HP (Hewlett-Packard) HP 33s manual

h p 3 3s sc ientif ic calc ulator us er' s g uid e H Edition 3 HP part number F2216-90001[...]

Notice REGISTER YOUR PRO DUCT AT: www.register.hp.com THIS MANUAL AND AN Y EXAMPL ES CONTAIN ED HER EIN ARE PROVIDED “AS IS” A ND ARE SUBJECT TO C HANGE WITHOUT NOTICE. HEWLETT- PACKARD COM PANY MAKE S NO WAR RANTY O F ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WA RRANTIES OF MERCHANTABILITY, NON-INFRINGEMEN[...]

Contents 1 Contents Part 1. B a s i c O p e ra t i o n 1 . Gett in g S tar ted Important Prelim inar ie s ....................................................... 1–1 T urning the C alcu l ator On a nd Off ................................. 1–1 Adj u st ing Disp la y Contr ast ............................................ 1–1 Hi ghli ghts o f th[...]

2 Contents P er iods and C ommas in N umber s................................ 1–18 Number o f De c imal P laces ......................................... 1–19 SHO Wing F ull 12 –Dig it Pr ec isi on ................................ 1–20 F r acti ons ........................................................................ 1–21 Enter ing F r[...]

Contents 3 3 . S to r i n g D a t a int o V ariables Stor ing and R ecalling Numbers ........................................... 3–2 V ie w ing a V ari able w ithout R ecalling It ................................. 3–3 R e v ie wing V aria bles in the V AR Catalog ............................... 3–3 Clear ing V aria ble s .....................[...]

4 Contents F ac tor i al .................................................................. 4–14 Gamma................................................................... 4–14 Pr oba bility ............................................................... 4–14 P arts of Nu mbers ............................................................ 4–16[...]

Contents 5 E diting and C learing E quations ........................................... 6–7 T ypes o f E quations............................................................. 6–9 Ev al uating E quati ons.......................................................... 6–9 Using ENTER f or E v aluation ........................................ 6–11[...]

6 Contents Using Comp le x Nu mbers in P olar Notati on........................... 9–5 1 0 . Base Conversions an d Arithmetic Ar ithmeti c in B ase s 2 , 8, and 16....................................... 10–2 The R epresentati on o f Number s......................................... 10–4 Negati ve Number s......................................[...]

Contents 7 Selecting a M ode ...................................................... 12–3 Pr ogr am Bou ndar ie s (LB L and R TN) .............................. 12–3 Using RPN , AL G and Equ ations in Pr ograms .................. 12–4 Data Inpu t and Output ............................................... 12–4 Enter ing a Pr ogram ...........[...]

8 Contents Se lecting a B ase Mode in a Pr ogram ......................... 12–2 2 Number s Ente r ed in Pr ogr am Line s ............................ 12–2 3 P oly nomial Expr es sions an d Hor ner's Method ................... 12–2 3 1 3 . Progr amming T ec hniques R outine s in Pr ograms ..................................................[...]

Contents 9 1 5 . Ma thematics Progr ams V ector Oper ati ons ........................................................... 15–1 Soluti ons of Sim ultan eou s E quati ons ................................. 15–12 P oly nomial R oot F inder ................................................... 15–20 Coor dinate T ransf o rmati ons ...................[...]

10 Contents R es etting the C alc ulator ..................................................... B–2 Clear ing Memory ............................................................. B–3 T he S tatu s of St ack L if t ....................................................... B–4 Disa bling Oper ations ................................................[...]

Contents 11 Underfl ow ...................................................................... D–14 E . More about Integ r ation Ho w the Integral Is E v alu ated .............................................. E–1 Conditi ons T hat Cou ld Cau s e Incorr ect Re sults ....................... E–2 Condit ions T hat Pr olong C alc ulati on T ime ..[...]

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Part 1 Basic Operation[...]

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Getting Sta r te d 1–1 1 Getting St ar t e d v Watch for thi s symbol in the margin. It identifie s exam ple s or keyst rokes th at are show n in RP N mode and m ust be perfo rmed di fferentl y in A LG mode. App endix C expl ains ho w to use yo ur c alcula tor in A LG mo de. Important Preliminar ies T u rn i n g t h e C a l c u l a t o r O n a n [...]

1–2 G et tin g Star ted H i g h l i g h t s o f t h e Key b o a rd a n d D i s p l a y S h i f t e d Key s Each key has three functions: one printed on its face, a left–shifted f u n c t io n (Green), an d a right–shi fted function (P urple). The shifted function names are printed in green and purple above each key. Press the appropri ate shi[...]

Getting Sta r te d 1–3 Pressing { or | turns on t he corresponding ¡ or ¢ annu nciator symbol at the top of the display. The ann unciator remains on until you press the next key. To cancel a shift key (and turn off its annunciator), press the same shift key again. A l p h a Keys Ri ght- shi fted fun ct io n Le ft-shifted func tion Letter for al[...]

1–4 G et tin g Star ted S i lv e r Pai n t Key s Those eight silver paint keys have their specific pressure points marked in blu e position in the illustration below. To use those keys, make sure to press down the corresponding position for the desired function. B a c k s p a c i n g a n d C l e a ri n g One of the first things you need to know i[...]

Getting Sta r te d 1–5 K e ys f o r C l e a r i n g K e y D e sc r i pt i on b Backspace.  K ey boar d –entry mode: Eras es the char acter immediately to t he left of "_" (the digit–entry curs or ) or backs out o f the curr e nt menu . (Men us ar e desc r ibed in "Using Menus" on page 1–7.) If the number is complet[...]

1–6 G et tin g Star ted K e ys f o r C l e a r i ng ( co n t i n u e d ) K e y D e sc r i pt i on {c The CLEAR menu ({ º } { # } {  } { ´ }) Contains options for clear ing x (the number in the X –register), all variables, all of mem ory, or all statistical data. If you select {  }, a new menu (  @ { &[...]

Getting Sta r te d 1–7 U s i n g M e n u s There is a lot more power to the H P 33s than what you see on th e keyboard. This is because 14 of the keys are menu keys. There are 14 menus in all, whic h provide many mor e function s, or mor e options for more functio ns. HP 3 3 s M e nu s M e nu N a m e M e nu Des crip tion C ha p t er Nu m e r i c [...]

1–8 G et tin g Star ted H P 3 3 s M e n us ( c o n ti n u e d ) M e nu Na m e M e nu Description C ha p t e r O th e r fu n c t i o n s MEM #  Memory status (bytes of m emory available); catalog of variables; catalog of programs (program labels). 1, 3, 12 MODES    * 8 Angular modes an d " ) "[...]

Getting Sta r te d 1–9 Example: 6 ÷ 7 = 0.857142857 1… K e ys : D is p l a y : 6  7 q %       ({   }) ( or  ) )   . Menus help you execute dozens of fu nctions by guiding you to them with menu choices. You don't have to rem[...]

1–10 G et t i n g Star ted R P N a n d A L G K e y s The calculator can be set to pe rform arithmetic operations in either R PN (Reverse Polish Nota tion ) or AL G (Algeb raic) mo de. In Reverse Polish Notation (RPN) mode, the intermediate results of calculations are stored automatically; hence, you do not have to use parentheses. In algebraic ( [...]

Getting Sta r te d 1–11 Th e D i s p l ay a n d A n n u n c i a t o r s Fir st Lin e Sec on d Li ne Annunc ia tors The display comprises two lines and annunciator s . The first line can display up to 255 characters. Entries with m ore than 14 characters will scroll to the left. However, if entries are m ore than 255 characters, the characters f r[...]

1–12 G et t i n g Star ted H P 3 3 s A n n un c i a t o rs A nn u n c i a t or M e an i ng C ha p t er £ The " £ (Busy)" an nunciator blin ks while an operation, equation, or program is executing. c d  When in Fractio n–display mode (press {  ), only one of the " c " or " d " halves of the " cd &quo[...]

Getting Sta r te d 1–13 H P 3 3 s A n n u nc i a t o r s ( c o n t i n ue d ) A nn u n c i a t or M e an i ng C ha p t er § , ¨ The  or  keys are active to scroll the display, i.e. there are more digits to the left and righ t. (Equation– entry and Program– entry mode aren’t i ncluded) Use | to see the rest of a decimal number; us[...]

1–14 G et t i n g Star ted Keyi n g i n N u m b e r s You can key in a number that has up to 12 di gits plus a 3–d igit exponent up to ±499. If you try to key in a number l arger tha n this, d igit entr y halt s a n d t h e ¤ annunciator briefly appears. I f you make a mistake while k eying in a numb er, pre ss b to backspace and delete t he [...]

Getting Sta r te d 1–15 Keying in Exponents of Te n Use a ( expo nent ) to key in numbers m ultiplied by powers o f ten. For example, take Planck's constant, 6.6261 × 10 –34 : 1. Key i n t h e mantis sa (the non –exp onent part) of the number . If the m an t i s sa i s nega tiv e , press ^ af ter ke ying in its di git s. K e ys : D is p[...]

1–16 G et t i n g Star ted Keys: Display: Description: 123  _ Digit entry not t er minated: the nu mber is not complete. If you ex ecute a function to calculate a result , the cursor disappears because the number is complete — digit ent ry has been terminated. # ) Digit entry is terminated. Pressing  terminates [...]

Getting Sta r te d 1–17 O n e – N u m b e r Fu n c t i o n s To use a one–number function ( such as  , # , ! , { @ , {$ , | K , {  , Q or ^ ) 1. Ke y i n t h e n u mbe r . ( Y ou don't need to press  .) 2. Pr ess the func tion k ey . (F or a shifted functi on, pr e ss the appr opr iate { or | shift k e y f irs t .) For [...]

1–18 G et t i n g Star ted For example, T o c a l cu l a te : P re s s : D is p l a y : 12 + 3 12  3  )  12 – 3 12  3  ) 12 × 3 12  3 z )  12 3 12  3  8)  Percent change from 8 to 5 8  5 |T .)  The order of entry [...]

Getting Sta r te d 1–19 N u m b e r o f D e c i m a l Pl a c e s All numbers are stored with 12–digit precision, but you can select the number of decimal places to be displaye d by pressing  (the displa y menu). Du ring some complicated internal calculations, the calculator uses 15–digit precision for intermediate results. The displayed nu[...]

1–20 G et t i n g Star ted Engineering F ormat ({  }) ENG format disp lays a numb er in a manner similar to scientific no tation, excep t that the exponent is a m ultiple of three (there can be up to three dig its before the " ) " or " 8 " radix mark). This format is most useful for scientific and engineer ing calcula[...]

Getting Sta r te d 1–21 For example, in the n umber 14.8745632019, you see on ly "14.8746" when the display mode is set to FIX 4, but the last si x digits ("632019") are present internally in the calculator. To temporarily display a number in full precision, press | . Th is show s you the mantissa (bu t no exponent) o f the[...]

1–2 2 G e t t i ng Star ted 2. K ey in the fraction numerator and pres s  ag ai n. The second  sepa r ates the n umer ato r fr om t he deno minat or . 3. K ey in the denominato r , then pres s  or a function key to t e r m i n a t e digit entry . T he numb er or r esul t is f orma tte d a cco r d ing to the current display format. The ab[...]

Getting Sta r te d 1–23 D i s p l ayi n g Fr a c t i o n s Press { to switch between Fraction– display mode and the c u r r e n t decima l displ ay mode . K ey s : D is p l a y : De s c ri p t i o n : 12  3  8  + _  Displays characters as you key them in.  ) Terminates dig it entry; displays th[...]

1–2 4 G et t i n g Started C a l c u l a t o r M e m o r y The HP 33s ha s 31KB of me mor y in which y ou can sto re any co mbination o f data (variables, equations, or progr am lines). C h e c k i n g Av a i l a b l e M e m o r y Pressing {Y displays the following menu: #  8 Where 8 is the[...]

RPN: The Automatic Memor y Stack 2–1 2 RPN: The Automati c Memory Stack This ch apter explains how calculations take place in the automatic memory stack in RPN mod e. You do not need to rea d and understan d this material to use th e calculator , but understanding the material will greatly en hance your use of the calculator, especially when prog[...]

2–2 RPN: The Automatic Memory Stack T 0.0000 "O ldest " n umb er Z Y X Displa yed 0.0000 0.0000 0.0000 Displa yed The most "recent" number is in the X–register: this is the nu mber you see in the second line of the display. In programming, the stack is used to pe rform ca lculations, to temporarily store intermediate results[...]

RPN: The Automatic Memor y Stack 2–3 R ev i ew i n g t h e S t a c k R ¶ (Roll Down) The (rol l dow n) key lets you rev iew the e ntire co nten ts of the s ta ck b y "rolling" the contents downward, one register at a time. Yo u ca n se e e a ch numb er when it enters th e X–r egist er. Suppose the stack is filled with 1, 2, 3, 4. (pr[...]

2–4 RPN: The Automatic Memory Stack Exchanging the X– and Y–Registers in the Stack Another key tha t manipula tes the stack co ntents is [ ( x exchange y ) . This key swaps the contents of the X– and Y–reg isters without affecting the rest of the stack. Pressing [ twice restores the orig inal order of the X– and Y–register co ntents. [...]

RPN: The Automatic Memor y Stack 2–5 3. The stack dr ops.  Notice that w hen the s tack lifts, it r eplace s the conte nts of the T– (top) r egist er with the cont ents of the Z–re gister , and th at the form e r conte nts of the T– registe r are l ost. Y o u ca n se e, th erefore, that th e sta ck's memo ry is l im it ed to four[...]

2–6 RPN: The Automatic Memory Stack Using a Nu mber Twice i n a Row You can use the replicating featu re of  to other advantages. To add a number to itself, press  . Filling the s tack w ith a c onsta nt The replicatin g effect of  together with the replicating effect of stack drop (from T into Z) allows you to f ill the stack with a [...]

RPN: The Automatic Memor y Stack 2–7  D uri n g p rog ra m e nt r y , b deletes the curr e ntly–displa y ed pr ogram line and  cancels pr ogr am entry .  During digit entry , b backspaces o ver the displa y ed number .  If the disp la y sho w s a labeled nu mber (su ch a s /) ) , pressi ng  or b cancels[...]

2–8 RPN: The Automatic Memory Stack 2. Re using a number i n a calculation . See appendix B for a comprehensive list of the functions that save x i n t he LAST X register. C o rr e c t i n g M i s t a ke s wi t h L A ST X Wrong One–Num ber Function If you execu te t he w r o n g one–number function, u se { to retrieve the nu mb er so y o u[...]

RPN: The Automatic Memor y Stack 2–9 Example: Suppose you made a mistake while calculating 16 × 19 = 304 There are three kinds of mistakes you cou ld hav e ma de : Wr o n g Calculation: M is t a k e : C or r e c t io n : 16  19  Wrong function {  { z 15  19 z Wrong first nu mber 1 6 { z 16  18 z Wrong second number {?[...]

2–10 RPN: The Automatic Memory Stack T ttt Z zz t 96. 7 04 Y 96 . 7 04 0 96 . 70 4 0 z X 96 . 70 4 0 52. 3 94 7 52. 3 9 47 149 .098 7 LAS T X ll 52. 3 94 7 T tt Z zt Y 149 . 09 8 7 z X 52. 3 94 7 2. 8 4 57 LAS T X 52. 3947 52.3 947 K ey s : D is p l a y : De s c r ip t i o n : 96.704  ) Enters first number. 52.3947  [...]

