Manual / Guide · 1969
HP 9100B Program Library (1969)
HP's library of 9100B programs for science, engineering, statistics and finance.
Manual / Guide · 1969
HP's library of 9100B programs for science, engineering, statistics and finance.
d "MU"tttl f /"" HttbllbtwsttH _#++wa tMbt*&& if IV.\« + Itt Cl 0:: « ::s:: U d l.LJ ...J ~ l.LJ :c ~ ~ Cl 0:: « ::s:: u «a.. I-I-- l.LJ ...J ~ Congratulations, you have just become the proud owner of a new Hewlett-Packard 9100B. Calculator. This calculator is a big brother to the successful Hewlett-Packard 9100A. The 9100B however, has several features which more than triple its computing power, these being: 1. A TWO PAGE memory allowing up to 392 program steps or 32 data storage registers. 2. A true SUBROUTINE capability permitting instant access to subroutines from any point in a program. l.LJ :c ~ 3. A convenient X..c-- ( ) operator allowing rapid data recall to the X register. ~ 4. A STEP PROGRAM "dual display" greatly simplifying program editing and modification. Cl 0:: « ::s:: u d l.LJ ...J ~ A detailed explanation of the use of these features is found in the 9100B Operating and Programming Manual (Hewlett-Packard Part No. 09100-90021) supplied with your calculator. We hope you find the 9100B Calculator and Library a useful tool and guide for your computational work. To better serve you and other 9100 Calculator users, we welcome you to send us program solutions you have :c l.LJ written. Please write them up in a format similar to the programs furnished in the Program Library and send ~ them to us. Also send in any comments you might have on the 9100B Calculator and Program Library to our E:1 Applications Group. We at Hewlett-Packard look forward to serving you. Cl 0:: « Sincerely, u « a.. HEWLETT-PACKARD COMPANY I-I-- ~~~ ::s:: l.LJ ...J ~ l.LJ :c Dave Cole Applications P.O. Box 301 Loveland, Colorado 80537 ~ ~ Cl 0:: « ::s:: U Ci I-- l.LJ ...J ~ l.LJ :c ~ ~ 1 INTRODUCTION TO LIBRARY This Program Library is intended to illustrate practical problem solutions available with the 9100B Calculator. Approximately two thirds of the programs in this library are compatible with the 9100A Calculator. Those programs which are applicable only to the "B" calculator will have a 9100B ONLY above the program number. Many programs are short enough so that they may be incorporated as subroutines in other programs. Each program consists of a description, equations (with references), examples and a list of the program steps. The programs have been placed in a three-ring binder with classification dividers so that changes, additions and reorganizations can be easily made. Each classification has a corresponding part number and each program within a category is numbered according to the classification part number. In each Program Library Classification is found a listing of the programs in that section. The first grouping contains 9100A programs (with "AfT program numbers). The second grouping contains "B" only programs for that classification. An inspection of the first group program numbers will disclose that certain "A" programs have been removed from the "B" Library. These deleted programs have been replaced by more extensive "B" programs. PROGRAM LIBRARY CLASSIFICATIONS HP Part No. 09100-70000 09100-70800 09100-71000 09100-72000 09100-73000 09100-73200 09100-73700 09100-74000 09100-74200 09100-75000 09100-75200 09100-75500 09100-75800 09100-76000 Mathematics Statistics Electronics Mechanics Business Physics Thermodynamics Surveying Structures Fluid Mechanics Life Sciences Chemical Secondary Education Miscellaneous You are invited to submit programs for inclusion in the Hewlett-Packard KEYBOARD, a periodic publication which contains useful information about the Hewlett-Packard 9100 Calculator systems. Submitted programs having a broad appeal or illustrating ingenious programming techniques will be included in the KEYBOARD with credit. Please return the Program Library card (in the pocket on the rear cover) indicating the Program Library disciplines in which you are interested. The following accessories are available: HP Part No. 09100-90020 09100-90021 09100-90022 09100-90024 5060-5919 4040-0350 9320-1183 9320-1184 9320-1185 9320-1186 9320-1187 2 Five Programming Pads Operating and Programming Manual 9100B Program