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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 .
2 Contents Complex number display format ( , , ·‚) ... ................. 1-24 SHOWing Full 12–Digit Precisio n ......... ...................... ........ 1-25 Fractions ............. ................... ................. .....
Contents 3 Using the MEM Catalog .................. ................. ................... ..... 3-4 The VAR cata log..... ................ .................... ................ ........ 3-4 Arithmetic with Stored Variables .... .................... ..
4 Contents 5. Fractions ....... .......................... ...................... .............. 5-1 Entering Fractions ... .................... ................... .................... ...... 5-1 Fractions in the Display ... ................... .....
Contents 5 Operator Precedenc e . .................... ................ ................... 6-1 4 Equation Functions ........ .................... ................ ................ 6-1 6 Syntax Errors....... ................... ................ ......
6 Contents Dot product .......... ................. ................... .................... .... 10-4 Angle between vecto rs ..... .................... ................ .............. 10-5 Vectors in Equations ... .................... ...............
Contents 7 Part 2. Programming 13.Simple Programming ...... ........................................... 13-1 Designing a Pro gram ...... .................... ................ ................... 1 3-3 Selecting a Mode ... ................ ............
8 Contents Clearing One or More Prog rams .............. ................... ...... 1 3-23 The Checksum .......................... ................... ................... 13-2 3 Nonprogrammable Functions ... .................... ................... ..
Contents 9 15.Solving and Integrating Programs ............. ................. 15-1 Solving a Program .... ................... .................... ................... ... 15-1 Using SOLVE in a Program ..................... ................... .......
10 Contents B. User Memory and the Stac k ....................... .................. B-1 Managing Calculator M emory ...................... ................... .......... B -1 Resetting the C alculator ............................ ................ ...
Contents 11 How SOLVE Finds a Root ............. .................... ................ ........ D-1 Interpreting Results ............. ................. ................... .................. D-3 When SOLVE Cannot Find a Root .........................
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 printed on the bottom of the key .
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 .
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 .
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 .
Getting Star ted 1-5 Ke ys for Clearing (continued) Key D es c r ip t i on 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.
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 .
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. Pre ss Õ Ö × Ø to mov e the underline to the item y ou w ant to selec t .
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 .
Getting Star ted 1-9 Pr essi ng bac ks out of the 2–le v el CLEAR or MEM men u , one le v el at a time . Re fe r to in the table on page 1–5 . Pr essi ng or cancels an y other menu . Pr essing another men u k ey r eplaces the old menu w ith the ne w one .
1-10 Getting Star ted T o s elect ALG mode: Pre ss 9{ ( ) to set the calc ulator to AL G mode . When the calculat or is in AL G mode, the AL G annunc iator is on .
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 .
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.
Getting Star ted 1-13 HP 35s Annunciators Annunciator Meaning Chapte r The " (Bus y)" annunci ator appears while an operati on , equation , or pr ogr am is execu t in g.
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 .
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 r esult of a calc ulatio n is bey ond thi s r ange , the err or message “ ” appears momentarily along w ith the annunc i ator .
1-16 Getting Star ted Ke ying in P owers o f T en The key i s us e d to e n te r p owe r s of t e n q u i ck ly. Fo r exa m p le, 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 .
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 .
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.
Getting Star ted 1-19 Example: Calculate 3.4 2 , firs t 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() .
1-20 Getting Star ted Ex ample Calc ulate 2+3 and 6 C 4 , f irs t 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 .
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 k ey t o e xc hange the co nten ts in the x - and y -r egisters .
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 .
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 .
1-24 Getting 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 .
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.
1-2 6 Getting Started 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.
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.
1-28 Getting Started An y other k e y also clear s the message , though the k e y functi on is not ente red If no message is dis play ed, but the annunciator appears, then yo u hav e pres sed an inactiv e or in vali d ke y .
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 .
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.
2- 2 RPN: The Automatic Memor y 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 .
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 .
2- 4 RPN: The Automatic Memor y 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.
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 ).
2- 6 RPN: The Automatic Memor y Stack Ho w ENTER W orks Y ou kno w that separate s two n umbers k ey ed in one aft er 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.
RPN: The Automatic Memory Stac k 2- 7 Filling the stack with a constant The r eplicating effec t of togethe r w ith the repli cating eff ect of s tac 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 .