RPN: The Automatic Memor y Stack 2–11 9.5 a 15 )   _  Speed of light, c . z )   Meters to R. Centaurus. 8.7 { )   Retrieves c . z )   Meters to Sirius. Chain Calculations in RPN mode In RPN mode, the automatic lifting and dropping of the stack&ap[...]

2–12 RPN: The Automatic Memory Stack Now study the following examples. Remember that you need to press  only to separate sequentially–entered numbers, su ch as at the beginni ng of a problem The operations themselves (  ,  , e tc .) separate subsequent numbers and save intermediate results. The last result saved is the fi rst one retri[...]

RPN: The Automatic Memor y Stack 2–13 E xe rc i s e s Calc ul at e: 0000 . 181 05 . 0 ) 5 3805 . 16 ( = x Solution: 16.3805  5 z# .05 q Calc ul at e: 5743 . 21 )] 9 8 ( ) 7 6 [( )] 5 4 ( ) 3 2 [( = + × + + + × + Solution: 2  3  4  5 z# 6  7  8  9 z # Calc ul at e: (10 – 5) ÷ [ (17 – 12) × 4] = 0.2500 Solution[...]

2–14 RPN: The Automatic Memory Stack This method takes one addi tional keystroke. Notice that th e first intermediate result is still the innermost parenthes es (7 × 3). The a dvantage to worki ng a problem left–to–r ight is that you d on't ha ve to use [ to reposition operands for nomcommu taiive fu nctions (  and q ). However, the [...]

RPN: The Automatic Memor y Stack 2–15 A Solution: 14  12  18  12 z 9  7 q Calc ul at e: 23 2 – (13 × 9) + 1/7 = 4 12.1429 A Solution: 23 ! 13  9 z 7  Calc ul at e: 5961 . 0 ) 7 . 0 5 . 12 ( ) 8 . 0 4 . 5 ( 3 = − ÷ × Solution: 5.4  .8 z .7  3  12.5 [  q# or 5.4  .8 z 12.5  .7  3 q#[...]

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S t o r i n g D a t a into Variables 3–1 3 Storing Data i n t o V a r i ab l e s The HP 33s has 31KB of user memory : memory that you can u se to store numbers, equations, and program lines. Numbers are stored in locations called variables , each named with a letter from A through Z . ( You can choose the letter to remind you of what is stored th[...]

3–2 Storing Data into Var iables Each black letter is associ ated with a key and a unique vari able. The letter keys are automatically active when needed. (The A..Z annun ciator in the display confirms this. ) Note that the variables, X , Y , Z and T are different storage locations from the X–register, Y–register, Z–register, and T–regist[...]

S t o r i n g D a t a into Variables 3–3 Vi e wi n g a Var i a b l e w i t h o u t R e c a l l i n g I t The | function shows you the conten ts of a variable without puttin g that number in the X–register. The display is labeled for the variable, such as: / ) In Fraction–di splay mode ( { ), part of the [...]

3–4 Storing Data into Var iables C l e a r i n g V ar i a b l e s Variables' values are retained by Continuous Memory until you replac e them or clear them. Clearing a variable stores a zero there; a value of zero takes no memory. To clear a single variable: Store zero in it: Press 0 I variable . To clear selected variable s: 1. Press {Y { #[...]

S t o r i n g D a t a into Variables 3–5 A 15 A 12 Re s u l t : 1 5 3 t h a t i s , A x T t T t Z z Z z Y y Y y X 3 X 3 R e c a l l A ri t h m e t i c Recall arithmet ic uses L , L , Lz , or Lq to do arithmetic in the X –register using a recalled number and to le ave the result in the display. Only the X–register is affected. New x = Pr[...]

3–6 Storing Data into Var iables K ey s : D i s p l a y : De s c ri p t i o n : 1 I D 2 I E 3 I F ) ) ) Stores the assumed values into the variable. 1 I D I E I  F   ) Adds1 to D , E , and F . | D / ) Displays the current value of D .[...]

S t o r i n g D a t a into Variables 3–7 |Z A )  Exchanges contents of t he X–register an d variable A. |Z A ) Ex changes contents of the X–register an d variable A. A 12 A 3 T t T t Z z Z z Y y Y y X 3 X 12 Th e Var i a b l e " i " There is a 27th variable that you can access directly — t he[...]

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Real–Number Functions 4–1 4 Real–Number Functions This chapter c overs most of the calculator's functions th at perform computations on real numb ers, includi ng some numeric functio ns used i n progr ams (such a s ABS, the absolute–value function):  Exponenti al and logar ithmi c f unc tio ns.  Q uo tie nt and Rem ai n der[...]

4–2 Real–Number Functions T o C al c u la t e : P re s s : Natural logarithm ( base e )  Common logar ithm (ba se 10) { Natural ex ponential  Common exp onentia l (antilo garithm) { Q u o t i e n t a n d R e m a i n d e r of D iv i s i o n You can use {F and |D to produce either the quotient or remainder o f division o perations inv[...]

Real–Number Functions 4–3 In RPN mode, to calculate a number y raised to a power x , key in y  x , then press  . (For y > 0, x can be any nu mber; fo r y < 0, x must be an odd integer; for y = 0, x must be positive.) To Calculate: Press: Result: 15 2 15 ! ) 10 6 6 { 88 ) 5 [...]

4–4 Real–Number Functions S e t t i n g t h e A n g u l a r M o d e The angular m ode specifies which uni t of measure to assume for ang les used in trigonometric functio ns. The mode does not convert numbers already present (see "Conversion Funct ions" later in this chapter). 360 degrees = 2 π radi ans = 400 grads To set an angular [...]

Real–Number Functions 4–5 Example: S h o w t h a t c o s i n e ( 5 / 7 ) π radians and cosine 128.57° are equa l (to four sign ificant digits). Keys: Display: Description:  {  }  Sets Radians mode; RA D annunciato r on.  5  7  ) 5/7 in decimal format. |NzR .) Cos (5 /7) π .  { ?[...]

4–6 Real–Number Functions Hy per bolic F unctions With x in the disp lay: To Calculate: Press: Hyperbolic sine of x (SINH). { O Hyperbolic cosin e of x (COSH). { R Hyperbolic tangent of x (TANH). {U Hyperbolic arc sin e of x (ASIN H). { { M Hyperbolic arc cosi ne of x (AC OSH). {{ P Hyperbolic arc tang ent of x (ATA NH). { { S[...]

Real–Number Functions 4–7  ) Total cost (base price + 6% tax) . Suppose that the $1 5.76 item c ost $16.12 last year. What is the perc entage change from last year' s price to this year's ? Keys: Display: Description: 16.12  ) 15.76 |T .) This year's price dropped a bout 2.2% from l[...]

4–8 Real–Number Functions Ph y sics Constants There are 40 physics constants in the CONST menu. You can press |  to view the following items. C ON S T M e n u It e m s Desc ripti on Val ue { F } Speed of light in vacuum 299792458 m s –1 { J } Standard acceleration of gravi ty 9.80665 m s –2 {  } Newtonian co nstant of gravit ation [...]

Real–Number Functions 4–9 It e m s Desc ripti on Val ue { TH } Classical electron radius 2.817940285 × 10 –15 m { ' µ } Characteristic im pendence of vacuum 376.730313461 Ω { λ F } Compton wavelengt h 2.426310215 × 10 –12 m { λ FQ } Neutron Compto n wavelength 1.319590898 × 10 –15 m { λ FR } Proton Compton waveleng th 1.3214[...]

4–10 Real–Number Functions C o o rd i n a t e C o nv e r s i on s The function names for these co nversions are y , x Æ θ , r and θ , r Æ y , x . Polar coordinates ( r , θ ) and rectangular coordin ates ( x , y ) are measured as shown in the illustration. The a ngle θ uses units set by the current ang ular mode. A calculated result for θ[...]

Real–Number Functions 4–11 Example: Polar to Rect an gular Con vers ion. In the following right triangles, find sides x and y in the triangle on the left, and hypotenu se r and angle θ in the triangle on the right. y 10 30 o x r 4 3 θ Keys: Display: Description:  {  }  Sets Degrees mode. 30  10 |s ) Calcu l[...]

4–12 Real–Number Functions R C R X c _ 36.5 o 77 .8 ohm s θ Keys: Display: Descript ion:  {  }  Sets Degrees mode. 36.5 ^ .) Enters θ , degrees of voltage lag . 77.8 ) _ Ente rs r , ohms of total impedance. |s ) Ca lculates x , ohms resistance, R . [ .) [...]

Real–Number Functions 4–13 |u ) Equals 8 minutes and 34.29 seconds.  { % } 4 ) Restores FIX 4 display format. A n g l e C o nv e r s i on s When converting to radian s, the number in the x–register is assumed to be degrees; when converting to degrees, the number in the x–re gister is assume[...]

4–14 Real–Number Functions P ro b a b i l i t y F u n c t i o n s Fa c to ri a l To calculate the factoria l of a displayed non- negative integer x (0 ≤ x ≤ 253), press { (the left–s hifted  key). G a m m a To calculate the gamma fu nctio n of a no ninteger x , Γ ( x ), key in ( x – 1) and press { . The x ! function calculates[...]

Real–Number Functions 4–15 The RANDOM fu nction uses a seed to generate a random numb er. Each random number generated becomes the seed for the next rand om number. Therefore, a sequence of random numbers can be repeated by starting with the same seed. You can store a new seed with the SEED function. If memory is clear ed, the seed is reset to [...]

4–16 Real–Number Functions P a r t s o f N u m b e r s These functions are primarily used in progra mming. Integer part To remove the fracti onal part of x and replace it with zeros, press |" . (For example, the integ er part of 14.2300 is 14.0 000.) Fractional part To remove the integer part of x and replace it with zeros, press |? . (For[...]

Real–Number Functions 4–17 N a m e s o f F u n c t i o n s You migh t have noticed that the name of a function appears in the display when you press and hold the key to e xecute it. (The name remains displayed for as long as you hold the ke y down.) For in stance, while pressing O , the display shows  . "SIN" i s the name of the[...]

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Fracti ons 5–1 5 Fractions "Fractions" in chapter 1 introduc es the basics about entering, di splaying, and calculating wi th fractions:  T o enter a fracti on, pr e ss  tw ice — after the integer part, and betw een the numerator and denominator . T o enter 2 3 / 8 , pre ss 2  3  8 . T o e nt er 5 / 8 , pr ess  5 [...]

5–2 Fractions If you didn' t get the same results as the example, y ou may have acc identally changed h ow fractions are displayed. (See "Chang ing the Fraction Display" later in this chapt er.) The next topic includes more examples of valid an d invalid i nput fractions. You can type fracti ons only if the n umber base is 10 — t[...]

Fracti ons 5–3 E nt e r e d V a l u e I nt e r n a l V al u e Di s p l ay e d F r a c t i o n 2 3 / 8 2.37500000000  + 14 15 / 32 14.4687500000  + 54 / 12 4.50000000000  + 6 18 / 5 9.60000000000  + 34 / 12 2.83333333333  + T 15 / 8192 0.00183105469  + S 1234[...]

5–4 Fractions This is espec ially important i f you change th e rules about h ow fractions are displayed. (See "Chang ing the Fraction Display" later.) For ex ample, if you forc e all fractions to have 5 as the denominator, then 2 / 3 is displayed as  +  c because the exact fraction is approxim ately 3.3333 / 5 , "a little[...]

Fracti ons 5–5  Y ou can select one of thr ee fr action f or mats. The next few topi cs show how to change the fraction display. Setting th e Maximum Denominat or For any fraction , the denominator is selected based on a value stored in the calculator. If you thi nk of fractions as ab / c , then /c corresponds to the value that controls the[...]

5–6 Fractions To select a frac tion format, you m ust change the states of two fla g s . Each fla g can be "set" or "clear," and in one case the state of fl ag 9 doesn't matter. C ha n g e T h e se F l a g s : T o G e t T h is F r a c ti o n F o r m a t : 8 9 Most precis e Clear — Fact ors of d en omi nat or Set Clear F[...]

Fracti ons 5–7 N u mb e r En t e r e d an d F r a c t i o n D i s p l a ye d F ra c t i o n F o r ma t ¼ 2 2.5 2 2 / 3 2.99 99 2 16 / 25 Most precis e 2 2 1/ 2 2 2/3 S 3 T 2 9/14 T Fact ors of denomi nator 2 2 1/ 2 2 11/1 6 T 3 T 2 5/8 S Fixed denomi nator 2 0/16 2 8/ 16 2 11/1 6 T 3 0/16 T 2 10/ 16 S ¼ For a /c value of 16. Example: Suppose a [...]

5–8 Fractions In an equation or program, the RND function does fracti onal rounding if Fraction–di splay mode is activ e. Example: Suppose you h ave a 56 3 / 4 –i nch space th at you want to divi de into six equ al sections. How wide is eac h sectio n, assuming y ou can conveni ently measu re 1 / 16 –inch incr ements ? W hat's the cumu[...]

Fracti ons 5–9 Fra c t i o n s i n P r o g ra m s When you're typi ng a program , you can type a number as a f raction — but it' s converted to its dec imal value. All numeric values i n a prog ram are shown as decimal values — Fracti on–display mode is ig nored. When you're run ning a program, displayed v alues are shown usi[...]

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Entering and Evaluating Equatio ns 6–1 6 Entering and Evaluating Equations H ow Y ou C a n U s e E q u a t i o n s You can use equation s on the HP 33s in several ways:  F or sp ecify ing an eq uation to e valuate (this cha pter ).  F or sp ecify ing an eq uation to s olv e f or unkno w n va lues (cha pter 7).  F or spec ify ing[...]

6–2 Entering and Evaluating Equations L ¾ Begins a new equ ation, turning on the " ¾ " equation– entry cursor. L turns on the A..Z annunciator so you ca n enter a variable name. V |d #/¾ L V types # and mov es the cursor to the right. .25 #/) _  Digit entry uses the "_" digit–entry cursor. z|Nz #/?[...]

Entering and Evaluating Equatio ns 6–3 Summary of Equation Oper ations All equations you create are saved in the equation list. This list is visible whe never you activate Equation mode. You use certain keys to perform operations involving equations. They 're described in more detail later. K ey O pe r a ti o n |H Enters and leaves Equation [...]

6–4 Entering and Evaluating Equations Entering Equations int o the Equation List The equation list is a collection of eq uations you enter. The list is saved in th e calculator's memory. Each equation y ou enter is automatically saved in the equation list. To enter an equatio n: 1. Make sur e the calculator is in its normal operating mode , [...]

Entering and Evaluating Equatio ns 6–5 N u m b e r s i n E q u a t i o n s You can enter any valid numbe r in an equati on except fracti ons and numbers that aren't base 10 numbers. N umbers are always shown using ALL displa y format, which di splays up to 12 characters. To enter a number in an equat ion, you can use th e standard number–e[...]

6–6 Entering and Evaluating Equations Pare n t h e s e s i n E q u a t io n s You ca n include parentheses in equatio ns to control the order in which opera tions are performed. Press |] and |` to insert parentheses. (For more information, see "Operator Precedence" later in this chapter.) Example: Entering an Eq uation. Enter the equati[...]

