages .   Selects dec imal base .  ?[...]

14-16 Programming T echniques Use the a bov e program t o see the diff er ent f orms o f fr acti on display : Loops Branc hing back war ds — that is , to a label in a pr ev ious line — makes it pos sible to ex ec ute part of a pr ogr am mor e than once . This is called looping .       [...]

Progr amming T ec hniques 14-17 This r outine is an e x ample of an inf inite loop . It can be used t o collect the initial data. After entering the three v alues, it is up to you to manually interr upt this loop b y pr essing  label line number to ex ec ute other r outines . Conditional Loops (G T O) When y ou w ant to perfor m an oper ation un[...]

14-18 Programming T echniques Loops w ith Counters (D SE, IS G) When y ou want to ex ec ute a loop a spec if ic number of times , use the   ( incr ement ; skip if gr eater than ) or   ( decrement ; skip if le ss than or equal to ) conditional f uncti on k ey s. Eac h time a loop functi on is e x ecut ed in a progr am , it automatical ly[...]

Progr amming T ec hniques 14-19  ii is the interval f or inc r emen ting and decr ementing (must be tw o digits o r unspecif ied). This value does not change. An unspec ified v alue for ii is assumed to be 01 (incr ement/dec re ment by 1). Gi v en the loop–contr ol nu mber ccccccc . fff ii, DSE dec rements ccccccc to ccccccc — ii , compar es[...]

14-20 Programming T echniques                 Pre ss  L  , then press   Z to see that the loop–contr ol number is no w 11. 0100. Indirectly Addr essing V ariables and Labels Indirect [...]

Progr amming T ec hniques 14-21 The Indir ect Address, (I) and (J) Many func tions that use A thr ough Z (as var ia bles or labels) can u se (I) or (J) to r ef er to A through Z (var iables or labels) or statistics re gisters indir ec tl y . The functi on (I) or (J) uses the v alue in va ri able I to J to determine w hic h var iable , label, or reg[...]

14 -2 2 Programming T echniques The INP U T ( I ) ,INP UT (J) and VIEW ( I ) ,VIEW (J) o perations label the display with the name of the indir ectl y–addre ssed v ar iable or r egister . The S UMS menu ena bles y ou to r ecall v alues f r om the statis tic s regis ter s. Ho w e v er , y ou must u se indir ect addr essing to do other operati ons,[...]

Progr amming T ec hniques 14 -23 Y ou can not sol v e or integr ate f or unnamed var iables or statisti c r egister s. Progr am Contr ol with (I)/(J) Since the conten ts of I can c hange each time a pr ogram runs — or e v en in differ ent parts of the same progr am — a pr ogr am instr uctio n such as S T O (I) or (J) can stor e value to a diffe[...]

14 -2 4 Programming T echniques Note: 1. If y ou want to r ecall the value f r om an undefined s tor age addres s, the err or message “   ”w ill be sho w n ” . (See A014 ) 2 . The calc ulator allocates memory for var i able 0 to the last non- z ero v ar iable . It is important to stor e 0 in v ari ables after usi[...]

Solv ing and Integrating Pr ograms 15-1 15 Solv ing and Integrating Pr ograms Solv ing a Pr ogr am In chapter 7 yo u saw ho w y ou can enter an eq uation — it's added to the eq uation list — and then solve it for an y var iable . Y ou can also enter a pr ogram that calculates a f uncti on, and then sol ve it for an y variable . This is esp[...]

15-2 Solving and Integr ating Progr ams 1. Begin the pr ogram w ith a label . T his label i dentif ie s the func tion that y ou want SOL VE to ev aluate (  label ). 2. Include an INPUT instru cti on for eac h var iable, inc luding the unkno w n . INPUT instruc tions ena ble y ou to sol v e fo r an y var iable in a m ulti–var i able funct[...]

Solv ing and Integrating Pr ograms 15-3 T o begin, put the calculato r in Progr am mode; if necessary , positio n the pr ogram pointe r to the top of pr o gr am memory . T ype in the pr ogr am: Pr es s  to cancel Progr am–entry mode . Use pr ogra m "G" to solv e fo r the pre ssur e of 0. 00 5 moles of car bon dio x ide in a 2–liter[...]

15-4 Solving and Integr ating Progr ams Ex ample: Program Using Equation . W rite a pr ogram that us es an equation to so lv e the "Ideal Gas Law ." No w calculate the change in pre ssure of the carbon dio x ide if its temp er ature dr ops by 10 °C fr om the prev ious ex ample .   val ue Sto res .0 05 i n N ; prompts[...]

Solv ing and Integrating Pr ograms 15-5 Keys : (In RPN mode) Display: Description:  L  Stores previous press ure.   H  Selects progr am “H. ”  P   Selects variable P ; prompts f or V .    Ret ai ns 2 i n V ; pr ompts f or N .   ?[...]

15-6 Solving and Integr ating Progr ams Using SOL VE in a Progr am Y ou can use the S OL VE oper ation as part of a progr a m . If appr opr iate , include or pr ompt for initial gue sse s (into the unkn o wn v a r iab le and into the X–register) bef or e e xec uting the SOL VE var iable instr ucti on. T he tw o instruc tions f or sol ving an eq u[...]

Solv ing and Integrating Pr ograms 15-7 Integrating a Pr ogram In chapter 8 you sa w how y ou can enter an equation (or expr ession) — it's added to the list of equ ations — and then integr ate it with r espect to an y var iable . Y ou can also en ter a pr ogram that calc ulates a f uncti on , and then int egr ate it w ith r esp ect to an [...]

15-8 Solving and Integr ating Progr ams 2. Select the pr ogr am that define s the func tion t o integr ate: pr ess   label . (Y ou can skip this step if yo u'r e re integr ating the same progr am.) 3. Enter the limits of in tegr ation: k ey in the lo w er limit and pr es s  , then k e y in the up per l imi t . 4. Select the var i able[...]

Solv ing and Integrating Pr ograms 15-9  A function pr ogrammed as an equation is u sually inc luded as an expr ession spec ifying the int egrand — though it can be an y type of equation . If you w ant the eq uation t o pr ompt f or v ar iable v alues ins tead of including INP UT instruc tions , make sur e flag 11 is set. 4. End the progr am w[...]

15-10 Solving and Integrating Pr ogr ams Using Integration in a Pr ogr am Integr ation can be e x ec uted fr om a progr am. R emember to inc lude or pr ompt f or the limits of integr ati on bef or e e x ec uting the integr atio n, and r emember that accurac y and ex ecution time ar e contro lled by the displa y f or mat at the time the pr ogr am ru[...]