2- 8 RPN: The Automatic Memor y Stack 1. Lifts the stack 2. Lifts the stack and replicates the X–register . 3. Overwr ites the X–register . 4. Clears x by o v erwr iting it with z ero .
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 .
2- 1 0 RPN: The Automatic Memor 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.
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.
2- 1 2 RPN: The Automatic Memor 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 .
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.
2- 1 4 RPN: The Automatic Memor y Stack Ex ercises Calculate: Solution: Calculate: Solution: Calculate: (10 – 5) ÷ [(17 – 12) × 4] = 0.
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 or king o u tw a r 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 .
2- 1 6 RPN: The Automatic Memor 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 .
RPN: The Automatic Memory Stac k 2- 1 7 A Solution: .
2- 1 8 RPN: The Automatic Memor 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 .
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.
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.
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.
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 .
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 ( ).
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 .
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 .
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.
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).
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.
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 pr ess . F or y < 0, x must be an integer . T rigonometry Entering π Pr es s to place the f irst 12 di gits of π into the X–r egist er .
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 ).
Rea l–Nu mb er Fu nc tio ns 4- 5 Example: Sho w that cosine (5/7) π r adians and cosine 128. 5 7° are 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 ).
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 ) becaus e they .
Rea l–Nu mb er Fu nc tio ns 4- 7 Suppos e that the $15.7 6 item cost $16.12 last y ear . What is the percentage change fr om last year's pri ce to this year's ? Ke ys: Display: Descriptio n: 8 ( ) Rounds dis play to tw o decimal places .
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 Desc ription 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.
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. Pre ss to displa y the ph ys ics cons tants men u .
4- 10 R eal–Number Functions Conv ersion F unctions The HP 3 5s support s four types of conv ersions . Y ou can convert between: re ctangular and polar formats f or comple x numbers degr ees.
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 .
4- 12 R eal–Number Functions Ex ample: Conv ersion w i th V e ctors. Engineer P .C. Bor d has dete rmined that in the R C c i r c uit sho w n , the tot al impedance is 77 .
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 .
4- 14 R eal–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 .
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 5 3) , pre ss * (the r ight–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 * .
4- 16 R eal–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 .
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.
4- 18 R eal–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.
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 .
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 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 .
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 .
Frac ti ons 5-5 T o set the maximum denominator value , enter the value and t hen pres s . 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 value to the X–register , pr ess .
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 .
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 th e flag menu .
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.
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 int o 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 .
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 .
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 spec ifyi ng an equation to e valuat e (this chapt er). F or spec ifying an equati on to sol v e fo r unkno wn v alues (c hapter 7).
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 .
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 .
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 .
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 .
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 pare ntheses . (F or more infor matio n, s ee "Operator Pr eced ence" later in this chapter .
Entering and E valuating Equations 6- 7 T o displ ay equa tions: 1. Pre ss . This ac ti vate s 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 po inte r is at the top of the list .
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 .
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 . S elect ( ).
6- 10 Enter ing and Evaluating Equations Expre ssions. The equati on does not contain an "=". F or ex ample, 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 .
Entering and E valuating Equations 6- 11 T o e valuate an equation: 1. Display the desired equation. (See "Displaying and Selecting Equations" above .
6- 12 Enter ing and Evaluating Equations If the equati on is an assi gnment , only the r igh t–hand side is e v aluated . 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 .
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 .
6- 14 Enter ing and Evaluating Equations T o c hange t he number , type the new n umber and pr ess . T his 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 .
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 .
6- 16 Enter ing and Evaluating 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 .
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.
6- 18 Enter ing and Evaluating 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 , . Notice that the SIN f uncti on is "nested" insi de the INV functi on .
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 .
6- 20 Enter ing and Evaluating Equations K ey s: Display: Description: ( × as required) π Display s the desir ed equati on . (hold) Displa y equati on's c hec ksum and length.
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 .
7- 2 Solving Equations 2. Pr es s then pre ss the ke y for the unkno wn v ari able . F or ex ample , press X to solv e f or x. The equatio n then pr ompts for 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 displa yed v alue is the one y ou want , pre ss .
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 ).
7- 4 Solving 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.