Entering and Evaluating Equatio ns 6–7    ! ! if there ar e no eq uati ons in the eq uation li st or if th e equa tion pointer is at the top of the lis t .  T he cur r ent equ ation (the last e qu ation y ou v ie w ed). 2. Pr es s  or  to step t hr ough the eq uation lis t and v ie w eac h equati on. T he li[...]

6–8 Entering and Evaluating Equations To edit an equation you're typing : 1. Pre ss b r epeatedly until y ou delete the unw anted number or fu nction . If you'r e typ ing a decimal number and the "_ " digit–entr y cu rsor is on , b deletes only the r i ghtmost c hara cter . If you delete all c harac ters in the number , the [...]

Entering and Evaluating Equatio ns 6–9 Keys: Display: Description: |H /ºº 1!.2 Shows the current equation in t he equation list. b º 1!. 2- ¾  Turns on Equation –entry mode and shows the " ¾ " cursor at the end of the equation. bb /ºº 1 !.2 ¾  Deletes the number 25. ?[...]

6–10 Entering and Evaluating Equatio ns Because many equati ons have two sides separated by "=", the basi c value of an equation is the difference between the values of the two sides. For this calculation, "=" in an eq uation essentially t reated as " ಥ ". The val ue is a measure of how well the equation balanc es.[...]

Entering and Evaluating Equatio ns 6–11 The evaluation of an equation takes no values from the st ack — it uses only numbers in the equation and variable values. The valu e of the equation is retu rned to the X–register. The LAST X register isn't affected. U s i n g E N T E R fo r E v al u a t i o n If an equation is displayed in the equ[...]

6–12 Entering and Evaluating Equatio ns a 6 q )  Changes cubic mi llimeters to liters (but doesn't change V ). U s i n g X E Q fo r E va l u a t i o n If an equation i s displayed in the equation list, you can press X to evaluate the equation. The entire equation is evaluated, regardless of the type of equation. The resu[...]

Entering and Evaluating Equatio ns 6–13  To c h a n g e t h e n u m b e r, t ype the ne w number and press g . This ne w number w r ites o ver the old value in the X–r egister . Y ou can enter a nu mber as a frac tion if you w an t. If y ou need to calc ulate a number , use normal keybo a rd c a lc ul at i o n s, t h e n p res s g . F or [...]

6–14 Entering and Evaluating Equatio ns O r de r O pe r a ti o n E xa m pl e 1 Functions and Parenth eses 1%- 2 , 1%-2 2 Power (  ) %: 3 U na r y M in u s ( ^ ) . 4 Multiply and Divide %º& , ª 5 Add and Subtract - , . 6 E q u al it y / So, for example, all operat ions inside par[...]

Entering and Evaluating Equatio ns 6–15 Equation Func tions The following table lists the functions that are valid i n equations. Appendi x G, "Operation Index" also gi ves this information . LN LOG EXP A LOG SQ SQRT INV IP FP RND ABS x! S G N IN TG IDIV RMD R SIN C OS TAN ASIN ACOS ATAN SINH COSH TANH ASINH ACOSH ATANH  DEG  RAD [...]

6–16 Entering and Evaluating Equatio ns 01.%(.2 01%(1.&22 Eleven of the equation functi ons have names that differ from their equivalent operations: Operation Equation function x 2 SQ x SQRT e x EXP 10 x ALOG 1/x IN V X y XROOT y x ^ IN T ÷ IDIV Rmdr RM D R x 3 CB 3 x CBRT Example: P erime ter o f a Tr apezoi d. Th[...]

Entering and Evaluating Equatio ns 6–17 Single letter name No impl ied multipli cati on D i v i s i o n i s d o n e befor e addition P ar ent hes es used to g rou p it e m s P=A+B+Hx(1 S IN(T)+1 S IN(F )) Ί Ί Th e next equation also obeys the syntax rules. This equation uses the inverse function, #1 1!22 , instead of the f ractional[...]

6–18 Entering and Evaluating Equatio ns Syn t a x E r ro r s The calculator doesn't check the syntax of an equation until you eval uate the equation and respon d to all the prom pts — only when a val ue is actually bei ng calculated. If an error is detected, #  is d is pl ay ed . Y ou ha ve t o ed it the equation[...]

Solving Equations 7–1 7 Solving Equations In chapter 6 you saw h ow you can use  to find the valu e of the left–hand variable in an assignment –type equation. Well, you can use SOLVE to fin d the value of any variable in any type of equation. For example, consider the equation x 2 – 3 y = 10 If you know the value of y in this equation, t[...]

7–2 Solving Equatio ns  If the displa y ed valu e is the one y ou w ant , pr es s g .  If you w ant a differ ent va lue, ty pe or calc ulate the value and pres s g . (F or details, s ee "R esponding to E qu ation Pr ompts" in c hap ter 6 .) You ca n halt a running calculatio n by pr essing  or g . When the root is found, [...]

Solving Equations 7–3  /#º!-) ºº!:  Terminates the equation and displays the left en d. | / / Checksum and len gth. g (accelerati on due to gravit y) is included as a v ariable so you c an chang e it for differen t units (9.8 m/s 2 or 32.2 ft/s 2 ). Calculate how ma ny meters an objec[...]

7–4 Solving Equatio ns Example: S olving the Ideal Gas Law Equation. The Ideal Gas Law describes the relationship between pressu re, volume, temperature, and the amoun t (moles) of an i deal gas: P × V = N × R × T where P is pressure (in atmos pheres or N/m 2 ), V is vo lume (in liters), N is t he number of moles of gas, R is th e universal ga[...]

Solving Equations 7–5 g #O / ) Stores 297.1 in T ; solves for P in a tmospheres. A 5–liter flask c ontains nitrogen g as. The pressure is 0.05 atmospheres when the temperature is 18°C. Calculate the density of the gas ( N × 28/ V , where 28 is the molecular weight of nitrogen). Keys: Display: Description[...]

7–6 Solving Equatio ns When SOLVE evaluates an equation, it do es it the same way X does — any "=" in the equation is treated as a " – ". For example, the I deal Gas Law equation is evaluated as P × V – ( N × R × T ). This ensures tha t an equality or assignment equation bal ances at the root, an d that an expression [...]

Solving Equations 7–7 I n t e rr u p t i n g a SO LVE C a l c u l a t i o n To halt a calculation, press  or g . The current best estimate of the root is in the unknown variable; use | to view it without disturbing the stack. C h o o s i n g I n i t i a l G u e s se s fo r S O L VE The two initial guesses come fr om:  T he number c ur[...]

7–8 Solving Equatio ns  If an equation does not allow certain values f or the unknown , gues ses can pre v ent these v alue s from occ urr ing. F or ex ample , y = t + log x r esults in a n err or if x ≤ 0 (messa ge !  ). In the following example, the e quation has more tha n one root, bu t guesses help find [...]

Solving Equations 7–9 Type in the equation: Keys: Display: Descript ion: |H  L V |d  #/¾ Selects Equation mode and starts the equation. |] 40  L H |`  #/1.2 ¾  z|] 20 L H |`  1.2º1 .2 ¾  z 4 zL H 2º1.2º º¾   #/1.2º 1. Terminates and disp[...]

7–10 Solving Equations K ey s : D is p l a y : D e sc r i p t i o n: ) This valu e from the Y–re g ister is the estimate made just prior to the final result. Since it is the same as the solution, the solution is an exact root. ) This value from the Z–register shows the equation equals zero at the root. T[...]

Solving Equations 7–11 Fo r M o r e I n f o r m a t i o n This chapter gives you instructions for solvin g for unknowns or roots over a wide range of appli cations. Appendi x D contains m ore detailed information about how the algorithm for SOLVE works, how to interpret results, what happens when no solution is fou nd, and conditio ns that can ca[...]

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Integrating Equations 8–1 8 Integrating Equations Many problems in m athematics, scien ce, and engineering require calculati ng the defini te integral of a function. If the function is denoted by f(x) and the interval of integratio n is a to b , then the integral can be expressed mathematically as ³ = b a dx (x) f I f ( x ) b x a I The quantity [...]

8–2 Integrating Equatio ns Integrating Equatio ns ( ³ F N ) To integrate an equation: 1. If the equ ation that de fine s the integr and's funct ion i sn't stor ed in the eq uation list , k e y it in (see "En ter ing E qua tions into the E q uation L i st" in chap ter 6) and leav e E quation mode . T he equation u sually conta[...]

Integrating Equations 8–3 Find the Bessel funct ion for x– values of 2 and 3. Enter the expression that defines th e integrand's funct ion: cos ( x sin t ) Keys: Display: Descript ion: {c {  } { & }  Clears memory. |H Current equati on or   ! ! Selects Equation mode. RL X  1%¾  Types the eq[...]

8–4 Integrating Equatio ns Now calculate J 0 (3 ) with the same limits of integration. Y ou must respeci fy the limits of inte gration (0, π ) since they were pushed off the stack by th e subsequent division by π . Keys: Display: Descript ion: 0 |N ) Enters the limits of inte g ration (lower limit first). |H  1%º [...]

Integrating Equations 8–5 K ey s : D is p l a y : D e s c ri p t i o n : |H The current equation or   ! ! Selects Equation mode. OL X 1% ¾  Starts the equation. |` 1%2¾ The closing right parenthesis is required in this case. qL X 1%2ª% ¾   1%2ª% Terminates th e equation. | [...]

8–6 Integrating Equatio ns S p e c i f y i n g A c c u ra c y The display format' s setting (FIX, SCI, ENG, or ALL) determines the precisio n of the integration calculation: the gre ater the number of digits displayed, the greater the precision of the calculated integral (and the greater the time r equired to calculate it). The fewer the num[...]

Integrating Equations 8–7 | X !!  ³ / )   The integ ral approximated to two decimal places. [ )  . The uncertainty of the approximation of the integ ral. The integ ral is 1.61±0.0161. Si nce the unc ertainty would n ot aff ect the approximation un til its thi rd deci mal pl[...]

8–8 Integrating Equatio ns  {  } ) Restores Degrees mode. This unc ertainty indicates th at the result mig ht be correct to only three decimal places. In reality, this result i s accurate to seven decimal places when compared with the actual value of this integ ral. Since the uncertain ty of a result is calculated co[...]

Operations with Complex Numbers 9–1 9 Operations with Complex Numbers The HP 33s can use complex numbers in the form x + iy . It has operat ions for comp lex arithmet ic (+, –, × , ÷ ), complex trigonometry (sin, cos, tan), and the mathematics functions – z , 1/ z , 2 1 z z , ln z , and e z . (where z 1 and z 2 are complex nu mbers). To ent[...]

9–2 Operations with Complex Numbers Since the im aginary and real parts of a complex number are entered and stored separately, you can easi ly work with or alter either part by its elf. y 1 Z 1 x 1 Compl ex fun ctio n y 2 y imag in ary part Z 2 x 2 x re a l pa r t Compl ex i np ut z o r z 1 an d z 2 Co m ple x res ult , z (d is pla y ed) (d is pl[...]

Operations with Complex Numbers 9–3 F un c t i o ns f o r O n e C om p l e x N u mb e r , z T o C a l c ul a te : P re s s : Change sign, –z {G^ Inverse, 1/z {G Natural log, ln z {G Natural antilog, e z {G Sin z {GO Cos z {GR Tan z {GU To do an ar ithmetic op eration with two c omplex nu mbers : 1. Enter the fir st com ple x nu mber , [...]

9–4 Operations with Complex Numbers Examples: Here are some examples of trigonometry and arithm etic with complex numbers: Evaluate sin (2 + i 3) Keys: Display: Description: 3  2 {GO  .) ) Result is 9.1545 – i 4.1689. Evaluate the expression z 1 ÷ (z 2 + z 3 ), where z 1 = 23 + i 13, z 2 = –2 + i z 3[...]

Operations with Complex Numbers 9–5  2  3 ^ .)  .) Enters imagin ary part of second complex number as a fraction . 3 {Gz .) ) Completes entry of second number and then multiplies the two complex numbers. Result is 11.7333 – i 3.8667. Evaluate 2 − z e , where z[...]

9–6 Operations with Complex Numbers r real (a, b) imaginary θ Example: Vec tor Addition. Add the following three loads. You will first need to convert the polar coordinates to rectangular coordi nates. y 1 8 5 l b 62 o 1 0 0 l b 26 1 o 17 0 lb 14 3 o L 1 L 2 L 3 x Keys: Display: Description:  {  }  Sets Degrees mode. 62  185 |s[...]

Operations with Complex Numbers 9–7 {G ) .) Adds L 1 + L 2 + L 3 . {r ) ) Converts vector back to polar form; displays r , θ[...]

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Base Conversions and Arithmetic 10–1 1 0 Base Conversions and Ar ithmetic The BASE menu ( {x ) lets you change the number base used for entering numbers and other operati ons (i ncluding programming). Changi ng bases also converts the displayed number to the new base. B AS E M e nu M e nu l a b el Des crip tion {  } Decimal mode. No a nn[...]

10–2 Base Conversions and Arithmetic {x {  }  Base 2. {x {  } ) Restores base 10; the original decimal value has been preserved, includi ng its fracti onal part. Convert 24FF 16 to binary base. The bin ary number will be more than 12 digits (the maximum displa y) long. K ey s : D i[...]

Base Conversions and Arithmetic 10–3 If the result of an operation cannot be represented in 36 bi ts, the display shows #$ and then shows the largest positive or negative number possible. Example: Here are some examples of arit hmetic in Hexadecimal, Octal, and Binary modes: 12F 16 + E9A 16 = ? Keys: Display: Description: {x { ?[...]

10–4 Base Conversions and Arithmetic Th e R e p r e s e n t a t i o n o f N u m b e r s Although the display of a number is converted when the ba se is changed, its stored form is not mod ified, so decimal numbers are not trunca ted — until they are used in ar ithmetic calcula tions. When a number appears i n hexadecimal, octal, or bin ary base[...]

Base Conversions and Arithmetic 10–5 R an g e o f N u m b e r s The 36-bit word size determin es the range of numbers that can be represented in hexadecim al (9 digits), octal (12 di gits), and binary bases (36 di gits), and the range of decim al numbers (11 digits) that can be conv erted to these other bases. R an g e o f N u m b e r s fo r B a [...]

10–6 Base Conversions and Arithmetic Wi n d o ws f o r Lo n g B i n a r y N u m b e r s The longest b inary number can ha ve 36 di gits — three times as many d igits as fit in the di splay. Each 12–dig it display of a long number is called a window . 36 - bi t nu m b e r Highest window Lowes t win d ow (di spl ayed) When a binary number is la[...]

Statistical Operations 11–1 1 1 Statistical Operati ons The statistics menus in th e HP 33 s provide functi ons to statistically analyze a set of one– or two–vari able data:  Mean, s ample and po pulation standard de v iations.  Linear r egre ssio n and linear estimation ( x ˆ and y ˆ ).  We i g h t e d m e a n ( x weig h [...]

11–2 Statistical Operations E n t e r i n g O n e – Va ri a b l e D a t a 1. Pre ss {c { Σ } to c lear ex i sting statisti cal data. 2. Key i n e a c h x –value and pre ss  . 3. The displa y sho ws n , the number of statistical data value s now acc umu lated . Pressing  actually enters two variables i nto the statistics registers becau[...]