Solv ing and Integrating Pr ograms 15-11 Restr ictions on Solving and Integr ating The SOL VE vari able and ∫ FN d va riab le instructi ons cannot call a r outine that contains another S OL VE or ∫ FN instructi on. T hat is , neither of these ins tructi ons can be used r e c ursi v el y . F or e x ample , attempting to calc ulate a multiple int[...]

15-12 Solving and Integrating Pr ogr ams[...]

Statistics Progr ams 16 -1 16 Statistic s Progr ams Cur ve F it ting This program can be used to fit one of four models of equations to y our data. These models are the s tr aight line , the logarithmic c urve , the e xponential c ur ve and the po wer c ur ve . T he pr ogram accepts tw o or more ( x , y ) data pairs and then calculates the corr ela[...]

16 -2 Statistics Programs T o fit logarithmi c c urves, v a lues of x mu st be positi ve. T o fit e xponential cu rves , val u es of y must be po siti ve . T o fit po w er c urves, bo th x and y must be positi ve . A  err or w ill occur if a negati ve n umber is enter ed for thes e cases . Data value s of lar ge magnitude bu[...]

Statistics Progr ams 16 -3 Progra m Listing: Progr am Lines: (In RPN mode) Description    T his r outine sets , the statu s for the s tr aight–line model .    Clear s flag 0, the indi cator f or ln X .    Clear s flag 1, the indi cator f or In Y .   ?[...]

16 -4 Statistics Programs    If flag 0 is set . . .   . . . tak es the natur al log of the X–inpu t.    Sto r es that v alue f or the corr ection r outine .    Prompts f or and st or es Y .    If flag 1 is set . . . [...]

Statistics Progr ams 16 -5    Display s, pr omp ts for , and, if changed , stor es x –v alue in X .   If flag 0 is se t . . .    Br anches to K001    Br anches to M001    Stores –va lu e i n Y . ?[...]

16 -6 Statistics Programs Chec ksum and length: 88 9C 18    This su br outine calc ulate s fo r the logarithmi c model.              Calcula tes = e ( Y – B ) ÷ M   Re turns to the calling r outine. Chec ks[...]

Statistics Progr ams 16 -7                Calculates = ( Y / B ) 1/M   Goes to O 005 Checksum and length: 8 5 2 4 21    Determines if D001 or B001 should be run  ?[...]

16 -8 Statistics Programs Flags Used: F lag 0 is set if a natur al log is r equired of the X inp u t. Fla g 1 is s et i f a n a t ura l l og i s req u ire d of th e Y input . If flag 1 is set in r outine N, then I001 is exec uted. If flag 1 is c lear , G001 is execu te d. Progr am instructions: 1. K e y in the pr ogr am r outines; pres s  when d[...]

Statistics Progr ams 16 -9 13 . F or a ne w case , go to step 2 . V ari ables Used: Example 1: F it a str aigh t line to the data belo w . Make an inten tional er r or w hen k e y ing in the third data pair and corr ect it w ith the undo r outine . Also , es timate y for a n x va l ue of 3 7 . E stimate x for a y value of 101. B Regr ession coeff i[...]

16-10 Statistics Pr ograms No w intenti onall y enter 3 7 9 instead of 3 7 .9 so that you can s ee ho w to cor r ect incorr ect entries .     Enter s y –valu e of data pair .    Enter s x –valu e of data pair .    Enter s y[...]

Statistics Progr ams 16 -11 Example 2: Repeat e x ample 1 (using the same data ) for logar ithmic , exponential , and po w er c urve f its. T h e table be lo w gi v es y ou the starting e x ec ution label and t he r esults (the corr elation and r egre ssion coeff ic i ents and the x – and y – estimates) f or eac h type of curve . Y ou w ill nee[...]

16-12 Statistics Pr ograms This progr am uses the bui lt–in integ r ation feature of the HP 3 5s to integrate the equation o f the normal fr equency curv e . The in v ers e is obtained using Ne wton's method to ite r ati ve ly s ear ch f or a v alue of x w hic h y i elds the gi ven pr obability Q(x) . x y "Upper tai l" a r e a x Q [...]

Statistics Progr ams 16 -13 Progra m Listing: Progr am Lines: (In RPN mode) Description    This r outine initiali ze s the normal distr ibuti on pr ogr am.   Stores defau lt val ue for m ean.       Pr ompts for and st ore s mean, M .   Stores[...]

16-14 Statistics Pr ograms    Adds the cor r ectio n to y ield a ne w X guess .       T ests to se e if the corr ecti on is si gnifi cant .    Goes bac k to start of loop if corr ecti on is sig nificant . Co ntin ue[...]

Statistics Progr ams 16 -15 Flags Used: None . Remark s: The acc ur acy of this pr ogr am is dependent on the dis play s etting. F or inputs in the ar ea between ±3 standar d de v iatio ns, a displa y of f our or mor e signif icant f igur es is adequate for mos t applications . At full pr ec ision , the input limit becomes ±5 st andard de vi atio[...]

16-16 Statistics Pr ograms 4. Af ter t he prompt for S , k ey in the populati on standar d dev iati on and pr ess  . (If the standar d dev iati on is 1, ju st pr ess  .) 5. To c a l c u l a t e X giv en Q ( X ), skip to step 9 of these instructions . 6. To c a l c u l a t e Q ( X ) giv en X ,  D  . 7. After the pr ompt , ke y in the val[...]

Statistics Progr ams 16 -17 Since your f r iend has been kno wn to ex agger ate f ro m time to time , yo u dec ide to se e how ra re a " 2 σ " date might be . Note that the pr ogr am may be r erun simply by pr essing  . Example 2: The mean of a set of test scores is 5 5 . The standar d dev iation is 15 . 3 . Assuming that the standar [...]

16-18 Statistics Pr ograms Th us , w e wo uld e xpect that o nly a bout 1 per cen t of the stude nts w ould do better than scor e 90. Grouped Standar d Deviation The s tandar d de v iati on of gr ouped data , S xy , is the standar d de v iati on of data points x 1 , x 2 , ... , x n , occur r ing at positi v e integer fr equenci es f 1 , f 2 , ... ,[...]

Statistics Progr ams 16 -19 This pr ogr am allo ws y ou to input data , co rr ect entries, and calc ulate the standar d dev iati on and we ighted mean of the grouped data . Progra m Listing: Progr am Lines: (In AL G mode) Description    Start grouped standar d dev i ation pr ogram .   Clears s tatisti cs[...]