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.
7- 6 Solving 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 k e y w ill hav e no eff ect .
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 Solving Equations The Y–r egister (press ) contains the pr evi ous e stimate f or the r o ot or eq uals 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 .
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 .
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 f ind the height o f the box (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 .
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 .
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.
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.
8-2 Integrating Equations Integrating Equations ( ∫ FN) T o integrate an equation: 1. If the equation that de fi nes the integr and's fu nctio n isn't stor ed in the equati on 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 .
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 .
8-4 Integrating Equations No w calc ulate J 0 (3) w ith the same limits of integr ati on . Y ou must r e-specify 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.
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 ( ) would r esult.
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 .
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) .
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 .
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 .
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.
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 complex number z 2 as descr ibed bef or e.
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 = 23 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) .
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.
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: Des cription: 9 ( ) Sets Degr ees 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.
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.
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 .
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 vecto r 2 .
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 = .
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 “ ”.
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 .
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 .
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 am is: A vec tor can be enter ed when pro mpted f or a va lue for a v a r iable .
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 .
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 enter numbers and for ce the display of numbers in dec imal , binary , octal and hex adec imal base . The LOGIC menu ( > ) pro v ides acce ss to logic f uncti ons.
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 hex adec 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 .
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 t o 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.
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 .
Base Conversions and Ar ithmetic and Logic 11-5 The r esult of an oper ati on is alw a ys an integer (an y fr actio nal portion 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 .
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 .
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.
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 .
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 s tandard de v iations .
12 -2 Statistical Operations En teri ng On e– V ariab l e D ata 1. Pr es s ( )to clear ex isting statistical dat a. 2. Key i n e a c h x –value and pres s . 3. The display sho w s n , the number o f statistical data v alues no w accumulated .
Statistical Operations 12-3 T o corr ect statistical data: 1. Reenter the incorr ect data, but instead of pr essing , pr ess . T his deletes the value(s) and dec r ements n .
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 . Pre ss ( ) for the mean of the x –values .
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 .
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 .
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 .
12 -8 Statistical Operations L.R. (Linear Regr ession) Menu T o find an estimat ed value f or x (or y ), ke y in a gi v en h y pothe tical v alue f or y (or x ), t hen pr ess () ( o r Õ () . T o find the values that defi ne the line that best f its y our data , pr ess follo wed b y , , or .
Statistical Operations 12-9 Enters data; displ ay s n . F iv e data pairs entered.
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 .
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 .
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.
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 ).
12 -14 Statistical Operations.
Pa r t 2 Pr ogr amming.
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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 .
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 .
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.
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 u rn to ma rk it s end (such as ).
Simple Progr amming 13-5 Using RPN operati ons ( whi ch w ork with the stac k, as e xplained in c hapter 2). Using AL G operations (as e xplained in appendi x C) . Using equations (a s 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 .
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 .
Simple Progr amming 13-7 5. End the progr am with a ret u rn instru ctio n, w hic h sets the progr am po inter bac k to after the progr am runs .
13-8 Simple Programming No w , er ase line A00 2 , and line A004 changes to “ A003 G T O .
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 .
13-10 Simple 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).
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 .
13-12 Simple 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 .
Simple Progr amming 13-13 Using INPUT f or Entering Data The INPUT instruction ( V ari able ) stops a ru nning progr am and displa ys a pr ompt for the gi v en va ri able .
13-14 Simple Programming 2. In the beginning of the pr ogr am , insert an INP UT instr ucti on fo r each v ar 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 var iable instr uc ti on to br ing that value bac k into the s tac k.
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 progr 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 .
13-16 Simple 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 .
Simple Progr amming 13-17 Keys : (In RPN mode) Display: Description: R H π Calc ulates the v olume . Chec ksum and length of equation . V Stor e the v olume in V .
13-18 Simple 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 .
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 essi ng ( run / stop ) during pr ogram entry ins erts a S T OP ins truc 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 e y boar d.
13-20 Simple 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 .
Simple Progr amming 13-21 3. Mo vi ng the c urso r”_” and pr ess r epeatedly 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 func tion is acti ve) Notice: 1. When the c urso r is acti ve in the pr ogr am line , Ø or × ke y w ill be disabled.