Statistical Operations 11–3 1. Reenter the incor rec t data , but instead of pr essing  , pr es s { . T his deletes the v alue(s) and decr ements n . 2. Enter the cor r ect v alu e(s) using  . If the incorrect values were the ones just entered, press { to retrieve them, then press { to delete them. (The in correct y –val ue was s[...]

11–4 Statistical Operations Statistical Calculations Once you have entered your da ta, you can use the functions in the statistics menus. S ta t i s t i c s M e n us M e nu K e y D e sc r ip t i on L.R. | The linear–regression me nu: linear estimation { º ˆ } { ¸ ˆ } and curve–f itting { T } { P } { E }. See ''Linear Regres s[...]

Statistical Operations 11–5 15.5 9.25 10.0 12.5 12.0 8.5 Calculate the mean of the times. (Treat all dat a as x –valu es.) Keys: Display: Description: {c { ´ }  Clears the statistics registers. 15.5  ) Enters the first time. 9.25  10  12.5  12  8.5   ) Enters the remaining data; six d[...]

11–6 Statistical Operations S a m p l e S t a n d a rd D ev i a t i o n Sample standard deviati on is a measure of how dispersed th e data values are about the mean sam ple standard deviation assumes the data is a sam pling of a larger, complete set of data, a nd is calculated usin g n – 1 as a divisor.  Pr es s | { Uº } f or the stan[...]

Statistical Operations 11–7 Example: Popula tion Standard Deviation. Grandma H inkle has four g rown sons with h eights of 170, 17 3, 174, and 1 80 cm. Find the population standard deviati on of their heights. Keys: Display: Description: {c { ´ }  Clears the statistics registers. 170  173  174  180   ) Ente[...]

11–8 Statistical Operations  T o find an estima ted v alue f or x (or y ) , ke y in a giv en h ypothetic al value f or y (or x ) , t hen press | { º ˆ } (or | { ¸ ˆ }) .  T o find the values that def ine the line that best fits y our data , pr ess | follo w ed b y { T }, { P }, or { E }. Example: C urve Fitting. The yield[...]

Statistical Operations 11–9 x 0 2 0 4 0 6 0 8 0 8. 5 0 7. 5 0 6.50 5.50 4. 5 0 r = 0 . 9 880 m = 0 . 03 87 b = 4 . 85 6 0 (7 0, y ) y X What if 70 kg of nitrog en fertilizer were applied t o the rice field ? Predict the grain yield based on the above stati stics. K ey s : D is p l a y : D e sc r i p t i o n:  70 )  _ ?[...]

11–10 Statistical Operations Normalizing Close, Larg e Nu mbers The calculator mi ght be unable to correctly calc ulate the standard deviation an d linear regression for a variable wh ose data values differ by a relatively sm all amount. To avoid th is, normalize the data by en tering each value as the differen ce from one central value (such as [...]

Statistical Operations 11–11 If you've entered statistical data, you can see the contents of the statistics re gisters. Press {Y { # }, then use  and  to view the statistics reg isters. Example: Viewing the Statis tics Regi sters. Use  to store data pairs (1,2) an d (3,4) in the stati stics registers. Then view the stored stat[...]

11–12 Statistical Operations S ta t i s t i c s R e g is t er s R e gi s t e r Nu m be r D es c r i pt i on n 28 Number of accum ulated data pairs. Σ x 29 Sum of accumu lated x –valu es. Σ y 30 Sum of accumu lated y –valu es. Σ x 2 31 Sum of squares of accumu lated x –values. Σ y 2 32 Sum of squares of accumu lated y –values. Σ xy 33[...]

Part 2 Programming[...]

[...]

Simple Progra mming 12–1 1 2 Simple Progr amming Part 1 of this manual introduce d you to functions an d operation s that you can use manua lly , that is, by pressing a key for each individual oper ation. And you saw how you can use eq uations to repeat calculations wi thout doing all of the keystrokes each time. In part 2, you'll learn ho w[...]

12–2 Simple Programming RPN mo de ALG mode  º   º   π  º  º  π   ! This very simple program a ssumes that the value for the radius is in the X– register (the display) when the program starts to run. It comput[...]

Simple Progra mming 12–3 Designing a Pr ogr am The following topics show what instructions you can put in a program. What you put in a program affects how it appears when you v iew it and how it works when you run i t. S e l e c t i n g a M o d e Programs cr eated and saved in RPN mode can only be edited and executed in RPN mode, an d programs or[...]

12–4 Simple Programming When a program finishes running, the last RTN instruction retu rns the program pointer to  ! , the top of p rogram memory. U s i n g R P N , A LG a n d E q u a t i o n s i n P ro g ra m s You can calculate in programs th e same ways you calculate o n the keyboard:  Using RPN operations (whi ch w ork[...]

Simple Programming 12–5 For output, you can di splay a variable with the VIEW instructi on, you can display a message derived from an equation, or you can leave unmarked values on the stack. These are covered later in th is chapter under "Entering and Displaying Data." E n t e r i n g a P r o g ra m Pressing {e toggles the calculator in[...]

12–6 Simple Programming 5. End th e pr ogram w ith a ret u rn i nstruction , w hich sets the progr am pointer back to  ! after the pr ogr a m runs . Pr es s | . 6. Pre ss  (o r {e ) to cancel pr ogram e ntry . Numbers in program lines are stored as precisely as you entered them , and they're displayed using ALL or SCI[...]

Simple Progra mming 12–7 Fu n c t i o n N a m e s i n P ro g ra m s The name of a function th at is used in a program li ne is not necessarily the same as the function's na me on its key, in its menu, or in an eq uation. The na me that is used in a program is usually a fuller abbrevi ation than th at which can fit on a key or in a menu. This[...]

12–8 Simple Programming Example: En tering a Prog ram with an Equation. The following program calculates the area of a circle using an equation, rather than using RPN operations like the previous prog ram. K e ys : ( In R P N mo d e ) Display: Descript ion: {e { V  ! Activates Program–entry mode; sets pointer to top o[...]

Simple Progra mming 12–9 R unning a Progr am To run or execute a prog ram, program entry cannot be acti ve (no program –line numbers display ed; PRG M of f). Pressing  will cancel Program–entry mode. E xe c u t i n g a P ro g ra m ( X E Q ) Press X label to execute the program labeled with that letter. If there is only one program i n memo[...]

12–10 Simple Programming 2 . Pr es s {V label to s et the progr am pointer to th e start of the pr ogr am (that is, at its LBL ins tru ctio n). T he ! instr ucti on mo v es the p r ogr am po int er w ithout starting e x ec ution . (If the pr ogr am is the fir st or onl y pr ogr am , y ou can pre ss {V to mo ve to its begin ning .) 3. [...]

Simple Progra mming 12–11 Entering and Displa ying Data The calculator's variables are used to store data input, intermediate results, and final results. (V ariables, as explained in chapter 3, are identified by a letter from A through Z or i , but the variable names have nothing to do with program labels.) In a program, you can get data i n[...]

12–12 Simple Programming Press g (run/stop) to resume the program. The value you keyed in then writes over the contents of the X–regis ter and is stored in the given va riable. If you have not changed the displayed valu e, then that value is retained in the X–register. The area–of– a–circle program with an IN PUT instruction looks like [...]

Simple Progra mming 12–13 For example, see the " Coordin ate Transformation s" program in c hapter 15. Routine D collects all the necessary input for the variables M, N, and T (lines D0002 through D00 04) that def ine the x and y coordinates a nd angle θ of a n ew system. To respond to a prompt: When you run th e program, it will stop [...]

12–14 Simple Programming  Pr es sing {c clear s the conte nts of the dis pla y ed var ia ble . Press g to continue the program, If you don' t want the program to stop, see "Displa ying Inform ation without Stopping" below. For example, see the prog ram for "Norm al and Inverse–N ormal Distributions" in chapter 16.[...]

Simple Progra mming 12–15 V = π R 2 H S = 2 π R 2 + 2 π RH = 2 π R ( R + H ) K e ys : ( In R P N mo d e ) D is p l a y : De s c ri p t i o n : {e{ V   ! Pro g ram, entry; sets pointer to top of memory. { C     Labels program. { R  " !  { H [...]

12–16 Simple Programming K e ys : ( In R P N mo d e ) D is p l a y : De s c ri p t i o n : | V  #$ # Displays volume. | S  #$  Displays surface area. |  ! En ds program. {Y {  }   / Displays label C and the length of the program in[...]

Simple Programming 12–17 The display is c leared by other di splay operations, an d by the RND operation if flag 7 is set (rounding to a f raction). Press |f to enter PSE in a program. The VIEW and PSE lines — o r the equation and PSE lin es — are treated as one operation when you execute a program one line at a ti me. Stopping or Interr upti[...]

12–18 Simple Programming To see the line in the program containing the error–causing instruction, press { e . The program will have stopped at that point. ( For instance, it might be a ÷ instruction, which caused a n illegal divisio n by zero.) Editing a Progr am You can modif y a program in program memory by i nserting, deletin g, and editing[...]

Simple Progra mming 12–19 2. Pr es s b . T his turns on the " ¾ " editing c ursor , but does not delete a nything in the equa tion . 3. Pre ss b as r equir ed to delete the functi on or number y ou w ant to change, then enter th e desir ed corr ections. 4. Pr es s  to end the equ ation . P ro g ra m M e m o r y V i ewi n g P ro g ra[...]

12–20 Simple Programming Memory Usage If during program entry you encounter th e message & " , then there is not enough room in program memory for the li ne you just tri ed to enter. You c an make more room available by c learing programs or other data. See "Clearing One or More Programs" below, or "[...]

Simple Progra mming 12–21 To clear all programs from memory: 1. Pre ss {e to displa y progr am lines ( PRGM annunciator on ) . 2. Pr es s {c {  } to clear pr ogr am memory . 3. The messag e   @ &  prom pts y ou for confir mation. Pre ss { & }. 4. Pr es s {e to cancel pr ogr am entry . Clearing all of memory ([...]

12–2 2 Simple Programming Nonprogr ammable F unc tions The following functions of the HP 33s are not programmable: {c {  } {V {c {  } {V label nnnn b{ Y  ,  ,  , |  {e |H {h , {j {  P ro g ra m m i n g w i t h BA S E You can program i nstructions to ch ange the base mode using {x . These settings[...]

Simple Progra mming 12–23 N u m b e r s E n t e re d i n Pro g ra m Li n e s Before starting program entry, set the base mode. The current setting for the base mode determines the base of the numbers that are en tered into program lin es. The display of these num bers changes when you ch ange the base mode. Program lin e numbers always appear in [...]

12–24 Simple Pro gramming K e ys : ( In A L G m o d e) D is p l a y : De s c r i pt i on : {e{ V   ! { A      { X   "! %  5   5 z º  L X  %  5 x .  ?[...]

Simple Progra mming 12–25 A more general f orm of this program for any equation Ax 4 + Bx 3 + Cx 2 + Dx + E would be:  "!  "!  "!  "!  ?[...]

[...]

Programming Techniques 13–1 1 3 Programming Techniques Chapter 12 covered the b asics of program ming. Thi s chapter explores more sophisticated but useful techniq ues:  Using subr outines to simplif y pr ograms b y separating and labeling por tions of the progr am that ar e dedicated to p articular tasks. T he use of subr outines also shor[...]

13–2 Programming Techniques C a l l i n g S u b ro u t i n e s ( X E Q , R T N ) A subroutine is a routine tha t is called from (executed by) another routine and returns to that same routine when the subroutine is finished. The subroutine must start with a LBL and end with a RTN. A subr outine is it self a routine, an d it can call other subrouti[...]

Programming Techniques 13–3 N e s t e d S u b ro u t i n e s A subroutine c an call another subroutine, and that subro utine can call yet an other subroutine. This "n esting" of subroutin es — the calling of a subroutine within another subroutine — i s limited to a stack of su broutines seven levels deep ( not counting the topmost p[...]

13–4 Programming Techniques In RPN mode,   Starts subroutine here.  "!  Enters A .  "!  Enters B .  "!  Enters C.  "!  Enters D.    Recalls the data.    ?[...]

Programming Techniques 13–5 A P ro g ra m m e d GTO In s t ru c t i o n The GTO label instruction (press {V label ) transfers the execution of a running program to the program line containing that label, wh erever it may be. The program co ntinues running fro m the new location, and never automatically returns to its point o f origination, so GTO[...]

13–6 Programming Techniques  To  ! : {V .  To a l i n e n u m b e r : {V label nnnn ( nnnn < 10000). For e x ample , {V A0005 .  T o a label: {V label —but only if program entry is not active (no progr am lines displa y ed; PRGM off) . For e x ample , {V A. Conditional Instructions Another way [...]

Programming Techniques 13–7  Flag test s. These ch eck the stat us of fl ags, wh ich can be ei the r set o r cle ar .  Loop counter s. T hes e ar e usually u sed to loop a specif ied n umber of time s. Tes t s o f C o m p a r i s o n ( x ? y , x ? 0) There are 12 comparison s available for programmi ng. Pressing {n or |o displays a me[...]

13–8 Programming Techniques Example: The "Normal and Inverse–Normal Distri butions" program in chapter 16 uses the x < y ? conditio nal in routine T : P ro g r a m L in e s : ( In R P N mo d e ) Des crip tion . . . ! ª Calculates th e correction for X guess . ! !- % Adds the c orrection to yield a new X [...]

Programming Techniques 13–9  Fl ag s 0, 1 , 2, 3, an d 4 have no preas signed me anings. T hat is, their states w ill mean whate v er y ou def ine them to mean in a giv e n pr ogr am. (See the ex am ple below .)  Flag 5, wh en s et, wi l l in t e rrup t a pro g ram whe n a n over fl ow oc cu rs wi t hi n the progr am , displa y ing ?[...]

13–10 Programming Techniques  Flag 1 0 c o nt ro ls p ro g ram exe cu t io n of e qu at i o ns : When flag 10 is clear (th e default s tate) , equations in running progr ams ar e ev aluated and the result put on the stack . When flag 10 is set, eq uations in running progr ams are displa y ed as messag es, c ausin g t hem to b ehave like a V[...]

Programming Techniques 13–11 Annunciat ors for Set Flag s Flags 0, 1, 2, 3 and 4 have annunc iators in the display that turn on when the corresponding flag is set. The presence or absence of 0 , 1 , 2 , 3 or 4 lets you know at any time whether any of these five flags is set or not. However, there is no such indi cation for the status of f lags 5 [...]

13–12 Programming Techniques Example: Using Flags. The "Curve Fittin g" program in chapter 16 uses flags 0 and 1 to determ ine whether to take the natural logarithm of the X– and Y–inputs:  Lines S000 3 and S0004 clear both of thes e flags so that lines W000 7 and W0011 (in the i nput loop r outine) do not take the natural log[...]

Programming Techniques 13–13 P ro g r a m L in e s : (In RPN mode) Description: . . .    Clears flag 0, the i ndicator for In X .    Clears flag 1, the i ndicator for In Y . . . .     Sets flag 0, the indicator for In X .    Clears flag 1, the in dicator for[...]

13–14 Programming Techniques Example: Cont rolling the Fraction Display. The following program lets you exercise the calc ulator's frac tion–display capability. The prog ram prompts f or and uses your inputs f or a fracti onal number and a denomi nator (the /c value). The program also contain s examples of how the three fracti on–display[...]

Programming Techniques 13–15 P ro g r a m L in e s : ( In A L G m o d e) Description:    Beg ins the fraction program.    Clears three fraction fla gs.          Disp lays messages.   Selects deci[...]