16-20 Statistics Pr ograms   Updates in r egister -30.       Increments (or decr ement s) N .               Display s cur r ent number of data pai[...]

Statistics Progr ams 16 -21 Flags Used: None . Progra m Instructions: 1. K ey in the progr am r outines; pr ess  when done . 2. Pr ess  S  to start enter ing ne w data. 3. Ke y i n x i –value (dat a poin t) and pr es s  . 4. Ke y i n f i –value (fr equency) and press  . 5. Press  after VIEWing the n umber of po ints en ter ed [...]

16 -2 2 Statistics Pr ograms Y ou err ed by ente ring 14 instead of 13 for x 3 . Undo your e rror by ex ec uting r outine U: G r o u p 123456 x i 581 3 1 5 2 2 3 7 f i 1 7 26 37 4 3 73 1 1 5 Keys : (In AL G mode) Display: Desc ription:  S   val u e Pr ompts fo r the f irs t x i .   val u e Stores 5 in X ; p romp ts for fir s[...]

Statistics Progr ams 16-23    Displa ys the counter .    Pr ompts f or the f ifth x i .    Pr ompts f or the f ifth f i .    Displa ys the counter .    Pr ompts fo r the si xth x i . ?[...]

16 -2 4 Statistics Pr ograms[...]

Miscellaneous Programs and Equations 17 -1 17 Miscellan eous Pr ogr ams and Equations Tim e V a lu e of M o n ey Gi v en an y four o f the fi v e v alues in the "T ime–V alue–of–Mone y equatio n" (TVM) , y ou can sol v e for the f ifth v alue . T his equati on is use ful in a w i de var i ety of financ ial applications such as consu[...]

17 -2 Miscellaneou s Progr ams and Equations Equation Entry: K ey in this equation:        Remark s: The TVM equatio n r equir es that I mu st b e n o n –ze ro t o avo id a     error . If y ou'[...]

Miscellaneous Programs and Equations 17 -3 The or der in w hic h yo u'r e pr ompted f or value s depends upon the var iable y ou're solv ing for . SOL VE instructions: 1. If y our fir st T VM calculati on is to sol ve f or inte r est r ate , I, pr es s   I . 2. Pr ess  . If neces sary , press × or Ø to scr oll throu gh the e[...]

17 -4 Miscellaneou s Progr ams and Equations V ariables Used: Ex ample: Pa r t 1. Y ou ar e f inancing the pur cha se of a car w i th a 3–y ear (3 6–month) loan at 10.5% ann ual inter est compounded mon thly . The purcha se pri ce of the car is $7 ,25 0. Y our do wn pa ymen t is $1,500. N The number of com pounding periods . I The periodic inte[...]

Miscellaneous Programs and Equations 17 -5 The ans w er is negativ e since the loan has been v ie w ed fr om the borro wer's perspec tiv e. Mone y r ecei v ed by the bor r o w er (the beginning balance) is positi v e , while mo ney pai d out is negati v e .   val ue Sto res 0 i n F ; pr o mpts f or B .  ?[...]

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Miscellaneous Programs and Equations 17 -7 Prime Number Gene r ator This pr ogr am accepts an y positi v e integer gr eater than 3 . If the number is a prime number (not e venl y di v isible by integer s other than itself and 1), then the progr am r eturns the inpu t value . If the inpu t is not a pr ime number , then the progr am r etur ns the fir[...]

17 -8 Miscellaneou s Progr ams and Equations LBL Y VIEW Pri me LBL Z P + 2 x → LBL P x P 3 D → → LBL X x = 0 ? yes no Star t no ye s Note: x is the value in the X -register .[...]

Miscellaneous Programs and Equations 17 -9 Progra m Listing: Progr am Lines: (In AL G mode) Description    T his r outine displa y s prime n umber P .    Checksum and length: 2C C5 6    T his rou tine adds 2 to P .    Checksum and length: EFB2 9 ?[...]

17 -10 M iscellaneous Progr ams and Equations Fla gs Use d: None . Progr am Instructions: 1. K e y in the pr ogr am r outines; pres s  when done . 2. K ey in a po siti ve int eger gr eater than 3 . 3. Pr es s  P  to run pr ogr am. Pr ime nu mber , P w ill be display e d . 4. T o see the ne xt prime nu mber , pr ess  . V ariables Used: R[...]

Miscellaneous Programs and Equations 17 -11 Cros s Pr oduct in V ectors Here is an e xam ple sho w ing ho w to u se the pr ogr am f unction t o calc ulate the c r oss pr oduc t . Cr oss p r oduct: v 1 × v 2 = ( YW – ZV ) i + ( ZU – XW ) j + ( XV – YU ) k whe re v 1 = X i + Y j + Z k and v 2 = U i + V j + W k Progr am Lines: (In RPN mode) Des[...]

17 -12 M iscellaneous Progr ams and Equations Ex ample: Calc ulate the c ro ss pr oduct of tw o v ectors , v1=2i+5j+4k and v2=i- 2j+3k Progr am L ines: (In RPN mode) Description    Defines the beginning of the c r o ss–pr oduct r outine.          ?[...]

Miscellaneous Programs and Equations 17 -13 Ke ys: Dis pla y: D escription:  R     R un R r ou tine to in put v ec tor v alue     Input v2 of x -component  z    Input v2 of y-compon ent     Input v2 of z- c o m p o n e n t  [...]

17 -14 M iscellaneous Progr ams and Equations[...]

Pa r t 3 Appendix es and Ref er ence[...]

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Support, Batteries, and Service A-1 A Suppor t , Batteries, and Ser v ice Calculator Suppor t Y ou can obtain answ ers to qu estions a bout using y our calc ulator fr om our Calc ulator Suppo rt Department. Our e xper ience sho w s that man y c ustomer s hav e similar questions a bout our pr oducts , so w e hav e pr o v ided the f ollo w ing sec ti[...]

A-2 Suppor t, Batteries, and Service A: Exponent of ten; that is, 2 .51 × 10 –13 . Q: The calc ulator has displa yed the mes sage   . What sh ould I do ? A: Y ou must c lear a portion of memory befor e proceeding . (See appendix B .) Q: Wh y does calculating the sine (or tangent) o f π ra dians disp lay a v ery sma[...]