13-2 2 Simple Programming Pre ss to mo ve the pr ogram po inter to . Pre ss label nnn to mo v e to a spec ifi c 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 number .
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 .
13-2 4 Simple 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 .
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 .
13-2 6 Simple 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 f our differ ent times .
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 .
13-28 Simple Programming A more gener al form of this pr ogr am fo r any equati on Ax 4 + Bx 3 + Cx 2 + Dx + E wo ul 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 to sim plify progr ams b y separ ating and labeling portions of the pr ogr am that ar e dedi cated to partic ular tasks.
14 -2 Pr ogramming T echniques If y ou plan to hav e only one pr ogr am in the calc ulator memory , yo u 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 .
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 .
14 -4 Pr ogramming T echniques 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 .
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 uti on of a running pr ogr am to the spec i f ied pr ogr am line .
14 -6 Pr ogramming T echniques To : . T o a specif ic line number : label line n umber ( line number < 1000). F or ex ample , A . F or ex ample , pres s A . T he displa y w ill sho w ” ” .
Progr amming T ec hniques 14 -7 Comparison tes ts. These compar e the X–and Y–r egisters, or the X–register and z er o . F lag tests . The se c heck the s tatus o f flags , whi ch can be e ither set or c lear . Loop counte rs . The se ar e usuall y used to loop a s pec ifi ed number of times.
14 -8 Pr ogramming T echniques 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 gue ss . L ine T013 compar es the a bsolut e value of the calc ulated cor rec tion w ith 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 .
14-10 Programming T ec hniques 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.
Progr amming T ec hniques 14-11 Flag 1 0 contro ls pr ogr am e xec ution 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.
14-12 Programming T ec hniques 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 y ou kn o w at an y time whether an y of these fi v e flags is s et or not .
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.
14-14 Programming T ec hniques If y ou r eplace lines S00 2 and S003 b y SF0 and SF1, then f lags 0 and 1 ar e set s o 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.
Progr amming T ec hniques 14-15 Progr am Lines: (In RPN mode) Desc ription: Begins the fr acti on pr ogr am . Clears thr ee f r actio n flags . Displays mess ages.
14-16 Programming T ec hniques 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 .
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 e x ec ute other r outines.
14-18 Programming T ec hniques 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 ( decr ement ; skip if le ss than or equal to ) conditional f uncti on k ey s.
Progr amming T ec hniques 14-19 ii is the interval f or inc r ementing and dec r ement ing (must be two di gits or 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 .
14-20 Programming T ec hniques Pre ss L , then press Z to s ee that the loop–contr ol number is no w 11.
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 .
14 -2 2 Pr ogramming T echniques The INP U T ( I ) ,INP UT (J) and VIEW ( I ) ,VIEW (J) o per ations 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.
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 p.
14 -2 4 Progr amming T ec hniques 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 .
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 .
15-2 Solv ing and Integrating Pr ograms 1. Begin the pr ogr am w ith a label . T his label i dentif ies the f uncti on that y ou want SOL VE to ev aluate ( label ). 2. Include an INP UT instruc tion f or eac h var ia ble , including the unkno wn.
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–entr y mode . Use pr ogra m "G" to solv e fo r the pre ssur e of 0.
15-4 Solv ing and Integrating Pr ograms 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 .
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 .
15-6 Solv ing and Integrating Pr ograms 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.
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 .
15-8 Solv ing and Integrating Pr ograms 2. Select the pr ogram that def ines the f unction to 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 integr ation: k ey in the lo w er limit and pr ess , then k ey in the up per l imi t .
Solv ing and Integrating Pr ograms 15-9 A functi on pr ogr ammed as an equati on is usuall y included 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.
15-10 Solv ing and Integrating Pr ograms 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.
Solv ing and Integrating Pr ograms 15-11 Restr ictions on Solving and Integr ating The SOL VE vari able and ∫ FN d vari ab 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 .
15-12 Solv ing and Integrating Pr ograms.
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 .
16 -2 Statistics Progr ams T o fit logarithmi c c urves, v a lues of x m ust be positi ve. T o fit e xponential c urves , 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 .
Statistics Progr ams 16 -3 Progra m Listing: Progr am Lines: (In RPN mode) Description This r outine s ets, the s tatus f or the str aigh t–line model . Clears f lag 0, the indicator f or ln X . Clears f lag 1, the indicator f or In Y .