13–16 Programming Techniques Use the above program to see the diff erent forms of fraction display: K e ys : ( In A L G m o d e) Display: Description: X F #@ value  Executes label F ; prompts for a fractional n umber ( V ). 2.53 g @ value  Stores 2.53 in V; prompts for denomina tor (D ). 16 g  )?[...]

Programming Techniques 13–17 This routin e (taken from the "Coordinate Transform ations" program on page 15–32 in c hapter 15) is an exam ple of an inf inite loop . I t i s u s e d t o c o l l e c t t h e initial data prior to the coordinate tran sformation. After enterin g the three values, it is up to the user to manually interrupt [...]

13–18 Programming Techniques Lo o p s wi t h C o u n t e r s (D S E , I S G ) When you want to execute a loop a specific number of times, use the {l ( increment ; skip if greater than ) or |m ( decrement ; skip if less than or equal to ) conditiona l function k eys. Each time a loop fu nction is execut ed in a p rogram, it automatically decrement[...]

Programming Techniques 13–19 Given the loop –control number ccccc cc. fffi i, ISG increme nts cccccc c to ccccccc + ii , compares the new ccccccc wi th fff, and makes program execution skip th e next progra m line if this c cccccc > fff. M  $  $ . . . $     N M  $ ! $ $?[...]

13–20 Programming Techniques I n d i r e c t ly A d d re s s i n g V a r i a b l e s a n d La b e l s Indirect addressin g is a techn ique used in adv anced pr ogramming to specify a variable or label without sp ecifying beforehand exactly wh ich one . This is determined when the program runs, so it depends on the intermediate results (or input) [...]

Programming Techniques 13–21 Th e I n d i r ec t A d d re ss , ( i ) Many functi ons that use A through Z (as variables or labels) can use  to refer to A through Z (v ariables or label s) or statistics regi sters indirectly . The function  uses the value in variable i to determine wh ich variable, label, or register to address. The followin[...]

13–2 2 Pro gramming Techniq ues STO ( i ) RCL ( i ) STO +, –, × , ÷ , ( i ) RCL +, –, × , ÷ , ( i ) XEQ ( i ) GTO ( i ) X<> ( i ) INPUT ( i ) VIEW ( i ) DSE ( i ) ISG ( i ) SOLVE ( i ) ³ FN d ( i ) FN= ( i ) P ro g ra m C o n t ro l w i t h ( i ) Since the contents of i can c hange each time a prog ram runs — or even in different[...]

Programming Techniques 13–23 &  & !- L & %1 1 L2 2 If i h o l ds : Th e n X EQ ( i ) c a l l s: T o : 1 LBL A Compute y ˆ for straig ht–line model. 2 LBL B Compute y ˆ for logari thmic model. 3 LBL C Compute y ˆ for exponential mode l. 4 LBL D Compute y ˆ for power model. 7 LBL G C[...]

13–24 Programming Techniq ues P ro g r a m L in e s : (In RPN mode) Description:    This routine collects all known values in three equations.  "!1 1 L2 2 Prompts f or and stores a number in to the variable addressed by i .    L Adds 1 to i and repeats the loo p until i [...]

Programming Techniques 13–25 P ro g r a m L in e s : ( In R P N mo d e ) Description:    Begi ns the program.    Sets equations for execution.    Disables equation prompti ng.  ) Sets counter for 1 to 26.  ! L Stores count[...]

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Solving and Integrating Progr ams 14–1 1 4 Solving and Integrating Programs S o l vi n g a P r o g r a m In chapter 7 you saw how you c an enter an equation — i t's added to the equation list — and then solve it f or any variable. You can al so enter a program that calculates a function, and then solve it for any variable. This is especi[...]

14–2 Solving and Integrating Programs 2. Incl ude an I NPUT inst ruction for ea ch varia ble, incl uding the unkn ow n . IN PUT instr uctio ns ena ble y ou to s olv e fo r any var iable in a multi–v ar ia ble f unction . INPU T fo r the unknown is ignor e d b y the calculator , so you need to w rite only one progr am that contains a separate IN[...]

Solving and Integrating Progr ams 14–3 R = The univ ersal gas constant (0.0821 liter– atm/mole–K or 8.314 J/mole–K) . T = Temperature (kelvi ns; K = °C + 273.1). To begin, put th e calculator in Program mode; if nec essary, position the program pointer to the top of program memory. K e ys : ( In A L G m o d e) Display: Description: {e{ V?[...]

14–4 Solving and Integrating Programs K e ys : ( In A L G m o d e) D is p l a y : D e sc r i p t i o n: |W  G  Selects "G" — the program. SOLVE evaluates to find the value of the unknown variable.  P #@ value  Selects P ; prompts for V . 2 g @ value  Stores 2 in V; prompts for N. .005 g @ value  Stores[...]

Solving and Integrating Progr ams 14–5 |  ! Ends the prog ram.  ) Cancels Program–entry mode. Checksum and len gth of program: 36FF 2 1 Now calculate the change in pressure of the carbon dioxid e if its te mperature drops by 10 °C from th e previous example. K e ys : ( In R P N mo d e ) Display: [...]

14–6 Solving and Integrating Programs U s i n g S O L VE i n a P ro g ra m You can use the SOLVE operati on as part of a prog ram. If appropriate, i nclude or p rompt for init ial guesses (into th e unknown variable an d into the X–register) be fore executing the S OLVE variable instruct ion. Th e two instruction s for solving an equation f or [...]

Solving and Integrating Progr ams 14–7 P ro g r a m L in e s : ( In R P N mo d e ) Description: %  % Setup for X . %  Index for X . % !  Branches to main routine. Checksum and len gth: 4800 21 &  & Setup for Y . &  Index for Y . &[...]

14–8 Solving and Integrating Programs 2. Select the pr ogr am that def ines the fu ncti on to integr ate: pr es s |W label . (Y ou can skip this s tep if y ou're r e integr at ing the s ame pr ogram .) 3. Enter the limits o f integr ati on: k e y in the lo w er limit and pre ss  , then key i n t h e upper limit . 4. Select the var i able [...]

Solving and Integrating Progr ams 14–9 Example: Pro gram Using Equation. The sine in tegral function in the example in chapter 8 i s ³ = t 0 dx ( Si(t) ) x x sin This fun ction can be evaluated by in tegrating a prog ram that defin es the integran d:   Defines the function.  1%2ª % The f unction as an expr[...]

14–10 Solving and Integrating Progr ams ³  G vari able The programmed ³ FN instruction does not produce a labeled display ( ³ = value ) since this might not be the sign ificant output for your program (that is, you might w a n t t o d o f u r t h e r c a l c u l a t i o n s w i t h t h i s n u m b e r b e f o r e d i s p l a y i n g i t [...]

Solving and Integrating Progr ams 14–11 Restrictions on Solv ing and Integrating The SOLVE variable an d ³ FN d variable instructions cannot call a routine that contains anot her SOLVE o r ³ FN instruction. That is, ne ither o f these instructio ns can be used recursively. For example, attemptin g to calculate a multiple integral will result in[...]

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Mathematics Programs 15–1 1 5 Mathematics Programs Vec t o r O p e r a t i o n s This program performs the basic vec tor operations of additi on, subtraction, cross product, and dot (or scalar) product. The prog ram uses three–dime nsional vectors and provides in put and output in rectangular or polar for m. Angles between vectors can also be f[...]

15–2 Mathematics Programs Vector addition and subtraction : v 1 + v 2 = ( X + U ) i + ( Y + V ) j + ( Z + W ) k v 2 – v 1 = ( U – X ) i + ( V – Y ) j + ( W – Z ) k Cross product: v 1 × v 2 = ( YW – ZV ) i + ( ZU – XW ) j + ( XV – YU ) k Dot Product: D = XU + YV + ZW Angle between vectors ( γ ): G = arccos 2 1 R R D × where v 1 = [...]

Mathematics Programs 15–3 Program Listing: P ro g r a m L in e s : ( In A L G m o d e) Description     Defines the beginning of the rectangular in put/display routine.  "! %  Displays or accepts input of X .  "! &  Displays or accepts input of Y . ?[...]

15–4 Mathematics Programs P ro g r a m L in e s : ( In A L G m o d e) Description  ! '  Stores Z = R cos( P ).  !  º65¸   θ 8T ´ ¸8º  Calculates R sin( P ) cos( T ) and R sin( P ) sin( T ).  ! %  Saves X = R sin( P ) cos( T ).[...]

Mathematics Programs 15–5 P ro g r a m L in e s : ( In A L G m o d e) Description   %    - "  ! % Saves X + U in X .   #    - &  ! & Saves V + Y in Y.   ' ?[...]

15–6 Mathematics Programs P ro g r a m L in e s : ( In A L G m o d e) Description  ! Calculates (ZU – WX ), whic h is the Y comp onent.  !     %   º #   .   &  ?[...]

Mathematics Programs 15–7 P ro g r a m L in e s : ( In A L G m o d e) Description   $   ¸8º ´ θ 8T  Calculates the magnitude of the U , V, W vector.  !  1    ª   Divi des the dot pr[...]

15–8 Mathematics Programs 3. Ke y i n R and pre ss g , k ey in T and pres s g , then ke y in P and press g . Contin ue at step 5 . 4. Key i n X and press g , k e y in Y and pres s g , and ke y in Z and pres s g . 5. T o ke y in a second vec tor , pre ss X E (for enter ), then go to step 2 . 6. P erfor m desired v ector oper atio n: a. Add vector [...]

Mathematics Programs 15–9 N (y) S W E (x) An ten n a Tra n s m i t t e r 7. 3 15. 7 K e ys : ( In A L G m o d e) Display: Description:  {  }  Sets Degrees mode. X R  %@ value  Starts rectangular in pu t /d i sp lay routine . 7.3 g  &@ value  Sets X equal to 7.3. 15.7 g '@ value  Sets Y equal to 1[...]

15–10 Mathematics Programs Z X Y 12 5 o 63 o F = 1 7 T = P = 1 7 1 215 o o F = 23 T = 80 P = 7 4 2 o o 1. 0 7m First, add the force vectors. K e ys : ( In A L G m o d e) D is p l a y : De sc r i p t i on : X P @ value  Starts polar input routi ne. 17 g !@ value  Sets radius equal to 17. 215 g @ value Sets T equal to 215. 17 g[...]

Mathematics Programs 15–11 g @ ) Displays P of resultant vector. X E @ ) Enters resultant vector. Since the moment equals the cross product of the radius vector and th e force vector ( r × F ), key in the vector representing the lever and take the cross product. K e ys : ( In A L G m o d e) D[...]

15–12 Mathematics Programs 125 g @ ) Sets T equal to 125. 63 g @ ) Sets P equal to 63. X D / ) Calculates dot product. g / ) Calculates angle between resultant force vector an d lever. g @ ) Gets back to input routin[...]

Mathematics Programs 15–13 Program Listing: P ro g r a m L in e s : (In RPN mode) Description     Starting point for input of coefficients.  )  Loop–control value: loops from 1 to 12, one at a time.  ! L Stores control value in index variable. Checksum and len gth:[...]

15–14 Mathematics Programs P ro g r a m L in e s : (In RPN mode) Description  º    .  ! ' Calculates H' × determinant = BG – AH .      º        º [...]

Mathematics Programs 15–15 P ro g r a m L in e s : (In RPN mode) Description     º        º    .  !  Calculates G' × determinant = DH – EG.   ¶  [...]

15–16 Mathematics Programs P ro g r a m L in e s : (In RPN mode) Description row.  %     Sets index valu e to point to last element in third row. Checksum and len gth: DA21 54     This routin e calculates product of column vect or and row pointed to by in dex value. [...]

Mathematics Programs 15–17 P ro g r a m L in e s : (In RPN mode) Description  º    º   Calculates A × E × I .      º    º    - Calcu lates ( A × E × I ) + ( D × H × C ). [...]

15–18 Mathematics Programs Program Instructions : 1. Key i n t h e p ro g ram ro u ti n es ; p ress  when done. 2. Pr es s X A to input coe ffi c ie nts of matr i x and column v ec tor . 3. K ey in coeffic ient or vector va lue (A through L) at each prompt and pr es s g . 4. Optional: pr ess X D to com pute deter mina nt of 3 × 3 s y stem . 5[...]

Mathematics Programs 15–19 K e ys : ( In R P N mo d e ) Display: Descript ion: X A @ value  Starts input routine. 23 g @ value  Sets first coefficient, A , equal to 23. 8 g @ value  Sets B equal to 8. 4 g @ value  Sets C equal to 4. 15 g @ value  Sets D equal to 15. . . . . . . Continues entry for E th[...]

15–20 Mathematics Programs g @ .) Displays next valu e. g @ ) Displays next valu e. g @ ) Displays next valu e. X I ) Inverts inverse to produce ori g inal matrix. X A @ ) Begins review of inverted matrix. g @ )?[...]

Mathematics Programs 15–21 b 0 = a 0 (4 a 2 – a 3 2 ) – a 1 2 . Let y 0 be the largest real root of th e above cubic. Th en the fourt h–order polynomi al is reduced to two quadr atic polynomi als: x 2 + ( J + L ) x + ( K + M ) = 0 x 2 + ( J – L ) x + ( K – M ) = 0 where J = a 3 /2 K = y 0 /2 L = 0 2 2 y a J + − × (the sign of JK – [...]

15–2 2 Mathematics Programs Program Listing: P ro g r a m L in e s : (In RPN mode) Description     Defines the begi nning o f the poly nomial root finder routine.  "!   Prompts for and stores the order of the polynom ial.  ! L Uses order as loop c ounter. Checks[...]

Mathematics Programs 15–23 P ro g r a m L in e s : (In RPN mode) Description     ! % First initial guess.  -+.  Second initial guess.  /  Specifies routine to solve.   # %  Solves for a real root.  !  Gets synth etic di[...]

15–24 Mathematics Programs P ro g r a m L in e s : (In RPN mode) Description  ! Checksum and len gth: B9A7 81     Starts second–order solution routine.     Gets L .     Gets M .  ! !  Calculates and displays [...]

Mathematics Programs 15–25 P ro g r a m L in e s : (In RPN mode) Description Checksum and len gth: C7A6 51     Starts fourth–order solution routine.    º   4 a 2 .     a 3 .  º   a 3 2 .  . 4 a [...]

15–2 6 Mathematics Programs P ro g r a m L in e s : (In RPN mode) Description   @  Complex roots ?  !   Calculate four roots of remai ning f ourth–order polynomial.     If not complex roots, determine largest real root ( y 0 )  º6¸@  ?[...]

Mathematics Programs 15–2 7 P ro g r a m L in e s : (In RPN mode) Description  !  Stores 1 or JK – a 1 /2.     ! ª   Calculates sign of C .     J .  º   J 2  .   J 2 -– a 2 . ?[...]

15–28 Mathematics Programs P ro g r a m L in e s : (In RPN mode) Description  ! "  Displays complex roots if any.  ! % Stores second real root.  #$ %  Displays second real root.  ! Returns to calling routine. Checksum and len gth: 96DA 30 "?[...]

Mathematics Programs 15–2 9 Because of roun d–off error in numerical computation s, the program may prod uce values that are not true roots of t he polynomial. The only way to conf irm the roots is to evaluate the polynomial manually to see if it is zero at the roots. For a third– or higher– order polynomial, i f SOLVE cannot fi nd a real r[...]