Support, Batteries, and Service A-3 Changing th e Batteries The calculato r is pow er ed by two 3-volt lithium co in batteries , CR203 2 . Replace the batter ie s as soon as po ssible w hen the lo w battery annunc ia tor (  ) appears. If the battery annunciator is on , and the display dims, y ou ma y lose data. If data is l ost , the ?[...]

A-4 Suppor t, Batteries, and Service 5. Insert a ne w CR203 2 lithium battery , m aking sur e that the positiv e sign (+) is fac ing ou twar d . 6. Remo ve and insert the other bat tery as in steps 4 thr ough 5 . Mak e sure that the positi v e sign (+) on eac h battery is fac ing outw ar d . 7. R eplace the batter y compar tment co ver . 8. Pres s [...]

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A-6 Suppor t, Batteries, and Service  →  →  → 9 → × → Ö → Õ →  →  →  → 6 → Ø →  →  →  →  →  →  →  →  →  → 4 →  →  →  →  →  →  →  →  →  →  →  →  →  →  →  →  →  →  → [...]

Support, Batteries, and Service A-7 Wa r ra n t y HP 3 5s Sc ie ntifi c Calc ulator ; W arr anty period: 12 months 1. HP war r ants to y ou , the end-user c us tomer , that HP hard w ar e , accessor i es and supplies w ill be f r ee fr om def ects in mater ials and w orkmanship after the date of pur cha se , for the per iod spec ified abov e . If H[...]

A-8 Suppor t, Batteries, and Service 6. HP MAKE S NO O THER EXPRE SS W ARRANTY OR CONDIT ION WHETHER WRITTEN OR ORAL. T O THE EXTENT ALL OWED B Y L OCAL LA W , ANY IMPLIED W ARRANTY OR CONDIT ION OF MER CHANT ABILITY , S A TISF A CTOR Y QUALI TY , OR FITNE SS FOR A P ART ICULAR PURPO SE IS LIMITED T O THE DURA TION OF THE EXPRE SS W ARRANTY SET FOR[...]

Support, Batteries, and Service A-9 Chi na 0 10 -68002 3 9 7 Hong K ong 2 80 5- 2 5 63 Indonesia +6 5 6100 6 68 2 Japan +85 2 2 80 5- 2 56 3 Malay sia +65 6100 6 68 2 N e w Z e a l a n d 09 - 57 4 -270 0 Philippines +65 6100 6 6 8 2 Singapore 6100 66 8 2 South K orea 2-5 61- 2 7 00 Ta i w a n + 8 52 28 05 -256 3 Thailand +6 5 6100 6 6 8 2 Vi etnam [...]

A-10 Suppor t, Batteries, and Service S w itz er land (German) 01 4 3 9 5 35 8 S w itz erland (Italian) 0 2 2 5 6 7 5 308 United Kingdom 020 7 4 5 8 0161 LA Country : T elephone numbers Anguila 1-800 - 711- 28 8 4 Antigua 1-800 -711- 2 8 84 Ar gentina 0 -800 - 5 5 5 -5 000 Ar uba 800-8000 ♦ 800 - 711- 2 8 84 Bahamas 1-800 - 711- 2 88 4 Barbados 1[...]

Support, Batteries, and Service A-11 Haiti 18 3 ♦ 800-711- 2 8 84 H o nd ur a s 80 0- 0- 1 2 3 ♦ 800-711- 2 8 84 Jamaica 1-800-711- 2 884 Martinica 0 -800 -990-011 ♦ 8 77 - 2 19-8 6 71 M exic o 01 - 8 0 0 - 4 7 4 - 68368 ( 8 0 0 H P INVENT) Montser rat 1-800 - 711- 2 88 4 Netherland An tilles 001-800 -8 7 2 - 2 881 ♦ 800 - 7 11- 2 88 4 Nica[...]

A-12 Suppor t, Batteries, and Service Regulatory information Feder al Communications Commission Notice This eq uipment has been tested and f ound to compl y w ith the limits for a Clas s B digital de v ice , pursuant to P ar t 15 of the FCC R ules . Thes e limits are designed t o pro vide r easonable pr otection against ha rmful interfer ence in a [...]

Support, Batteries, and Service A-13 Houston , TX 77 2 6 9- 2000 or call HP at 2 81-514 -33 33 T o identify your pr o duct , r ef er to the part , seri es , or model number located on the pr oduc t . Canadian Notice This Cla ss B digital appar atus meets all requ irements of the C anadian Interference- Cau sing E quipment R egulatio ns. Av is Canad[...]

A-14 Suppor t, Batteries, and Service Japanese Notic e 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 ?[...]

User Memory and the Stack B-1 B User M emory and t he Stack This appendi x co v ers  The allocation and requir ements of user memory ,  Ho w to r es et the calc ulator w ithout aff ecting me mory ,  Ho w to c lear (pur ge) all of us er memory and r ese t the sy stem defa ults, and  Which op eratio ns a ffec t sta ck li ft. Managing Calc[...]

B-2 User Memory and the Stack T o see the memor y r equirements of spec ifi c equations in th e equation list: 1. Pr ess  to acti vate E quati on mode . (    or the left end of the c urr ent eq uation w i ll be displa y ed.) 2. If necessary , scro ll thr ough the equati on list (pr es s × or Ø ) until y ou see the[...]

User Memory and the Stack B-3 Clear in g Memory The usual w a y to clear u ser memory is to pr ess   (  ). H o w e v e r , there is als o a mor e po w erful c lear ing pr ocedur e that r esets additional inf or mation and is use ful if the k e y boar d is not f unctio ning pr operl y . If the calc ulator fails t o r espond to k ey[...]

B-4 User Memory and the Stack Memory may inad vertentl y be clear ed if th e calc ulator is dr opped or if po w er is int errupt ed. The Status of Stack Lift The f our s tac k r egister s ar e alw a y s pr esen t , and the stac k al w ay s has a stac k–lift stat us . Th at is to sa y , the stac k lift is al wa ys enabled or disabled re g ard i ng[...]

User Memory and the Stack B-5 Disabling Operations The f iv e oper ations  , / , - ,   (  ) and   (  ) disable stac k lift. A n umber ke yed in after on e of these disabling operations w r ites ov er the number cur rentl y in the X–register . The Y–, Z– and T– re gi st er s rem a in u nc ha n ge d. In add[...]

B-6 User Memory and the Stack The Status o f the L AST X R egister The f ollo w ing oper ations sa v e x in the LAS T X register in RPN mode: Notice that /c does no t affect the LAS T X registe r . The r ecall-arithmeti c sequence Xh  va riab le stores x in LAS Tx and Xh vari ab le  stores the recalled number in L AS Tx. In AL G mode, the LAS[...]