16 -4 Statistics Progr ams If flag 0 is set . . . . . . take s the natur al log of the X–input . Stor es that v alue f or the corr ection r ou tine. Prompts f or and stor es Y .
Statistics Progr ams 16 -5 Display s, pr ompts for , and, if changed , stor es x –v alue in X . If flag 0 is set . . . Branc hes to K001 Branc hes to M001 Sto res – val ue in Y .
16 -6 Statistics Progr ams Chec ksum and length: 88 9C 18 This subr outine calc ulates for the logar ithmic model . Cal culates = e ( Y – B ) ÷ M Retur ns to the calling r outine .
Statistics Progr ams 16 -7 Calculates = ( Y / B ) 1/M .
16 -8 Statistics Progr ams Flags Used: F lag 0 is set if a natur al log is r equired of the X inp u t. Fla g 1 i s 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.
Statistics Progr ams 16 -9 13 . F or a new 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 lu e of 3 7 .
16-10 Statistic s Progr ams 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 .
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 .
16-12 Statistic s Progr ams 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 hi ch y ields the giv en pr o babi lity Q(x) .
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. Prompts f or and stor es mean , M .
16-14 Statistic s Progr ams Adds the corr ecti on to y ield a new X gues s . T es ts to see if the co rr ecti on is signif ic ant . Goes back to start of loop if corr ecti on is signif icant .
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 .
16-16 Statistic s Progr ams 4. After the p rompt for S , k e y in the population st andard de v iation and pr es s . (If the standar d dev iati on is 1, ju st pr ess .) 5. To c a l cu l a t e X give n Q ( X ), skip to step 9 of these instructions.
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 .
16-18 Statistic s Progr ams 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 o f data points x 1 , x 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 iati on progr am.
16-20 Statistic s Progr ams Updates in register -30. Increments (or decr ements) N .
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. Pre ss S to start enter ing ne w data . 3. Key i n x i –value (data po int) and pr ess . 4. Key i n f i –v alue (fr equenc y) and press .
16 -2 2 Statistics Progr ams Y ou err ed by ente ring 14 instead of 13 for x 3 . Undo your e rror by exec uting r outine U: G r o u p 1234 56 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: Description: S val u e Pr ompts fo r the f irs t x i .
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 .
16 -2 4 Statistics Progr ams.
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 .
17 -2 Miscellaneous Programs 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 .
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 .
17 -4 Miscellaneous Programs 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.
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 .
17 -6 Miscellaneous Programs and Equations Pa r t 2 . What inter est r ate w ould r educe the monthly pa y ment b y $10 ? Pa r t 3 . Using the calc ulated inter es t rate (6 .
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 .
17 -8 Miscellaneous Programs 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 This r outine displa y s prime n umber P . Checksum and length: 2C C5 6 This r outine ad ds 2 to P .
17 -10 Miscellaneous Programs and Equations Fla gs Use d: None . Progr am Instructions: 1. K ey in the pr ogram r outines; press w hen done . 2. K ey in a positi ve in teger gr eater than 3 . 3. Pr es s P to run pr ogram. Pr ime number , P will be displa y ed .
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 .
17 -12 Miscellaneous Programs 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 o f the cr o ss–pr o duct r outine.
Miscellaneous Programs and Equations 17 -13 Ke ys: Display: D escription: R R un R r ou tine to in put v ec tor v alue .
17 -14 Miscellaneous Programs 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.
A-2 Support, Batteries, and Ser vice 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 .
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.
A-4 Support, Batteries, and Ser vice 5. Insert a new CR20 3 2 lithium battery , making sure that the positi v 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 sur e that the positi v e sign (+) on eac h battery is fac ing outw ar d .
Support, Batteries, and Service A-5 3. Re mov e the bat ter ie s (see "Changing the Batter ies") and lightl y pr es s a coin against both batter y contacts in the calculator . Re place the batteries and turn on the calc ulator . It should display .
A-6 Support, Batteries, and Ser vice → → → 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 .
A-8 Support, Batteries, and Ser vice 6. HP MAKE S NO O THER EXPRE SS W A RRANTY 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 .