15–30 Mathematics Programs A through E Coef ficients of polynomial; scratch. F Order of polynomial; sc ratch. G Scratch. H Pointer to polynomial coefficients. X The value of a real root , or the real part of com plex root i The imag inary part of a compl ex root; also used as an index variable. Example 1: Find the roots of x 5 – x 4 – 101 x 3[...]

Mathematics Programs 15–31 Example 2: Find the roots of 4 x 4 – 8 x 3 – 13 x 2 – 1 0 x + 22 = 0. Because th e coeffici ent of the highest–order term must be 1, divide that coefficient into each of the other coefficie nts. K e ys : ( In R P N mo d e ) Display: Descript ion: X P @ value  Starts the polynomial root fi nder; prompts [...]

15–3 2 Mathematics Programs Example 3: Find the roots of th e following quadratic polyn omial: x 2 + x – 6 = 0 K e ys : ( In R P N mo d e ) Display: Descript ion: X P @ value  Starts the polynomial root fi nder; prompts for order. 2 g @ value  Stores 2 in F ; prompts for B . 1 g @ value  Stores 1 in B ; prompts for A [...]

Mathematics Programs 15–33 y y' x x' [] m, n New coordina te syst em Ol d c oor dina te syst em [0, 0 ] x P u y v θ[...]

15–34 Mathematics Progr ams Program Listing: P ro g r a m L in e s : ( In R P N mo d e ) D es c r i pt i on     This routine d efines the new coordinate sy stem.  "!   Prompts for and sto res M , the new origin's x –coordinate.  "!   Prompts[...]

Mathematics Programs 15–35 P ro g r a m L in e s : ( In R P N mo d e ) D es c r i pt i on  "! #  Prompts for and stores V .   "  Pushes V up and recalls U .   !  Pushes U and V up and recalls T .   Sets radius to 1 for the computation o[...]

15–36 Mathematics Programs 7. Pre ss X N to start the old–to–ne w tr ansfor mati on r outin e. 8. Key i n X and pre ss g . 9. Ke y i n Y , pre ss g , and s ee the x –c oor dinate, U , in the ne w s y stem . 10 . Pr es s g and see the y –coor dinate, V , i n the new s y st em. 11 . F or another old–to–new tr ansfo rmation, pr ess g a n[...]

Mathematics Programs 15–3 7 y y' x P 3 (6, 8) P 1 ( _ 9, 7 ) P 2 ( _ 5, _ 4) P' 4 (2 .7 , _ 3.6 ) (, ) = ( 7 , _ 4) T = 27 MN o (M , N) T K e ys : ( In R P N mo d e ) Display: Description:  {  }  Sets Degrees mode since T is given in de grees. X D @ value  Starts the routine that defines the transformation. 7 g ?[...]

15–38 Mathematics Progr ams g %@ .) Resumes the old–to–new routine for next p roblem. 5 ^g &@ ) Stores –5 in X . 4 ^g "/ .) Stores –4 in Y . g #/ ) Calculates V . g %@ .) Resumes the old–to–new routine for next p roblem[...]

Statistics Programs 16–1 1 6 Statistics Programs C u r ve Fi t t i n g This program can be used to fit one of four m odels of equations to your data. These models are the straight line, the logarithmic curve, the exponential cu rve and the power curve. The program acc epts two or more ( x , y ) data pairs and then calculates the correla tion coef[...]

16–2 Statistics Programs y x y B M x =+ Straight Line Fit S y x y B e Mx = Exp onenti al C urv e Fit E y x y B M I n x =+ Logarithmic Cu rve Fit L y x y B x M = Pow e r C u r v e Fi t P To fit logarit hmic curves, values of x must be positive. To fit exponential curves, values of y must be positive. To fit power curves, both x and y must be posit[...]

Statistics Programs 16–3 Program Listing: P ro g r a m L in e s : (In RPN mode) Description    This rou tine sets, the status for the stra ight–line mo del.    Enters i ndex value for later storage i n i (for indirect addressing).    Clears flag 0, the i ndicator for ln X . ?[...]

16–4 Statistics Programs P ro g r a m L in e s : (In RPN mode) Description '  Sets the loop counter to zero f or the first input. Checksum and len gth: 5AB9 24 $  $  Def ines the beginn ing of the input loop. $  Adjusts the loop counter by one to prompt f or input. $ -?[...]

Statistics Programs 16–5 P ro g r a m L in e s : (In RPN mode) Description  !  Stores b in B .  #$  Displays value.  P Calculates coeff icient m .  !  Stores m in M .  #$  Displays value. Checksum and lengt h: 9CC9 36 &?[...]

16–6 Statistics Programs P ro g r a m L in e s : (In RPN mode) Description   %     º   -  Calculates y ˆ = M In X + B .  ! Returns to the calling routine. Checksum and len gth: A5BB 18    ?[...]

Statistics Programs 16–7 P ro g r a m L in e s : (In RPN mode) Description  !  !   ! ¸ %   ! º !  Calculates Y = B (X M ).  ! !  Returns to the calling rou tine. Checksum and len gth: 018C 18     Th is subroutine calc[...]

16–8 Statistics Programs 5. Repeat step s 3 and 4 for each data pair . If you disco ver that y ou h av e made an err or after you hav e pr ess ed g in step 3 (w ith the &@ valu e prom pt still visible), press g again (displa ying the %@ val ue prompt) and pr es s X U to undo (remov e ) the last data pair . If you disco v er that you made an e[...]

Statistics Programs 16–9 Example 1: Fit a straight lin e to the data below. Make an intenti onal error when keying in the third data pair and c orrect it with the un do routine. Also, estimate y for an x value of 37. Estimate x for a y value of 101. X 40.5 38.6 37.9 36.2 35.1 34.6 Y 104.5 102 100 97.5 95.5 94 K e ys : ( In R P N mo d e ) D is p l[...]

16–10 Statistics Programs 100 g %@ ) Enters y –value of data pai r. 36.2 g &@ ) Enters x –value of data pai r. 97.5 g %@ ) Enters y –value of data pai r. 35.1 g &@ ) Enters x –value of data pai r. 95.5 g %@ ) Enters y [...]

Statistics Programs 16–11 L ogarithmic Exponential Power To start: X L X E X P R 0.9965 0.9945 0.9959 M –139.0088 51.1312 8.9730 B 65.8446 0.0177 0.6640 Y ( y ˆ when X =37) 98.7508 98.5870 98.6845 X ( x ˆ when Y =101) 38.2857 38.3628 38.3151 Normal and In v erse–Normal Distr ibut ions Normal distributi on is frequently used to model the beh[...]

16–12 Statistics Programs Program Listing: P ro g r a m L in e s : ( In R P N mo d e ) D es c r i pt i on    This routine initializes t he normal d istribution pro gram.    Stores def ault value for mean.  !   " !  Prompts for and stores m ean, M . ?[...]

Statistics Programs 16–13 P ro g r a m L in e s : ( In R P N mo d e ) D es c r i pt i on ! ! - %  Adds the correction to yield a new X guess . !   ! ) ! º6¸@  Tests to see if the correction is s ignifica nt. ! ! !  Goes back to start o f loop i[...]

16–14 Statistics Programs P ro g r a m L in e s : ( In R P N mo d e ) D es c r i pt i on   ª   º      ª  -+.  H %   ! Returns to the calling routine. Checksum and len gth: 1981 42 Flags Us ed: None.[...]

Statistics Programs 16–15 6. To c a l c u l a t e Q ( X ) giv e n X , X D. 7. Af ter the pr ompt , k e y in the v alu e of X and pres s g . T he re sult, Q ( X ), i s display ed . 8. To c a l c u l a t e Q ( X ) for a new X with the same mean an d standard dev iation , pre ss g and go to step 7 . 9. To c a l c u l a t e X giv en Q ( X ), p r e s [...]

16–16 Statistics Programs X D %@ value  Starts the distribution program and prompts for X . 3 g / ) Enters 3 for X and starts com putation of Q ( X ). Displays the ratio of the population smarter than everyone within three standard deviations of the mean. 10000 z ) Mu ltiplies by the population. [...]

Statistics Programs 16–17 55 g @ ) Stores 55 for the mean. 15.3 g ) Stores 15.3 for the standard deviation. X D %@ value  Starts the distribution program and prompts for X . 90 g / ) Enters 90 for X and calculates Q ( X ). Thus, we would expect that on ly about 1 percent of t[...]

16–18 Statistics Programs Program Listing: P ro g r a m L in e s : ( In A L G m o d e) D es c r i pt i on   Start grouped standard dev iation prog ram. ; Clears statistics registers (28 through 33).   !  Clears the count N . Checksum and len gth:[...]

Statistics Programs 16–19 P ro g r a m L in e s : ( In A L G m o d e) D es c r i pt i on  !-1L2  Updates ¦ i i f x 2 in reg ister 31.    !-  Increments (or decreme nts) N .     ?[...]

16–20 Statistics Programs Program Instructions : 1. Key i n t h e p ro g ram ro u ti n es ; p ress  when done. 2. Pr es s X S to start enter ing new data . 3. Ke y i n x i –value (data point) and pres s g . 4. Key i n f i –value (fr equenc y) and pre ss g . 5. Pre ss g after VIEW ing the n umber o f points e nter ed . 6. Repeat steps 3 thr[...]

Statistics Programs 16–21 Group 1 2 3 4 5 6 x i 5 8 13 15 22 37 f i 17 26 37 43 73 115 K e ys : ( In A L G m o d e) D is p l a y : D e s c ri p t i o n : X S %@ value  Prompts for the first x i . 5 g @ value  Stores 5 in X ; prompts for first f i . 17 g / ) Stores 17 in F ; displays the counter. g %@ )[...]

16–2 2 Statistics Programs g %@ ) Prompts for the f ourth x i . 15 g @ ) Prompts for the f ourth f i . 43 g / ) Displays the c ounter. g %@ ) Prompts for the fifth x i . 22 g @ ) Prompts for the fifth f i . 73 g / ?[...]

Miscellaneo us Programs and Equations 17–1 1 7 Miscellaneous Programs and Equations Ti m e V a lu e o f M o n ey Given any four of the five values in the "Time–Value–of–Mon ey equation" (TVM), you can solve for the fifth value. This eq uation is useful in a wide va riety of financi al applications suc h as consumer and hom e loans[...]

17–2 Miscellaneous Programs and E quations Equation Entry: Key in this equa tion: ºº1.1-ª2:.2ª -º1-ª2:.-  K e ys : ( In R P N mo d e ) Display: Description: |H   ! ! or current e quation  Selects Equation mode. L P z 100 º  _  Starts enter[...]

Miscellaneo us Programs and Equations 17–3 SOLVE instru ctions: 1. If y our fi rst TV M calc ulation is to sol ve f or inter es t r ate , I, pr es s 1 I I. 2. Pr es s |H . If neces sary , pres s  or  to s cr oll throug h the equation list until y ou come to the T VM equation . 3. Do one of the follo w ing f iv e oper ations: a. Pr es s  [...]

17–4 Miscellaneous Programs and E quations B = 7 , 2 5 0 _ 1,5 0 0 I = 10 . 5 % p e r y e a r N = 3 6 m o n t h s F = 0 P = ? K e ys : ( In R P N mo d e ) D is p l a y : D es c r i pt i on :  { % } 2  Selects FIX 2 display format. |H (  as needed ) ºº1. 1-ª Displays the leftmost part of the TVM equation. [...]

Miscellaneo us Programs and Equations 17–5 Part 2. What interest rate would reduce the m onthly payment by $10 ? K e ys : ( In R P N mo d e ) Display: Description: |H ºº1. 1-ª Displa ys the leftmost hart of the TVM equation.  I @ .) Selects I ; prompts for P . {J @ .) Roun[...]

17–6 Miscellaneous Programs and E quations g @ ) Retains P ; prompts for I . g @ ) Retains 0.56 i n I ; prompts for N. 24 g @ 8) Stores 24 in N ; prompts f or B . g # / .8) Retains 5750 i n B ; calculates F , the future balance. Ag ain, [...]

Miscellaneo us Programs and Equations 17–7 LB L Y V IEW Pri m e LBL Z P + 2 x → LBL P x P 3 D → → LB L X x = 0 ? ye s no Start no ye s Note: x is t he v a l u e i n t h e X - r e g i s t e r.[...]

17–8 Miscellaneous Programs and E quations Program Listing: P ro g r a m L in e s : ( In A L G m o d e) D es c r i pt i on &  &  This routine displays prime number P . & #$   Chec ksum and len gth: AA7A 6 '  '  This routi ne adds 2 to P . '[...]

Miscellaneo us Programs and Equations 17–9 P ro g r a m L in e s : ( In A L G m o d e) D es c r i pt i on %    % º > ¸@  Tests to see whether all possible factors have been tried. % ! &  If all fact ors have been tried, branches to th e display routine. %  C[...]

17–10 Miscellaneous Programs and E quations K e ys : ( In A L G m o d e) D is p l a y : De s c ri p t i o n : 789 X P / ) Calculates next prime number after 789. g / ) Calculates next prime number after 797.[...]

Part 3 Appendixes and Referen ce[...]

[...]

Support, Batteries, and Service A–1 A Support, Batteries , and Servic e Calculator Support You can obtain answers to ques tions about usi ng your c alculator from our Calculator Support Departmen t. Our experience shows that m any customers have similar question s about our products, so we h ave provided the followi ng section, "Answers to C[...]

A–2 Support, Batter ies, and Service A: You must clear a portion of m emory before proceedin g. (See appendix B.) Q: Why does calculating the sine (or tangent) of π radians di splay a very small number instead of 0 ? A: π cannot be represented ex actly with the 12–digit precisio n of the calculator. Q: Why do I get incorrect answers when I us[...]

Support, Batteries, and Service A–3 Once you've removed the batteries, replace them within 2 minutes to avoid losing stored information. (Have the new batteries readily at hand before you open the battery compartment.) To install batteries: 1. Have two fr esh button–cell batteries at hand . A v oid tou ching the battery terminals — handl[...]

A–4 Support, Batter ies, and Service Warning Do not mu til ate, punc tu re, or dis pose o f bat te ries in fi re . The bat teries can b urst or e xplode , re leasi ng haz ard ous chem icals . 5. Insert a new CR20 3 2 lithium battery , making sur e that the positi ve si gn (+) is facing ou twar d . Replace the plate and push it in to its or iginal[...]

Support, Batteries, and Service A–5  If t he c alc ula tor res ponds to ke ys trok es bu t you sus pect th at it is mal functionin g: 1. Do the self–test des cr ibed in the next sec tion . If the calcu lator fails the s elf tes t, it r equir es s ervi ce . 2. If the c alc ulator passe s the self–tes t , y ou may ha ve made a mistak e op[...]

A–6 Support, Batter ies, and Service War ra n t y HP 33s Scientif ic Calculato r; Warranty perio d: 12 months 1. HP warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and workm anship after the date of purchase, for th e period specified above. If HP receives notic e of such d[...]

Support, Batteries, and Service A–7 7. TO THE EXTENT ALLOWED BY LOCAL LAW, THE REMEDIES IN THIS WARRANTY STATEMENT ARE YOUR SOLE AND EXCLUSIVE REMEDIES. EXCEPT AS INDICATED ABOV E, IN NO EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR DI RECT, SPECIAL, INCIDE NTAL, CONSEQUENTIAL (I NCLUDI NG LOST PROFIT OR DAT A), OR OTHE R DAMAG[...]