User Memory and the Stack B-7 Accessing Stack Register Contents The values held in the four stack r egisters, X, Y , Z and T , are accessible in RPN mode in an equatio n or pr ogr am using the RE GX, RE G Y , REG Z and REG T commands. T o use t hese instructions , pres s d fir st . Then , pr essing < pr oduces a menu in the display sh ow ing the[...]

B-8 User Memory and the Stack[...]

AL G: Summ ary C-1 C AL G: Summar y About AL G This appendi x summar i z es some featur es uniq ue to AL G mo de , including ,  T w o ar gument ar ithmetic  Exponenti al and Logar ithmi c functi ons (  ,  ,  ,  )  T rigonometric functions  P arts of numbers  R e vi e w ing the st ack  Oper[...]

C-2 AL G: Summary 5. Unar y Minus +/- 6. × , ÷ 7. +, – 8. = Doing T wo argument Arithmetic in AL G This dis c ussi on of ar ithmeti c using AL G re places the f ollo w ing parts that ar e aff ected by AL G mode . T w o argumen t ar ithmetic oper ations ar e affec ted b y AL G mode:  Simple ar ithmetic  P o w er func tions (  ,  ) ?[...]

AL G: Summ ary C-3 P ow er F unctions In AL G mode, to calc ulate a numbe r y rai s e d t o a p ower x , k e y in y  x , then pr es s  . P ercentage Calculations The P ercent Function. The  key di v ides a number b y 100. Example: Suppos e that the $15.7 6 item cost $16.12 last y ear . What is the percentage change fr om last year's p[...]

C-4 AL G: Summary P ermutations and Combinations Ex ample: Combinations of P eople. A company em plo y ing 14 women and 10 men is f orming a si x–perso n safety committee. Ho w many differ ent comb inations o f people are pos sible ? Quotient and Remainder Of Division Yo u c a n u s e  (  ÷ ) a n d  ( ?[...]

AL G: Summ ary C-5 If y ou w er e to k e y in  , the calc ulator w ould calc ulate the r esult , -10 7 .64 71. Ho w ev er , that’s not what y ou want . T o delay the di v ision until y ou’v e subtr acted 12 f ro m 8 5, use par entheses: Y ou can omit the mult iplicati on sign ( × ) be fo r e a left par enthesis. I[...]

C-6 AL G: Summary T rigonometric F unctions Assume the unit of t he angle is 9  (  ) Hy perb olic functions T o Calculate: Press: Display: Sine of x .    Co sine of x .    T angent of x .   ?[...]

AL G: Summ ary C-7 Pa r t s o f n u m b e r s Re v iew ing the Stack The  or    k ey pr oduces a menu in the display— X–, Y–, Z–, T–r egister s, to let you re view the entire conte nts of th e stack . The diff er ence betw een the  and the   ke y is the location of the under line in the displa y . Pr essing the  ?[...]

C-8 AL G: Summary The v alue of X-, Y -, Z -, T -r egister in AL G mode is the same in RPN mode . After nor mal calc ulation , sol v ing, pr ogramming, or in tegr ating, the v alue of the f our re gisters w ill be the same as in RPN or AL G mode and ret ained w hen yo u sw itch between AL G and RPN logic modes. Integrating an Equation 1. K e y in a[...]

AL G: Summ ary C-9 T o do an oper ation with one comple x number : 1. Select the f uncti on . 2. Enter the co mplex number z . 3. Press  to calculate. 4. T h e c a l c u l a t e d r e s u l t w i l l b e d i s p l a y e d i n L i n e 2 a n d t h e d i s p l a y e d f o r m w i l l be the one that y ou ha ve s et in 9 . T o do an arithmetic opera[...]

C-1 0 AL G: S ummary Ex amples: Ev aluate ( 4 - 2/5 i )  (3 - 2/3 i ) Arithmetic in Bases 2, 8, and 16 Her e ar e some e xam ples of ar ithmetic in Hex adec imal, Oc tal , and Binary modes: Ex ample: 12F 16 + E9A 16 = ? K ey s: Display: Desc ription:  8 Ë  (  ) Sets di splay form 4  6 Õ  4  6 [...]

AL G: Summ ary C-11 77 60 8 – 4 326 8 = ? 100 8 ÷ 5 8 = ? 5A0 16 + 10011000 2 = ? Entering S tatistical T wo–V ariable Data In AL G mode, r emember to enter an ( x , y ) pair in rev erse or der ( y  x or y   x ) so that y ends up in the Y–r egister and X in the X–r egiste r . 1. Pre ss   (4 Σ ) to clear ex isting statistica[...]

C-12 AL G: Summary 4. The display show s n the number o f statisti cal data pairs y ou hav e acc umulat ed . 5. C ontinue enter ing x , y –pairs. n is updated with eac h entry .  If y ou w ish to delete the incorr ect values that we re j us t enter ed , pr ess z 4 . After de leting the incorr ect statisti cal data , the calc ulator w ill displ[...]

AL G: Summ ary C-13 Linear Regression Linear r egr ession, or L .R . (also called linear estimatio n) , is a statistical method fo r finding a s tr aight line that be st f its a set o f x , y –dat a.  T o find an estimated v alue f or x (or y ), ke y in a giv en h ypothetical v alue for y (or x ) ,pre ss  , then pre ss   () ( o r  [...]

C-1 4 AL G: S ummary[...]

More about Solving D-1 D Mo r e about Solv ing This appendi x pr o vi des inf ormatio n about the S OL VE operati on be y ond that giv en in chap ter 7 . How S OL VE F inds a Ro ot S OL VE f irst atte mpts to so lv e the eq uation dir ectly f or the unkno wn var iable. If the attempt f ails, S OL VE cha nges to an ite rati ve(r epetiti v e) pr oced[...]

D-2 M ore about Sol ving  If f(x) has one or mor e local minima or minima, eac h occ urs singly betw een adjacent r oots o f f(x) (fig ur e d, belo w). In most situati ons, the calc ulated r oot is an accu rat e estimate of the theo r etical , infinite ly pr ec ise r oot of the equati on . An "ideal" so lution is one f or w hic h f(x) [...]