Support, Batteries, and Service A-9 Chi na 0 10 -68002 39 7 Hong K ong 28 05- 25 63 Indonesia +6 5 6100 6 68 2 Japan +85 2 28 05- 25 63 Malay sia +6 5 6100 66 8 2 N e w Z e a l a n d 0 9 - 57 4 -270 0.
A-10 Support, Batteries, and Ser vice 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 : Telephone numbers Anguila 1-800-7.
Support, Batteries, and Service A-11 Haiti 18 3 ♦ 800-711- 2 8 8 4 H o nd ur a s 80 0-0- 12 3 ♦ 8 00 - 711- 28 8 4 Jamaica 1-800 - 711 - 2 8 84 Martinica 0 -800 -99 0 -011 ♦ 8 77 - 219-86 71 M e.
A-12 Support, Batteries, and Ser vice 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 .
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.
A-14 Support, Batteries, and Ser vice 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 .
User Memory and the Stack B-1 B User M emory and t he Stack This appendi x co v ers The allocation and requirements of user memory , Ho w to r eset the calc ulator withou t affec ting memory , Ho w to clear (pu rge) all o f us er memory and re set the s y ste m def aults, and Which o perat ions affe ct st ack li ft.
B-2 User Memor y and the Stac k T o see the memor y r equirements of spec ifi c equations in th e equation list: 1. Pr es s to ac ti vate E quation mode . ( or the left end of the c urr ent eq uation w i ll be displa y ed.
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 .
B-4 User Memor y and the Stac k 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 .
User Memory and the Stack B-5 Disabling Operations The f iv e oper ations , / , - , ( ) and ( ) disable st ack 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 .
B-6 User Memor y and the Stac k 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 r egister in RPN mode: Notice that /c does no t affect the LAS T X registe r . The r ecall-arithmeti c sequence Xh varia bl e stor es x in L AS Tx and Xh vari ab le stores the r ecalle d number in L AS Tx.
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 .
B-8 User Memor y and the Stac k.
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 argumen t arithmeti c Exponenti al and Logar ithmic f uncti.
C-2 AL G: Summary 5. Unary 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 .
AL G: Summ ary C-3 P ow er F unctions In AL G mode, to calc ulate a numbe r y rai s ed 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.
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.
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. How eve r , that’s not w hat y ou w ant . 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.
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 e y pr oduces a menu in the displa y— X–, Y–, Z–, T–r egisters , to let you re view the entire conte nts of th e stack . The diff er ence betw een the and the k ey is the locati on of the unde rline in the dis play .
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.
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 c omplex number z . 3. Pre ss 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 .
C-1 0 AL G: Summary 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.
AL G: Summ ary C-11 77 60 8 – 4326 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 u p in the Y–regis ter and X in the X–r egister .
C-12 AL G: Su mmary 4. The display sho w s n the number of st atistical dat a pairs y ou hav e acc umulat ed . 5. Continue en tering x , y –pairs . n is updated w ith each en try . If y ou w ish to delete the incorr ect values that we re j us t enter ed , pr ess z 4 .
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.
C-1 4 AL G: Summary.
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.
D-2 More about Solving If f(x) has one or more local minima or minima , each occ ur s singly between 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 .
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 finds an estimate f or w hic h f(x) equals z ero .
D-4 More about Solving 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: Display: Desc ription: Select E quation mode .
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 functi on's gr aph has a dis continuity 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).
D-6 More about Solving Va l u e s o f f(x) may be appr oaching inf i nity at the location w her e the gr aph 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 .
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 hi ch f(x) equals z er o . Ho we ver , at x = 1 .
D-8 More about Solving 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 : The sear ch terminat es near a local minimum or max imum (s ee fi gur e a , belo 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: Displa y: Description: Selects E quation mode .
D-10 More about Solving 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 .
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: Display: D escription: X Y our negati v e guesse s f or the r oot .
D-12 More about Solving 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.
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 .
D-14 More about Solving.
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 use.
E-2 More about Integration 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 .
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 .
E-4 More about Integration 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 ati on.
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-6 More about Integration 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 .
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 .
E-8 More about Integration 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 , w hic h looks about .
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 .