A–8 Support, Batter ies, and Service Norway +47-63849309 Portugal +351-229570200 Spain +34-915-64209 5 Sweden +46-851992065 Switzerland +41-1- 4395358 (German ) +41-22-827878 0 (French ) +39-02-754197 82 (Italian) Turkey +420-5- 41422523 UK +44- 207-4580161 Czech Republic +420-5-41422523 South Africa +27-11-2376200 Luxembourg +32-2-7126219 Oth er[...]

Support, Batteries, and Service A–9 N.Amer ica Country : Telephone numbers USA 1800- HP INVENT Canada (905) 206-4663 or 800-HP INVENT ROTC = Rest of th e country Please logon to http://www.hp.com for the latest service and support informat ion. Re g u l a to r y I n f o rm a t i o n This section contai ns informatio n that shows how the HP 33 s s[...]

A–10 Support, Batteries, and Service F ile name 33s-English-Manual-05 04 2 7 -Pu blication(E ditio n 3) P age : 3 8 7 Print ed Date : 2005/4/2 7 Si z e : 13.7 x 21.2 cm Japan 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 に基づく第二情報技術装置です。 この装置は、 家庭環境で?[...]

User Memory and the Stack B–1 B User Memory and the St ack This appen dix covers  T he allocation and r equir ements of us er memory ,  Ho w to re set the calc ulator w ith out affect ing memory ,  How to c lear (purge) all o f user memory and reset the s y stem d efa ults, and  Which oper ations affect stack lift. M anagi[...]

B–2 User Memory and the Stack 2. If n ec essar y , scroll through th e equatio n l ist ( press  or  ) until you see the desired eq uation. 3. Pre ss | to see the chec ksum (he x adec imal) and length (in b ytes) of the equation . F or ex ample , /  /  . To see the total memory requirements of specific progra[...]

User Memory and the Stack B–3 C l e a r i n g M e m or y The usual way to clear user memory is to press {c {  }. However, there is also a more powerful clearin g procedure that resets addi tional informati on and is usefu l if the keyboa rd is not functionin g prop erly. If the calculator fails to respon d to keystrokes, and you are unab[...]

B–4 User Memory and the Stack Memory may inadv ertently be c leared if the c alculator is dro pped or if power i s interrupted. Th e S t a t u s of S t a c k Li f t The four stack regi sters are always present, and the stack al ways has a stack–lift status . T h a t i s t o s a y , t h e s t a c k l i f t i s a l w a y s enabled or disabled reg[...]

User Memory and the Stack B–5 DEG, RAD, GRAD FIX, SCI, ENG, ALL DEC, HEX, OCT, BIN CLVARS PSE SHOW RADIX . RADIX , CL Σ g and STOP  an d  * and b * Y { # }** Y {  }** V V  label nnnn EQN  FDISP  Errors e and program entry  Switching binary windows Digit entry ¼ Ex cept w hen used lik e CL x . ¼¼[...]

B–6 User Memory and the Stack F ile name 33s-English-Manual-04112 9-Pu blication(Edition 3) P age : 38 8 Printed Date : 2004/12/8 Si z e : 13 .7 x 21.2 cm The S tatus o f the LAS T X R egister The following operations save x in the LAST X register: +, –, × , ÷ x , x 2 , 3 x , x 3 e x , 10 x LN, LOG y x , X y I/x, INT÷, Rmdr SIN, COS, TAN ASI[...]

ALG: Summary C–1 C ALG: Summary About AL G This appendi x summarizes some features uni que to ALG mode, i ncluding ,  T wo–number ar ithmeti c  Chain calculation  Reviewi ng t he st ack  Coor dinate con ver sions  Oper ations w ith com ple x nu mbers  Integr ating an eq uati on  Ar ithmetic in bases 2 ,[...]

C–2 ALG: Summary Doing T wo–nu mber Arithmetic in AL G This disc ussion of arithmetic using ALG replaces the following parts that are affect ed by ALG mode. One-n umber functions (such as # ) work the sa me in ALG and RPN m odes. Two–number arith metic operations are aff ected by ALG mode:  Simple ar ithmeti c  Po w e r f u n c t [...]

ALG: Summary C–3 T o C a l cu l a te : Pr e s s : D is p l a y : 12 3 12  3  :/ 8)  64 1/3 (cube root ) 3  64   º / ) P ercentage Calculations The Pe rcent Funct ion. Th e Q key divides a number by 100. Combin ed with  or  , it adds or subtracts percentages. T[...]

C–4 ALG: Summary Example: Suppose that the $1 5.76 item c ost $16.12 last year. What is the perc entage change from last year' s price to this year's ? Keys: Display: Description: 16.12 |T 15.76   )0 ) / .) This year's pri ce dropped about 2.2% from last year's price.[...]

ALG: Summary C–5 File na me h p 3 3s_ user 's ma nual _Eng lis h_E_H DPM20PI E30. doc P a ge : 409 Printe d Date : 2005/10/17 Siz e : 13.7 x 21.2 cm P arentheses Calculations In ALG mode, you can use p arentheses up to 13 levels. Fo r example, suppose you want to calculate: 9 12 85 30 × − If you were to key in 30 ¯ 85 Ã , the calculator[...]

C–6 ALG: Summary 750 z 12 q 360  or 750 z 12 q 360  In the second case, the q key acts like the  key by displaying the result of 750 × 12. Here’s a long er chain calculation: 9 . 1 68 5 . 18 75 456 × − This calculatio n can be written as: 456  75 q 18.5 z 68 q 1.9  . Watch what happen s in the display as you key i t in:[...]

ALG: Summary C–7 You ca n press  or  (o r  and | ) t o r e vi e w the entir e con tents of the stack and recall them. Ho wev er, in normal operation in ALG mode, the stack in ALG mode di ffers from the one in RPN mode. (Because when you press  , the result is not placed into X1, X2 etc.) Only after evaluating equations, prog rams, [...]

C–8 ALG: Summary  8 ´ ¸8º &/) Displays y . If you want to perform a coordin ate conversion as part of a chain calc ulation, you need to use parentheses to impose the required order of operati ons. Example: If r = 4.5, θ = π 3 2 , what are x, y ? Keys: Display: Description:  {  }  Sets[...]

ALG: Summary C–9 O p e ra t i o n s w i t h C o m p l ex N u m be r s To enter a complex numb er 웛 x + iy . 1. T ype the real part , x , then the func tion k e y . 2. T ype the imagin ary part, y , then pre ss {  G . Fox example, to do 2 + i 4 , press 2  4 {  G . To view the res ult of com plex opera tions 웛 After keying in the compl[...]

C–10 ALG: Summary Examples: Evaluate sin (2 워 3 i ) Keys: Display: Description: |]  2   3 { G|`  1 워 L2 /) O 1 워 L2 /)  1 워 L2 /.)  Result is 9.1545 – i 4.1689 Examples: Evaluate the expression z 1[...]

ALG: Summary C–11 File na me h p 3 3s_ user 's ma nual _Eng lis h_E_H DPM20PI E30. doc P a ge : 409 Printe d Date : 2005/10/18 Siz e : 13.7 x 21.2 cm Examples: Evaluate (4 － i 2/5)(3 － i 2/3) Keys: Dis play: Desc ription: º y 4 Ã Ë 2 Ë 5 ¹ c º | º y 3 Ã Ë 2 Ë 3 ¹ c º | Ï      ?[...]

C–12 ALG: Summary F ile name hp 3 3s_user's m anual_ English_E_ HDP M20 PIE3 0.doc P age: 40 9 Printe d Date : 2005/10/18 Siz e : 13.7 x 21.2 cm 100 8 ÷ 5 8 = ? 100 ¯ 5 Ï   Integer part of result. 5A0 16 + 10011000 2 = ? ¹ ¶ {  } 5A0 Ù    Set base 16; HEX annunc[...]

ALG: Summary C–13 K ey s : D i s p l a y : D es c r i pt i on : {c { ´ }  Clears existing stati stical data. 4 [ 20  8 Q/) Enters the first new data pair. 6 [ 400  8 Q/) Display shows n , the number of data pairs you entered. {  !º ) Brin[...]

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More ab out Solv ing D–1 D More about Solving This appendi x provides inform ation about the SOLVE oper ation beyond that g iven in chapter 7. H ow S O L VE Fi n d s a Ro o t SOLVE first attempts to solve th e equation directly for the unknown variable. If the attempt fails, SOLVE changes to an iterative(repetitive) procedure. The iterative opera[...]

D–2 More ab out Solv ing f ( x ) x a f ( x ) b x f ( x ) x c f ( x ) x d Functio n Wh ose Roots C an Be Found In most situations, the calculat ed root is an accurate estimate of the t heoretical, infin itely precise root of the equation . An "ideal" solution i s one for which f(x) = 0. However, a very small non–zero value for f(x) is [...]

More ab out Solv ing D–3 I n t e r p r e t i n g Re s u l t s The SOLVE operation will produce a solution under either of the following conditions:  If it finds an estimate for which f(x) equals zero. (See figure a, below.)  If it finds an es timate w her e f(x) is not eq ual to z ero , but the calcu lated r oot is a 12–digi t numbe[...]

D–4 More ab out Solv ing Keys: Display: Descript ion: |H  Select Equation mode. 2 ^z L X  3  4 z L X  2  6 zL X   8       .º%:-º %:. º Enters the equation. | / / Checksum and len gth.   Cancels Equation mode. Now, solve th[...]

More ab out Solv ing D–5 | / / Checksum and len gth.   Cancels Equation mode. Now, solve the equation to find its positive and n egative roots: K ey s : D is p l a y : D e sc r i p t i o n: 0 I X 10  _ Your initial guesses for the positive root. |H %:-%. Selects Equ ation mode; displays the[...]

D–6 More ab out Solv ing f ( x ) x a f ( x ) x b Sp eci al Case: A Di s co nti n ui ty a nd a P ole Example: Disc ont inu ous Fu nc tion . Find the root of the equati on: IP( x ) = 1.5 Enter the equation: Keys: Display: Descript ion: |H  Selects Equation mode. |"L X | `| 1.5    1%2/) Enter the equation. | [...]

More ab out Solv ing D–7  X # %/ ) Finds a root with g uesses 0 and 5. | )  Shows root, to 11 decimal places. | )  The previous estimate is slightly bigger. .) f(x ) is relatively large. Note the differen[...]

D–8 More ab out Solv ing Now, solve to find the root. Keys: Display: Descript ion: 2.3 I X 2.7  ) _  Your initia l guesses for the root. |H %ª1%:.2 . Selects Equation mode; displays the equation.  X ! No root fo und for f(x) . 8 8 8 ) f(x) is relative[...]

More ab out Solv ing D–9 f ( x ) x a f ( x ) x b f ( x ) x c Case Wher e No R oot Is Fou nd Example: A Rela tive M inimum. Calculate the root of thi s parabolic equation : x 2 – 6 x + 13 = 0. It has a minimu m at x = 3. Enter the equation as an expression : K ey s : D is p l a y : D e sc r i p t i o n: |H  Selects Equation mode. L X  2 ?[...]

D–10 More ab out Solv ing   Cancels Equation mode. Now, solve to find the root: K ey s : D is p l a y : D e sc r i p t i o n: 0 I X 10   _  Your initia l guesses for the root. |H %:.º%-  Selects Equation mode; displays the equation.  X  !  Search fails with g uesses 0 and 10 b| ?[...]

More ab out Solvin g D–11 ) Previous estimate is t he same. | )  f (x) = 0 Watch what happens wh en you use negative values for guesses: K ey s : D is p l a y : D e sc r i p t i o n: 1 ^I X .) Your negative guesses for the root. 2 ^|H .#1%2 Selects Equ at[...]

D–12 More ab out Solv ing Now attempt to find a negative root by entering guesses 0 a nd –10. Notice that the function is und efined fo r values o f x between 0 an d –0.3 since those values produce a positive den ominator but a negati ve numerator, causin g a negative square root. Keys: Display : Descript ion: 0 I X 10 ^  . _  |H [...]

More ab out Solv ing D–13   ¶   ! Checksum and len gth: B956 75 You can subsequen tly delete line J0003 to save m emory. Solve for X using in itial guesses of 10 –8 and –10 –8 . K e ys : ( In R P N mo d e ) Display: Description: a 8 ^I X 1 ^a 8 ^  .  . _  Enters guesses. |W J .[...]

D–14 More ab out Solv ing U n d e r f l ow Underflow occurs when the magnitude of a number is smaller than the calculator can represent, so it substi tutes zero. This can af fect SOLVE results. For example, consider the equation 2 1 x whose root is inf inite in value. Because of underflow, SOLVE returns a very large value as a root. (The calculat[...]

More about Integration E–1 E More about Integration This appen dix provides in formation about i ntegration beyon d that g iven in c hapter 8. H ow t h e I n t e g ra l I s E va l u a t e d The algorithm used by the inte gration operation, ³  Gº , calculates the inte gral of a functi on f(x) by computing a weighted average of the function[...]

E–2 More about Integration As explained in chapter 8, the uncertai nty of the final approxi mation i s a number derived from the display form at, whic h specifies the un certainty for the fun ction. At the end of each iteration , the algorithm compares the approximati on calculated during th at iteration with the approximations calculated d uring[...]

More about Integration E–3 f ( x ) x With this number of sample points, the algorithm will c alculate the same approximation f or the integral of an y of the functions shown . The actual integrals of the functi ons shown with solid blue and bl ack lines are abo ut the same, so the approximation wi ll be fairly accurate if f(x) is o ne of these fu[...]

E–4 More about Integration Keys: Display : Descript ion: |H  Select equation mode. L X z %º%1 ¾  Enter the equation. L X |`   %º%1.%2 End of the equation. | / / Checksum and len gth.   Cancels Equation mode. Set the display format to SCI 3, specif y the lower and upper [...]

More about Integration E–5 f ( x ) x The graph i s a spike very close to the orig in. Because no sample point h appened to discover the spike, the algorithm assumed that f(x) was identically equal to zero throughout the interval of integration. Even if you increased the number of sample points by calculati ng the integral in SCI 11 or ALL format,[...]

E–6 More about Integration Note that the rapidity of variation in the function (or its low–order derivatives) must be determined with respect to the width of the interval of integration. Wi th a given number of samp le points, a fu nction f(x ) that has three fluctuations can be better characterized by its samples when these variation s are spr[...]

More about Integration E–7 In many cases yo u will be familiar enough with the function you want to integrate that you will know wheth er the function has any quick wi ggles relative to the interval of inte gration. If yo u're not familiar with t he function, a nd you su spect that it may cause problems, yo u can quic kly plot a f ew points [...]

E–8 More about Integration [ )  . Uncertaint y of approximation . This is the correct answer, but it took a very long ti me. To understand why, compare the graph of the function between x = 0 and x = 10 3 , which looks abou t the same as that shown in the previous example, with the g raph of the function between x = 0 and x =[...]

More about Integration E–9 Because the calculati on time depends on h ow soon a certain densi ty of sample points is achiev ed in the re gion where the function is interesting, the calculation of the integral of any f unction will be prolonged if the interval of integratio n includes mostly regions where the function is not interesting. Fortunate[...]