More about Solving D-3 Interpr eting Results The S OL VE operatio n will pr oduce a solution under either of the follow ing conditions:  If it f inds an estimate for w hi ch f(x) eq uals z er o. (See f igur e a , belo w .)  If it finds an estimate wher e f(x) is not equal t o z er o, but the calc ulated root is a 12–digit number adjacen t t[...]

D-4 M ore about Sol ving No w , sol v e the equati on to f ind the r oot: Ex ample: An Equation with T w o Roots. F ind the two r oots of the para bolic eq uation: x 2 + x – 6 = 0. Enter the eq uation as an e xpr ession: K ey s: Displa y: Desc ription:  Select E quation mode .   X    X   X [...]

More about Solving D-5 Now , solv e the equatio n to find its positi ve and negativ e r oots: Certain cases r equir e spec ial consi derati on:  If the func tion's gr aph has a discontinuity that cr os ses the x –ax is, then the S OL VE oper atio n r etur ns a va lue adjacent t o the discontin uity (see fi gur e a , below). In this case ,[...]

D-6 M ore about Sol ving  Va l u e s o f f(x) may be appr oac hing inf inity at the location wher e the graph changes si gn (see f igur e b , belo w). This situatio n is called a pole . Si nce the S OL VE operation determines that there is a sign change between two neighbo ring v alues o f x , it r eturns the po ssible r oot . Ho w ev er , the v[...]

More about Solving D-7 No w , sol v e to fi nd the r oot: Note the difference between the last two estimates, as w ell as the relati vel y large val ue for f(x) . The pr o blem is that ther e is no v alue of x for w hic h f(x) equals z ero . Ho we ver , at x = 1 . 99999999999 , t h ere i s a ne ig h b ori n g va lu e of x that yie lds an opposite s[...]

D-8 M ore about Sol ving No w , sol ve t o find the r oot . When S OL VE Cannot Find a R oot Sometimes S OL VE fails to find a r oot . T he follo wing conditions caus e the mess age    :  T he sear ch t erminate s near a local minimum or max imum (s ee fi gur e a , belo w).  T he sear ch halts beca use S OL VE is w [...]

More about Solving D-9 Example: A Relati ve Minimum. Calc ulate the r oot of this parabo lic eq uation: x 2 – 6 x + 13 = 0. It has a minimum at x = 3. Enter the equation as an expr essi on: K ey s: Display: Desc ription:  Selects E quation mode .  X   X   Enters the eq uatio n. f ([...]

D-10 More about Solv ing No w , sol ve t o find the r oot: Ex ample: An Asymptote . F ind the r oot of the eq uation Enter the eq uation as an e xpr ession .     Chec ksum and length .  Cancels E quati on mode . K ey s: Display: Desc ription:  X   _ Y our initial gu esse s for the[...]

More about Solving D-11 W atch what happens when y ou use negativ e v alues f or guesses: Example: Find the root of the equation. Enter the equation as an expr essi on:  F irs t attempt to f ind a positi v e r oot: Ke ys: Dis pla y: Desc ription:  X   Y our negati v e guess es f or the r oot .  [...]

D-12 More about Solv ing No w attempt to f ind a ne gativ e root b y ent ering guess es 0 and –10. Noti ce that the fun ct ion is un defi ne d fo r va lu es of x bet w een 0 and –0. 3 since tho se v alues produce a positi ve denomina tor bu t a negati v e numer ator , causing a negativ e square root. Ex ample: A Local "Flat" Region . [...]

More about Solving D-13 Solve for X us ing i nit ial gu esses of 1 0 –8 and –10 –8 . Rou nd – O f f E rror The limited (12–digit) pr ec isio n of the calc ulator can cause er r or s due to r ounding off , whi ch adv ers ely affect the iterati ve s olutions of S OL VE and integration . F or exam p le, has no r oots be cau se f(x) is al w a[...]

D-14 More about Solv ing[...]

More about Integration E-1 E More about Integr ation This appendi x pro v ides inf or mation abo ut integr ati on be y ond that gi ven in c hapte r 8. How the Integr al Is Ev aluated The algorithm used by the integration operation , ∫   , calc ulates the integr al of a func tion f(x ) by computing a w eighted a ver age of the f unctio[...]

E-2 M ore about Integr ation As explained in c hapter 8 , the uncertainty of the final appr o x imation is a number deri v ed fr om the displa y f or mat, w hic h spec if ies the uncertainty f or the functi on . At the end of eac h iter atio n, the algo rithm com par es the appr o x imati on calc ulated during that iter ati on w ith the appr o x im[...]

More about Integration E-3 With this nu mber of sample po ints, the algo rithm w ill calc ulate the same appro ximation f or the integr al of any o f the functions sho w n . The actual integr als of the func tions sho wn with s olid blue and blac k lines are a bout the same , so the appro ximation w ill be fair ly acc ur ate if f(x) is one of these[...]

E-4 M ore about Integr ation T r y it and see what happens. Enter the func tion f(x) = x e – x . Set the displa y fo rmat to S CI 3, spec if y the low er and upper limits of integration as z er o and 10 499 , than start the integr ation . The ans wer r etur ned by the calc ulato r is clear ly incor r ect , since the actual int egr al of f(x) = xe[...]

More about Integration E-5 The gr ap h is a spik e v ery cl ose to the o ri gin . Becaus e no sample point ha ppened to disco ve r the spik e, the algor ithm assumed that f(x) w as ide nticall y equ al to z er o thro ughout the interval o f integr atio n. E ven if y ou inc r eased the n umber of sample points b y calc ulating the integral in S CI 1[...]

E-6 M ore about Integr ation Note that the r api dity of var iati on in the f unctio n (or its lo w–or der der i vati v es) mu st be deter mined w ith re spect t o the w idth of the in terval of in tegr ation . W ith a gi ve n number of sample po ints , a functi on f(x) that has three f luctuatio ns can be better char acteri zed b y its samples w[...]

More about Integration E-7 In man y cases y ou w ill be famili ar enough w ith the f unction y ou want to integr ate that y ou w ill kno w whe ther the func tion has an y quick w iggle s r elati ve to the interval of integr ati on . If y ou'r e not f amiliar w ith the f unctio n, and y ou su spect that it ma y cause pr oblems, yo u can quic kl[...]

E-8 M ore about Integr ation This is the co rr ect ans w er , but it took a very long time. T o understand w hy , compar e the gr aph of the f uncti on betw een x = 0 and x = 10 3 , whi ch loo ks about the same as that sho wn in the pr e v io us e x ample , w ith the gr aph of the func tion betw een x = 0 and x = 10: Y ou can s ee that this functi [...]