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 s y mbol comes on to call y our attentio n to the message . F or signif icant conditi ons, the mes sage r emains until y ou c lear it .
F-2 Messag es Indicates the "top" o f equation memory . The memo ry scheme is c ir c ular , so is also the "equatio n" after the last equati on in equati on memory .
Mes s ag es F-3 Exponentiation er r or : Attempted to raise 0 to the 0 th pow er or to a negativ e pow er . Attempted t o r aise a negativ e number t o a non– intege r po w er . Attempted to raise compl e x number (0 + i 0) to a number w ith a negati ve r eal part .
F-4 Messag es SOL VE (include EQN and P G M mode)cannot find 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 .
Mes s ag es F-5 Self–T est Messages: St a ti s ti cs e rro r: Attempt ed to do a s tatisti cs calc ulati on w ith n = 0. Attempted to ca lculate s x s y , , , m , r , or b with n = 1. Attempted to calculate r , or with x –data onl y (all y –values equal to z er o) .
F-6 Messag es.
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 .
G-2 Oper ation I nde x Ø Display s next entry in catal og; mov es to ne xt equation in eq uation list; mo ve s pr ogr am point er to ne xt line (during progr am entry); exec utes the c urr ent pr ogr am line (not dur ing progr am entry) . 1–2 8 6–3 13–11 13–20 Ö or Õ Mov es the cursor and does not delete any content .
Operation Index G-3 Σ x 2 ÕÕÕ ( ) Retur ns the sum of 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 –value s. 12–11 1 Σ y ÕÕ ( ) Retur ns the sum of y –values .
G-4 Oper ation I nde x A thr ough Z var i able V alue of named var iable . 6–4 1 ABS A bsolut e value . Ret urn s . 4–17 1 AC OS Arc cos ine . Ret urns cos –1 x. 4–4 1 AC OS H Hy perbolic ar c cosine . Ret urns cosh –1 x .
Operation Index G-5 b ( ) Indicates a b inary number 11–2 1 Displa ys the bas e–con ve rsion me nu . 11–1 BIN ( ) Selects Binary (base 2) mode.
G-6 Oper ation I nde 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.
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 Caus es the e xpone nt display for the number be ing displa y ed to change in multiple of 3 .
G-8 Oper ation I nde 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 Grads angular mode.
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 great est int eger equal to o r less than giv en number .
G-10 Oper ation I nde x LBL label label La bels a pr ogr am w ith a single lette r for r efer ence b y the XEQ, G T O, or FN= operati ons . (Used onl y in progr ams.) 13–3 LN Natur al logarithm . Ret urn s lo g e x . 4–1 1 LO G Common logarithm .
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 Ac tiv ate s or cancels (t oggles) Progr am–entr y mode .
G-12 Oper ation I nde x RCL+ vari able vari abl e 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 ÷ vari able var iable .
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 Re starts the r andom– number sequence with the seed . 4–15 SF n ( ) n Sets flag n ( n = 0 through 11).
G-14 Oper ation 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 .
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 Th e argumen t 1 r oot of ar gument 2 .
G-16 Oper ation I nde x x = y ? ÕÕÕÕÕ ( ) If x = y , ex ec utes ne xt pr ogr am line; if x ≠ y , skips ne xt progr am line. 14–7 Display s the " x ? 0" c ompar ison tests menu . 14–7 x ≠ 0 ? ( ≠ ) If x ≠ 0, exe cut es next pr ogr am line; if x =0, skips the ne xt pr ogr am line .
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 pow er .
G-18 Oper ation I nde 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 key _.
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 arg.
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.
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.
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.
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, 1.
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.
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 evaluatio.
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, 1.
Index- 10 size limit 2-4, 9-2 unaffected by VIEW 13-15 stack lift. See stack default state B-4 disabling B-4 enabling B-4 not affecting B-5 operation 2-5 standard deviations calculating 12-6, 12-7 grouped data 16-18 normal distribution 16-1 1 standard-deviation menu 12-6, 12-7 statistical data.
Index- 11 solving for 7-1 , 15-1, 15- 6, D-1 storing 3-2 storing from equation 6-12 typing name 1-3 viewing 3-4, 13-15, 1 3-18 vectors absolute value 10-3 addition, subtraction 10-1 angle between two .
Index- 12.
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