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Messages F–1 F Messages The calculator responds to c ertain con ditions or keystroke s by displayin g a message. The ¤ symbol com es on to call your attention to the message. For significa nt conditio ns, the message remains until yo u clear it. Pressing  or b clears the message; pressing any other key clears the message and execu tes that ke[...]

F–2 Messages F ile name 33s-English-Manual-04112 9-Pu blication(Edition 3) P age : 38 8 Printed Date : 2004/12/8 Si z e : 13 .7 x 21.2 cm  The calculator is calcu lating t he integra l of a n equation or program. This m ight take a while .  A running SOLVE or ∫ FN operation[...]

Messages F–3 % !! Attempted to refer to a nonexistent program label (or line number) wit h V , V , X , or {  }. Note that the error % !! can mean  y ou e xplic itly (fro m the k e y boar d) called a pro g ram label tha t does not e x ist; or  the progr am t hat y ou called r efer r[...]

F–4 Messages # The calculator is solving an equation or program for its root. This might take a while. !12 Attempted to calculate the sq uare root of a negative number. !!   Statisti cs error:  Attempted to do a statistic s calculation w ith n = 0.  Attempted to calc ulate s x s[...]

Operation Index G–1 G Operation Index This secti on is a quick referenc e for all functions an d operations and thei r formulas, where appropriate. Th e listing is in alphabetical order by the fu nction's n ame. This name is the one used in program lines. For example, the function named FIX n is executed as  { % } n . Nonprogrammab [...]

G–2 Operation Index N am e K e y s an d D e s cr i pt i o n Pa g e ¼  Displays previous entry in cata log; moves to previous equation in equation list; moves program pointer to previous step. 1–24 6–3 12–9 12–18  Di splays next entry in catalog ; moves to next equation in equation list; moves program pointer to next line (du ring p[...]

Operation Index G–3 N am e K e y s an d D e s cr i pt i o n Pa g e ¼ Σ +  Accumu lates ( y , x ) into statistics registers. 11–2 Σ – { Removes ( y , x ) from statistics registers. 11–2 Σ x | { ;º } Returns the sum of x –values. 11–10 1 Σ x 2 | { ;º  } Returns the sum of squares of x –values. 11–10 1 Σ xy | [...]

G–4 Operation Index N am e K e y s an d D e s cr i pt i o n Pa g e ¼ ³ FN d variable | { ³  G _} variable Integrates the displayed equati on or the program selected by FN=, using lower limit of the variable of integration in th e Y–register an d upper limit of the variable of integration in th e X–register. 8–2 14–7 ( |] Open [...]

Operation Index G–5 N am e K e y s an d D e s cr i pt i o n Pa g e ¼ ASINH {{M  Hyperbolic arc sin e. Returns sinh –1 x . 4–6 1 ATAN {S Arc tangen t . Returns tan –1 x . 4–4 1 ATANH {{ S Hyperbolic arc tang ent . Returns tanh –1 x . 4–6 1 b | { E } Returns the y–interc ept of the regression line: y – m x . 11–10 1 {[...]

G–6 Operation Index N am e K e y s an d D e s cr i pt i o n Pa g e ¼ {c Displays menu to clear numbers or parts of memory; clears indicated variable or program f rom a MEM catalog; clears displayed equation. 1–6 1–24 {c {  } Clears all stored d ata, equations, and programs. 1–24 {c {  } Clears all prog rams (calculator in[...]

Operation Index G–7 N am e K e y s an d D e s cr i pt i o n Pa g e ¼ CMPLX × {Gz Complex multiplication . Returns ( z 1x + i z 1y ) × ( z 2x + i z 2y ). 9–2 CMPLX ÷ {Gq Complex division . Returns ( z 1x + i z 1y ) ÷ ( z 2x + i z 2y ). 9–2 CMPLX1/ x {G Complex reciprocal . Return s 1/(z x + i z y ). 9–2 CMPLXCOS {GR Complex cosine . [...]

G–8 Operation Index N am e K e y s an d D e s cr i pt i o n Pa g e ¼ COSH {R Hyper bolic cosine . Returns cosh x . 4–6 1 | Functions to use 40 physics constants.  4–8 DEC {x {  } Selects Decimal mode. 10–1 DEG  {  } Selects Degrees angular mode. 4–4  DEG {v Radians to degrees . Returns (360/2 π ) x . 4?[...]

Operation Index G–9 N am e K e y s an d D e s cr i pt i o n Pa g e ¼  Separates two numbers ke yed in sequentially; completes equation entry; evaluates the displayed equation (and stores result if appropriate). 1–17 6–4 6–11 ENTER  Copies x into the Y–register, lifts y into the Z–register, lifts z into the T–register, and loses[...]

G–10 Operation Index N am e K e y s an d D e s cr i pt i o n Pa g e ¼ FS ? n |y {  @ } n If flag n (n = 0 through 11) is set, executes the next program line; if flag n is cl ear, skips the nex t program lin e. 13–11  GAL | Converts liters to gallons. 4–13 1 GRAD  {  } Sets Grads angular mode. 4–4 GTO label {V label [...]

Operation Index G–11 N am e K e y s an d D e s cr i pt i o n Pa g e ¼ ( i ) LI Indirect . Value of variable whose letter corresponds to the numeric value stored in variable i. 6–4 13–21 2  IN | Converts centimeter s to inches. 4–13 1 IDIV {F Produces the quotient of a divisi on operation involv ing two integers.  6–15 2 IN[...]

G–12 Operation Index N am e K e y s an d D e s cr i pt i o n Pa g e ¼  KG {} Converts pounds to kilograms. 4–13 1  L { Converts gallons to liters. 4–13 1 LAST x {  Returns number stored in the LAST X register. 2–7  LB |~  Converts kilogram s to pounds. 4–13 1 LBL label { label Labels a program wi th a single lette[...]

Operation Index G–13 N am e K e y s an d D e s cr i pt i o n Pa g e ¼ OCT {x { ! } Selects Octal (base 8) mode. 10–1 | Turns the calculator of f. 1–1 Pn,r {_ Permutations of n ite ms taken r at a time. Returns n ! ÷ ( n – r )!. 4–14 2 {e Activates or cancels (toggles) Program–entry mode. 12–5 PSE |f Pause . Halts program ex[...]

G–14 Operation Index N am e K e y s an d D e s cr i pt i o n Pa g e ¼ RCL variable L variable Recall. Copies variable into the X–register. 3–5 RCL+ variable L variable Returns x + variable. 3–5 RCL– variable L variable . Returns x – variable. 3–5 RCLx variable Lz variable . Returns x × variable. 3–5 RCL ÷ variable Lq  va[...]

Operation Index G–15 N am e K e y s an d D e s cr i pt i o n Pa g e ¼ R µ | Roll up . Moves t to the X–register, z to the T–register, y to the Z–register, and x to the Y–register in RPN mode. Displays the X1~X4 menu to review the stack in ALG mode. 2–3 C–6 | Displays the standard–deviation Menu. 11–4 SCI n  {  } n[...]

G–16 Operation Index N am e K e y s an d D e s cr i pt i o n Pa g e ¼ pg Inserts a blank space character durin g equation entry. 13–14 2 SQ ! Square of argumen t. 6–15 2 SQRT # Square root of x . 6–15 2 STO variable I variable Store. Copies x into variable. 3–2 STO + variable I variable Stores variable + x into variabl e. 3–4 STO ?[...]

Operation Index G–17 N am e K e y s an d D e s cr i pt i o n Pa g e ¼ TAN U Tangent . Returns tan x . 4–3 1 TANH {U Hyperb olic tangent . Returns tanh x . 4–6 1 VIEW variable | v ariable Displays the labeled contents of variable without recalling the value to the stack. 3–3 12–13 X Evaluates the displayed e quation . 6–12 XEQ lab[...]

G–18 Operation Index N am e K e y s an d D e s cr i pt i o n Pa g e ¼ x w R eturns weighted mean of x values: ( Σ y i x i ) ÷Σ y i . 11–4 1 | Displays the mea n (arithmetic average) me nu. 11–4 x <> variable |Z x exchan ge . Exchanges x with a vari able. 3–6 x <> y [ x exchange y . Moves x to the Y–register and y to the[...]

Operation Index G–19 N am e K e y s an d D e s cr i pt i o n Pa g e ¼ x ≠ 0 ? |o { ≠ } If x ≠ 0, executes next program line; if x =0, skips the next progra m line. 13–7 x ≤ 0 ? |o { ≤ } If x ≤ 0, executes next program line; if x >0, skips next progra m line. 13–7 x <0 ? |o {<} If x <0, executes next program line; if x[...]

G–20 Operation Index N am e K e y s an d D e s cr i pt i o n Pa g e ¼ y x  Power . Returns y raised to the x th power. 4–2 1  Notes: 1. Fu nctio n can be u sed in eq ua tions . 2. F unction a ppears only in equati ons.[...]

Index– 1 F ile name 33s-English-Manual-05 05 0 2 -Publicati on(Editi on 3) P age : 3 88 P r i n t e d D a t e : 2 0 0 5 / 5 / 2 Siz e : 13.7 x 21.2 cm Index Special Characters , 6–5 ∫ FN. See integr ati on % functi ons, 4–6  . See equation–en try curs or ~ . See backspac e k e y " . See integrati on z , 1–14 â , 1–2 3 π , 4?[...]

Index– 2 asy mptotes of functions, D–8 B backspace k ey canceling VIE W , 3–3 clear ing messa ges, 1–5, F–1 clear ing X–register , 2–2 , 2–6 deleting pr ogram li nes , 12–18 equation entry , 1–5, 6–8 leav ing menus, 1–5, 1–9 operation , 1–5 progr am entry , 12–6 starts editin g, 6–8 , 12–6 , 12–18 balance (financ[...]

Index– 3 progr am , 1–2 4, 12–20 usi n g, 1 –24 var iable , 1–2 4, 3–3 chain calculations, 2–11 change– percentage functions, 4–6 changing sign of number s, 1–14 , 1–17 , 9–3 checks ums equations, 6–18 , 12–6, 12–21 progr ams, 12–20 CLEAR menu, 1–6 clear ing equations, 6–8 g en e ral i n fo rm at i o n, 1 – 5 m[...]

Index– 4 adju s ting contr ast , 1–1 annunciators , 1–11 function names in, 4–17 X–register sho w n , 2–2 display f ormat affects integrati on, 8–2 , 8–5, 8–7 affects numbers, 1–19 affects rounding, 4–16 default , B–3 peri ods and commas in, 1–18 , A–1 setting, 1–19 , A–1 DISPLA Y menu, 1–19 do if true, 13–6 , 14[...]

Index– 5 functions, 6–5, 6–15, G–1 in progr ams, 12–4, 12–6 , 12–21, 13–10 integrating , 8–2 lengths, 6–18, 12–6 , B–2 list of . See equation lis t long, 6–7 memor y in, 12–14 multiple r oots, 7–8 no root , 7–6 number s in, 6–5 numeri c value o f , 6–9 , 6–10, 7– 1, 7–5, 12–4 oper atio n summary , 6–3 p[...]

Index– 6 frac tional–par t function, 4–16 F r action–displa y mode affects rounding, 5–7 affects VIEW , 12– 13 setting, 1–2 3, 5–1, A–2 fractions accur acy indicator , 5–2 , 5–3 and equations, 5–8 and progr ams, 5–8, 12–13, 13–9 base 10 only , 5–2 calculating with , 5–1 denominators, 1–2 2 , 5–4, 5–5, 13–9 [...]

Index– 7 imagin ary part ( complex numbers) , 9–1, 9–2 indirect addr essing, 13–20, 13–21, 13–2 2 INPU T alw a y s prom pts, 13–10 enteri ng progra m data, 12–11 in in tegratio n progr ams, 14–8 in SOL V E pr ogr ams, 14–2 re sponding to, 12–13 integer–part fun ction , 4–16 integr at io n accur acy , 8–2 , 8–5, 8–6, [...]

Index– 8 order o f calculation , 2–13 real–number , 4–1 stack oper ation , 2–4, 9–1 matri x inv ersion , 15–12 max imum o f func tion , D–8 mean me nu , 11–4 means (sta tist ics) calculating, 11–4 normal distribution , 16–11 memory amount availa ble, 1–2 4 clear ing, 1–6, 1–2 4, A–1, A–4, B–1, B–3 clear ing equat[...]

Index– 9 internal r epr es entati on, 1–19 , 10–4 large and small , 1–14, 1–16 limitations, 1–14 mantissa, 1–15 negativ e , 1–14, 9–3, 10–4 order in calculations , 1–18 peri ods and commas in, 1–18 , A–1 prec ision , 1–19 , D– 13 prime , 17–6 ra nge of , 1–16, 10–5 real , 4–1, 8–1 recalling , 3–2 re using, [...]

Index– 10 checksums, 12–21 clear ing, 12–5 duplicate , 12–5 enteri ng, 12–3, 12–5 ex ecuting, 12–9 indirect addr essing, 13–20, 13–21, 13–22 mov ing to, 12–10, 12–19 purpose , 12–3 typ ing name , 1–3 vie w ing, 12–20 progr am lines. See progr ams pr ogr am na mes . See progr am la bels progr am pointer , 12–5, 12– [...]

Index– 11 testing, 12–9 using integration, 14–9 using SOL V E , 14– 6 var iable s in, 12–11, 14–1, 14–7 prom pts affect stack , 6– 13, 12–12 clear ing, 1–5, 6–13, 12–13 equations, 6–12 INPUT , 12– 11, 12–13, 14–2 , 14–8 progr ammed equations, 13–10, 14–1, 14–8 re sponding to, 6–12 , 12– 13 show in g hidde[...]

Index– 12 F ile name 33s-English-Manual-05 05 0 2 -Publicati on(Editi on 3) P age : 38 8 P r i n t e d D a t e : 2 0 0 5 / 5 / 2 Siz e : 13.7 x 21.2 cm S OL V E , D–13 statistics, 11–9 tr ig func tions , 4–4 rou t i n e s calling, 13–2 nesting, 13–3, 14–11 parts of pr ogr ams, 13–1 RPN compar ed to equations, 12–4 in pr ogr ams, 1[...]

Index– 13 effe ct of  , 2–5 equation usage , 6–11 ex changing with v ari ables , 3–6 ex changing X an d Y , 2–4 fillin g w ith cons tant , 2–6 long calculations, 2–11 operation , 2–1, 2–4, 9–1 progr am calculations, 12–12 progr am input, 12–11 progr am output, 12–11 purpose , 2–1, 2–2 register s, 2–1 re v ie w ing[...]

Index– 14 time value of mone y , 17– 1 transf orming coor dinates, 15–3 2 T–register , 2–4 trigonometr ic functions, 4–4 , 9–3 trou bleshooting, A–4 , A–5 turning on and off, 1–1 TV M, 17–1 twos comp lement, 10–2 , 10–4 two–var ia ble statistic s, 11–2 U uncer tainty ( integrati on), 8– 2 , 8– 5, 8–6 underflow , [...]

Index– 15 clear ing in program s, 12–6 display ed , 2–2 during progr ams pau se , 12–17 ex changing with v ari ables , 3–6 ex changing with Y , 2–4 not clear i ng , 2–5 part of stack , 2–1 testing, 13–7 unaffected b y VIEW , 12–14[...]