More about Integration E-9 Because the calc ulation time depends on how soon a certain density of sample points is ac hie v ed in the r egion w her e the func tion is int er esting , the calc ulation o f the integr al of an y f unctio n w ill be pr olonged if the int erval of int egrati on inc ludes mostl y r egio ns wher e the fu nctio n is not in[...]

E-10 More about Integration[...]

Mes s ag es F-1 F Me s sa g e s The calc ulator r espo nds to certain conditions or k e y str okes b y display i ng a message . T he  sy mbol comes o n to call your attenti on to the message . For signif icant conditi ons, the mes sage r emains until y ou c lear it . Pr essing  or  clear s the message and the pr evi ous dis p lay con tent [...]

F-2 Message s    Indicates the "top" o f equation memory . Th e memory scheme is c ir c ular , so    is also the "equatio n" after the last equati on in equati on memory .  The calculator is calc ulating the integr al of an equation or p[...]

Mes s ag es F-3    Exponentiati on err or :  Attemp ted to raise 0 to the 0 th pow er or to a negativ e pow er .  Attempted to r aise a negati ve nu mber to a non– intege r po w er .  Attemp ted to raise complex number (0 + i 0) to a number w ith a negati ve r eal part .     Attemp[...]

F-4 Message s    S OL VE (include E QN and P GM mode)cannot f ind the r oot of the equati on using the c urr ent initial guesse s (see page ). These conditions inc lude: bad guess , soluti on not fo und, po int of inte r est , left unequal to r igh t . A S OL VE operati on e x ec uted in a pr ogr am does not pr oduce this[...]

Mes s ag es F-5 Self–T est Messages:   Sta t i st ic s e rro r:  Attempted to do a s tatisti cs calc ulation w ith n = 0.  Attemp ted to calculate s x s y , , , m , r , or b w ith n = 1.  At tempted to cal culate r , or with x –data only (all y –values equal to z er o) .  Attemp ted to calculate , , r , [...]

F-6 Message s[...]

Operation Index G-1 G Ope r atio n I n de x This sec tion is a quic k r ef er ence f or all func tions and operati ons and the ir for mulas , wher e appr o pr iate . T he listing is in alphabetical or der by the function's name . This name is the one used in pr ogr am lines . F or e x ample , the f unction named FI X n is ex ecuted as  8 ?[...]

G-2 Operati on Inde x Ø Display s next entry in catal og; mov es to ne xt equation in eq uation lis t; mo ve s pr ogr am point er to ne xt line (during pr ogram entry); exec utes the c urr ent pr ogr am line (not dur ing pr ogra m entry). 1–2 8 6–3 13–11 13–20 Ö or Õ Mov es the curs or and does not delete any content . 1–14  Ö or ?[...]

Operation Index G-3 Σ x 2   ÕÕÕ (   ) Re turns the sum o f squar es o f x – val u es. 12–11 1 Σ xy  ÕÕÕÕÕ (   ) Retur ns the sum of pr oducts o f x –and y –values . 12–11 1 Σ y   ÕÕ (  ) Re turns the sum o f y –values . 12–11 1 Σ y 2   ÕÕÕÕ (   ) Re turns the s[...]

G-4 Operati on Inde x A thr ough Z  var iable V alue of named var iable . 6–4 1 ABS   Absolut e value . Ret urn s . 4–17 1 AC OS   Arc cosi ne . Ret urns cos –1 x. 4–4 1 AC OS H    Hy perbolic ar c cosine . Ret urns cosh –1 x . 4–6 1 9  (  ) Acti vates Algebr aic mode . 1–9 AL OG   Commo[...]

Operation Index G-5 b   (  ) Indicates a b inary number 11–2 1   Displa ys the bas e–con ver sion me nu . 11–1 BIN   (  ) Selects Binary (base 2) mode. 11–1  T urns on calculat or ; clear s x ; clear s messages and prompts; cancels menus; cancels catalog s; cancels equation entry; cancels program[...]

G-6 Operati on Inde x CL V ARx   (  ) Clear s indir ect v ar iable s wh ose addre ss is greater than the x address to z er o . 1–4 CLS TK   (  ) Cle ars all stack le ve ls to z ero . 2–7  CM   Con v erts inches to centimeters. 4–14 1 nCr  x Combinati ons of n items taken r at a time . R[...]

Operation Index G-7 ENG n  8  (  ) n Selects Engineer ing dis play w ith n digits f ollo w ing the f irst di git ( n = 0 thro ugh 11). 1–2 2 @ and 2 Cau ses the e xpo nent displa y f or the number be ing displa y ed to change in multiple of 3 . 1–2 2  Separates two n umbers k ey e d in sequentially; completes equation entr [...]

G-8 Operati on Inde x FS ? n   (  ) n If flag n (n = 0 thr ough 11) is set , e xec utes the next pr ogr am line; if flag n is clear , skips the ne xt progr am line. 14–12  GA L   Con v erts liters to gallons. 4–14 1 GRAD 9  (  )Sets Gr ads angular mode. 4–4   label nnn Sets pr ogr am point[...]

Operation Index G-9 INT÷  (  ÷ ) P r o d u c e s the quoti ent of a di v isio n oper ation inv ol ving tw o integers . 4–2 1 INT G  (  ) Obtains the gr eatest int eger equal to o r less than giv en number . 4–18 1 INP UT vari able   va riab le Recalls the variab l e to the X–regist er , dis[...]

G-10 Operat ion I nde x LBL label   label La bels a pr ogr am w ith a single lette r fo r re fer ence by the XEQ, G T O, or FN= operati ons . (Used onl y in progr ams.) 13–3 LN  Natural logar ithm . Ret urn s lo g e x . 4–1 1 LO G   Common logar ithm . Ret urn s lo g 10 x . 4–1 1   Display s menu f or linear r egre ssi[...]

Operation Index G-11 OR  >  (  ) Log ic op era tor 11–4 1   T urns the calc ulator off . 1–1 nPr  { Pe r m u t a t i o n s of n items taken r at a time. R etur ns n ! ÷ ( n – r )!. 4–15 1   Acti vates or cance ls (toggles) Progr am–entr y mode . 13–6 PS E   Pa u s e . Halts pr ogr am e xec ution b[...]

G-12 Operat ion I nde x RCL+ vari able   va riab le Ret urn s x + vari able . 3–7 RCL– va riabl e   var iable . Ret urn s x – var iable . 3–7 RCLx va ria bl e   variab le . Ret urn s x × variab le. 3–7 RCL ÷ v ari able   var iable . Ret urn s x ÷ variab le. 3–7 RMDR  (  ) Produces th[...]

