Gebruiksaanwijzing /service van het product 35s van de fabrikant HP
Ga naar pagina of 379
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.
Notice REGISTER Y OUR PRODUCT A T: www .r egister .hp .com THI S MANU AL AND ANY EXAMPLES CO NT AI NED HEREIN ARE PRO VI DED “ AS I S” AND ARE SUBJECT T O CHANGE WITHOUT NO TICE.
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 pr inted 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 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.
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. 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 .
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 .
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 .
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 Chapter 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 result of a calc ulation is bey ond this 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 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 .
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 , 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() .
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 .
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 .
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 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 .
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 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.
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 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 .
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 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 .
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 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.
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 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.
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 .
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 .
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 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.
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 .
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 M emor 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 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 .
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 .
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 .
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 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 .
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 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 ).
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 .
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 .
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.
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 .
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 .
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 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 .
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 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 .
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 * .
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 .
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 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.
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 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 .
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 the 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 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 .
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 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).
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 parenthe ses . (F or mor e info rmati on, 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 . 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 .
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 . Select ( ).
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 .
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 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 .
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 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 .
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 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 .
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 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 .
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 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.
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 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 ).
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 a.
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 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 .
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 .
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 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 .
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 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 .
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 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.
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 .
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 comp lex number z 2 as descr ibed befor 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 = 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) .
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: Description: 9 ( ) Sets Degr ee s 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 vector 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 a m 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 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 .
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 .
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.
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 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 .
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 standar d dev iati ons.
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 .
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 .
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.
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 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 .
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.
.
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 ur n to m ar k i ts end (such as ).
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 .
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 retu rn instructi on , w hic h sets the pr ogram point er 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 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).
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 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 .
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 .
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.
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 .
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 .
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 .
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 .
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.
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 .
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.
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 .
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 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 .
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 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 .
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 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.
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 .
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 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 .
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 .
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 ” ” .
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.
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 .
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 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.
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.
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 .
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 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.
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 .
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 .
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 .
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.
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 .
14-20 Programming T echniques Pre ss L , then press Z to see 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 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.
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 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 .
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 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 .
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.
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 .
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 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.
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 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 .
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.
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.
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 .
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 .
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 .
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 .
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.
Statistics Progr ams 16 -7 Calculates = ( Y / B ) 1/M .
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.
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 .
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 .
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 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) .
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 .
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 .
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 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 .
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 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 , .
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 .
16-20 Statistics Pr ograms Updates in r egister -30. Increments (or decr ement s) 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. 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 .
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 .
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 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 .
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 .
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 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.
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 .
.
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 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 .
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 .
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 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 .
17 -14 M iscellaneous Progr ams and Equations.
Pa r t 3 Appendix es and Ref er ence.
.
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 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 .
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 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 .
.
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 .
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 M.
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 -27.
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 .
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 .
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 .
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 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 .
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.
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.
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 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 .
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 .
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.
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 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.
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 .
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.
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. 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.
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 .
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 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 .
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 ampl.
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 .
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 .
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: 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.
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 .
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.
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 .
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).
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 .
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 .
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).
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 .
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 .
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.
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 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 use.
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 .
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 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 .
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 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 .
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 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 abou.
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 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 .
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 .
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 .
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 .
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) .
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 .
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 .
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 .
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 .
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.
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.
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 .
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.
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 .
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 .
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 .
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 .
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).
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 .
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 .
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 .
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 .
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 _.
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.
Een belangrijk punt na aankoop van elk apparaat HP 35s (of zelfs voordat je het koopt) is om de handleiding te lezen. Dit moeten wij doen vanwege een paar simpele redenen:
Als u nog geen HP 35s heb gekocht dan nu is een goed moment om kennis te maken met de basisgegevens van het product. Eerst kijk dan naar de eerste pagina\'s van de handleiding, die je hierboven vindt. Je moet daar de belangrijkste technische gegevens HP 35s vinden. Op dit manier kan je controleren of het apparaat aan jouw behoeften voldoet. Op de volgende pagina's van de handleiding HP 35s leer je over alle kenmerken van het product en krijg je informatie over de werking. De informatie die je over HP 35s krijgt, zal je zeker helpen om een besluit over de aankoop te nemen.
In een situatie waarin je al een beziter van HP 35s bent, maar toch heb je de instructies niet gelezen, moet je het doen voor de hierboven beschreven redenen. Je zult dan weten of je goed de alle beschikbare functies heb gebruikt, en of je fouten heb gemaakt die het leven van de HP 35s kunnen verkorten.
Maar de belangrijkste taak van de handleiding is om de gebruiker bij het oplossen van problemen te helpen met HP 35s . Bijna altijd, zal je daar het vinden Troubleshooting met de meest voorkomende storingen en defecten #MANUAl# samen met de instructies over hun opplosinge. Zelfs als je zelf niet kan om het probleem op te lossen, zal de instructie je de weg wijzen naar verdere andere procedure, bijv. door contact met de klantenservice of het dichtstbijzijnde servicecentrum.