Operation Index G-13 SC I n  8  (  ) n Selects Sci entifi c display w ith n dec imal plac es . ( n = 0 thr ough 11.) 1–2 2 SEED   Res tarts the rando m– number sequence with the seed . 4–15 SF n   (  ) n Sets flag n ( n = 0 through 11). 14–12 SG N  (  ) Indicate s the sign of x [...]

G-14 Operat ion I nde x STOP  Ru n /stop. Begins progr am e x ec ution at the cur r ent pr ogr am line; stop s a running progr am a nd display s the X–r egister . 13–19   Display s the summati on menu . 1 2–4 s x   (  ) Retur ns sample standard dev iation of x –v alues: 12–6 1 s y   Õ (  ) Retur ns sample[...]

Operation Index G-15   () Given a y –value in the X–r egiste r , returns the x – estim ate based on the regr ession line: = ( y – b) ÷ m. 12–11 1 !  * F actor ial (or gamma). Re turns ( x )( x – 1) ... (2)(1), or Γ ( x + 1) . 4–15 1 XROO T  The argu ment 1 r oot of ar gument 2 . 6–16 1 w  ÕÕ ( w )Returns we [...]

G-16 Operat ion I nde x x = y ?   ÕÕÕÕÕ (  ) If x = y , ex ecu tes ne xt pr ogra m line; if x ≠ y , skips next pr ogr am line . 14–7   Display s the " x ? 0" compar ison tests menu . 14–7 x ≠ 0 ?   ( ≠ ) If x ≠ 0, execu te s next pr ogram line; if x =0, skips the ne xt pr ogr am line . 14–7 x ≤ 0 [...]

Operation Index G-17 Notes: 1. F uncti on can be used in equati ons.   Õ () Gi v en an x–v alue in the X–re gister , returns the y –estimate based on the regr ession line: = m x + b . 12–11 1 y x  Po w e r . Ret ur ns y raised to the x th po w er . 4–2 1 Name Ke ys and Des cription P age  y ˆ  ˆ y ˆ[...]

G-18 Operat ion In de x[...]

Index- 1 Inde x Special Characters ∫ FN. See integration % functions 4-6  1-15  in fractions 1-26 π 4-3, A-2   annunciator in fractions 5-2 in fractions 5-3   annunciators equations 6-7 binary numbers 11-8 equations 13-7  . See backspace k ey _. See digit-entry cursor  . See integration annunciators 1-3  annunciator 1-[...]

Index- 2 binary numbers. See numbers arithmetic 11-4 converting to 11-2 range of 11-7 scrolling 11-8 typing 11-1 viewing all digits 11-8 borrower (finance) 17-1 branching 14-2, 14 -16, 15-7 C %CHG arguments 4-6, C-3 Å adjusting contrast 1-1 canceling prompts 1-4 canceling VIEW 3-4 clearing messages 1-4 clearing X-register 2-3, 2-7 leaving catalogs[...]

Index- 3 temperature units 4-14 time format 4-13 volume units 4-14 coordinates converting 4-10 correlation coefficient 12-8, 16 -1 cosine (trig) 4-4, 9-3, C- 6 curve fitting 12-8, 16-1 D Decimal mode. See base mode decimal point A-1 degrees angle units 4-4, A-2 converting to radians 4-14 denominators controlling 5-4, 14-10, 14-14 range of 1-26, 5-2[...]

Index- 4 memory in 13-16 multiple roots 7-9 no root 7-8 numbers in 6-5 numeric value of 6-10, 6-11, 7-1, 7-7, 13-4 operation summary 6-3 parentheses 6-5, 6-6, 6-15 precedence of operators 6 -14 prompt for values 6-11, 6 -13 prompting in pr ograms 14-11, 15-1, 15-8 roots 7-1 scrolling 6-7, 13-7, 13-16 solving 7-1, D-1 stack usage 6-11 storing variab[...]

Index- 5 G  finds PRGM TOP 13- 6, 13-21, 14- 6 finds program labels 13-10, 1 3- 22, 14-5 finds program lines 13-22, 14- 5 gamma function 4-15 go to. See GTO grads (angle units) 4-4, A-2 Grandma Hinkle 12-7 Greatest integer 4-18 grouped standard dev iation 16-18 GTO 14-4, 14-17 guesses (for SOLVE) 7-2, 7-7, 7-8, 7- 12, 15-6 H help about calculato[...]

Index- 6 logarithmic functions 4-1, 9- 3, C-5 logic AND 11-4 NAND 11-4 NOR 11-4 NOT 11-4 OR 11-4 XOR 11-4 loop counter 14-18, 14-23 looping 14-16, 14-17 Ł ukasiewicz 2-1 M  program catalog 1-28, 13-22 reviews memory 1-28 variable catalog 1-28 mantissa 1-25 mass conversions 4-14 math compl ex-nu mber 9 -1 general procedure 1-18 intermediate resu[...]

Index- 7 1-18 periods and commas in 1-23, A-1 precision D-13 prime 17-7 range of 1-17, 11-7 real 4-1 recalling 3-2 reusing 2-6, 2-10 rounding 4-18 showing all digits 1-25 storing 3-2 truncating 11-6 typing 1-15, 1-16, 11-1 O Ä 1-1 OCT annunciator 11-1, 11 -4 octal numbers. See numbers arithmetic 11-4 converting to 11-2 range of 11-7 typing 11- 1 o[...]

Index- 8 deleting 1-28 deleting all 1-5 deleting equations 13-7, 13-20 deleting lines 13-20 designing 13-3, 14-1 editing 1-4, 13-7, 13-20 editing equations 13-7, 13-20 entering 13-6 equation evaluation 14-11 equation prompting 14-11 equations in 13-4, 13-7 errors in 13-19 executing 13-10 flags 14-9, 14-12 for integration 15-7 for SOLVE 15-1, D-1 fr[...]

Index- 9 rolling the stack 2-3, C-7 root functions 4-3 roots. See SOLVE checkin g 7-7, D-3 in programs 15-6 multiple 7-9 none found 7-8, D-8 of equations 7-1 of programs 15-1 rounding fractions 5-8, 13-18 numbers 4-18 round-off fractions 5-8 integration 8-6 SOLVE D-13 statistics 12-10 trig functions 4-4 routines calling 14-1 nesting 14-2, 15-11 par[...]