Library Diagnostic Card and Envelope Box of Ten Magnetic Program Cards Dust Cover Pull-Out Card (English) Pull-Out Card (French) Pull-Out Card (German) Pull-Out Card (Italian) Pull-Out Card (Spanish \JIm. i*+bt'fI b c h h"'±"'+b'!t 'd'WfjuttNb dW 111 1'h Ii) ! d tl Program Library Usage To facilitate the use of the 9100B Program Library, brief discussions of: Manual Program Entry, Program Loading from Magnetic Card, 9100B Peripherals and are included here. The Operating and Programming Manual (HP Part No. 09100-90021) covers these topics in greater detail and should be consulted for further information. Manual Program Entry Initially, the program steps must be manually entered into the calculator step-by-step. Then, you may record the program on a magnetic card furnished with your calculator. The use of the magnetic card eliminates repeated manual re-entry. Programs recorded on the magnetic card may be entered instantly, using the ENTER button on the calculator. Mter entering the program steps into the calculator, it is suggested that you use the sample data to verify test answers. If you do not get the correct answers, it is suggested that you carefully check each program step to see if the program is correctly entered into the appropriate location and/or re-read the user instructions. This may be done by comparing the step location and the code number to the printed program. You can do this very conveniently using the STEP PROGRAM key in the program mode. Program Loading In general, 9100B programs will occupy both the (+) and (-) calculator pages. The most efficient manner to load a 2-page program is to load Side A into the (+) page and Side B into the (-) program page. This can easily be accomplished by placing no END statements on the (+) program page. The END statement may be included on the (-) program page. Load the program as follows: PRESS: END c~ ENTER PROGRAM: Side A (Since there is no END on Side A, the calculator will advance to (- )(0)(0) automatically). ENTER PROGRAM: Side B (With or without an END, the calculator will advance to (+)(0)(0) ready for execution) . In the Program Library the above two instructions will be replaced by the single instruction: ENTER PROGRAM: Side A followed by Side B To insure that an extraneous END statement does not get recorded on Side A, all unused registers on the (+) page should be filled with CONTINUE's prior to recording. 9100B Peripherals Several peripheral devices are available to complement the 9100B Calculator, these being: 9125A 9120A 9160A 9150A o x - Y Plotter Printer Optical Card Reader Display Monitor The "B" library has been written to simplify the attachment of the 9125A and 9120A to the 9100B. At appropriate input and output points in a program CONTINUE's have been placed for use in calling the printer or plotter. In most cases the plotting programs incorporate plotting Subroutines allowing the user to specify units in terms of inches, or centimeterso 3 - - - - - - - - _.. _-_.._-_......•. _-_._-_._---------------------------------------- 9100B/ 9100A Program Library Cross-Reference The 9100B Program Library contains several B Only programs which previously were "A" programs. These programs were either multiple pass or storagelIiiiIted on the 9100A Calculator. After conversion, these programs offer the advantages of being single pass, having ample storage, and in some cases yielding plotted output. The table given below lists these converted programs. --Program Title "A" Library Part Number 70015 "B" Library Part Number NUMERICAL INTEGRATION USING SIMPSON'S RULE WHEN f(x) IS 70409 KNOWN 70018 CONVOL UTION 70408 70019 4th OR 5th DEGREE POLYNOMIAL ROOTS 70405 70020 INTEGRAL OF THE FORM F(X) = x f f(u)du 70410 A 70810 WEIBULL DISTRIBUTION PARAMETER CALCULATION FOR FAILURE DATA 70902 70814 MULTIPLE LINEAR REGRESSION 70901 70815 NON-LINEAR REGRESSION-LEAST SQUARES PARABOLA 70903 71002 TCHEBYSHEFF FILTER DESIGN-FINITE TERMINATIONS 71501 71011 S PARAMETER TO Y PARAMETER CONVERSION 71502 74008 COORDINATE GEOMETRY AND ENCLOSED AREA 74102 74011 TRAVERSE WITH COMPASS RULE ADJUSTMENT OPTION 74101 ('--\ \,~../i 4 t+#LMWt"rWMF!!Ww't¥fS'"!t'! #t Hdtd±Hktt:tltb+wf.HW MATHEMATICS tlm"W Ott II !, PI'li Iii"t" ",," Ii 09100-70000 70001 - n! Calculates n! for positive integer n. (n < 70) 70002 - POLYNOMIAL EVALUATION Evaluates polynomials of the form: f(z) = Cnz n + Cn _1 Zn - 1 + . . . + C 1z + Co for complex Ci ' i=l, . . . , n and complex z. 70003 - NUMERICAL INTEGRATION USING SIMPSON'S ONE-THIRD RULE Uses Simpson's rule to obtain the area under a curve. The equation used is: h A = "3 (YO + 4Y 1 + Y 2) 70006 - 1st ORDER DIFFERENTIAL EQUATIONS Solves differential equations of the form: YI o = f(x, y) 0::: <C ~ U <C C~ Il.LJ ...J 70007 - RAISING A NUMBER TO A POWER Solves the equation: 70008 - 2nd ORDER DIFFERENTIAL EQUATIONS Solves differential equations of the form: 3: l.LJ y" ::r.: ~ ~ = f(x, y, y/) 70009 - QUADRATIC EQUATION Solves ax 2 + bx + c = 0 for the roots. 70010 - FINITE DIFFERENCE INTERPOLATION USING GAUSS'S BACKWARD FORMULA Uses Gauss's backward formula for interpolation in tabular data with equal abscissa spacing. The program fits a cubic equation through the tabular data. 70011 - CUBIC EQUATION Solves x 3 + px 2 + qx + r o for the real and complex roots. 70013 - FACTORS OF n Gives all factors of an integer no 70014 - REAL ROOTS OF f(x) Calculates real roots of f(x) by starting from Xo and incrementing until f(x) changes sign, then converges on the root. f(x) is programmed in by the user. 70016 - SIMULTANEOUS SOLUTION OF TWO EQUATIONS IN TWO UNKNOWNS The program solves two independent equations of the form: ax+by = e cx + dy = f x and yare the unknowns to be found. PRINTED IN U.S.A. 1 _ _i'ZVEa:tilUU: : ii$( P ¥4MMMU4 :,:.." MA THEMA TICS (CON'T) 12 70017 - n! (n < 10 ) Calculates n! for positive integer n. () ,- 70021 - POLYNOMIAL EVALUATION (1 ~ n ~ 10) Repeatedly evaluates for a given x, a real polynomial of the form: .. f() x = AnXnA + n- 1x n-1 . . . A 1x + A 0 f or 1 < - n < - 10 70022 - 3 X 3 MATRIX INVERSION OR SIMULTANEOUS SOLUTION OF THREE EQUATIONS IN THREE UNKNOWNS Solves three linear independent equations in three unknowns simultaneously or inverts a 3 x 3 matrix. 70023 - FOURIER SERIES Calculates the Fourier Series coefficients that represent a periodic time function f(t) with period T. The specific f(t) is programmed into the calculator by the user. 70024 - GAMMA FUNCTION Evaluates the gamma function (X) f(v) for 0 :5 v ~ 10 9 where f(v) = J e- t tV- 1dt o 70025 - BESSEL FUNCTION Calculates the value of the Bessel function In(x) of the first kind of integer order n where x2 k L k =0 (- 4) k! (n + k) ! 70401 - HYPERGEOMETRIC SERIES EXPANSION Given a, b, and c, this program determines the coefficients of the hypergeometric series F(a, b, c; X). This program is useful in solving Gauss's differential equation. 70402 - (3 X 3) MATRIX MULTIPLICATION Given two (3 x 3) matrices A and B, this program determines the product matrix C = A. B . 70403 - ROOTS OF A 4th DEGREE POLYNOMIAL This program determines the roots (real and complex) of a 4th degree polynomial of the form X4 + a1 x3 + a2x2 + a3X + a4 where ai is real. 70404 - NUMERICAL SOLUTION OF TWO FIRST ORDER DIFFERENTIAL EQUATIONS This program may be used to solve a wide variety of pairs of first order differential equations of the form : f(X, Y,Z), dz = g (X, Y, Z) . dx 70405 - ROOTS OF A 6th DEGREE POLYNOMIAL The program determines the roots (real and complex) of a 6th degree polynomial of the form X6 + a1 x5 + a2 x4 + a3 x3 + a4x2 + a 5X + a6 where ai is real. 70406 - CHARACTERISTIC EQUATION OF A (3 X 3) MATRIX AND EIGENVALUE DETERMINATION Given a (3 x 3) matrix A, this program computes the characteristic equation >., 3 + p >.,2 + q A +r = 0 and then determines the eigenvalues by using Program 09100-70011 as a Sub-Program. 2 ----------------------- o ~'bWMIDI.!W.WWIeJ!"M.'bl.NWtI!ltjMHtItad*\. 1 h±*!'t\"NHtWIl"'Wk'*d#WMt!MfthrlW% 'HhlL!HIWWI'MW'M"' "tit,S!,," ,t 'it Iii MHLl!iHtIltWW!L"'¥f til'bt±\',Mb*'t H,NriW*Iri.. It. LI."!II ' .... - ... ¥H+ ... "j'Sd.MW'M/hlhWWrlM eml'H +w,' +lA'8!11h"'IHI I t , n"WHI I HI HUlW U ' MATHEMATICS (CON'T) o 70407 - SIMULTANEOUS SOLUTION OF FOUR LINEAR EQUATIONS IN FOUR UNKNOWNS Given a system of four linear equations in four unknowns defined by the matrix equation this program uses Cholewski's method to determine the Xi'S. 70408 - CONVOLUTION INTEGRAL WITH PLOT This program evaluates and plots y(t), the convolution of e(t) and h(t). Mathematically t y(t) = f e ( T) h(t - T ) d T • o 70409 - NUMERICAL INTEGRATION USING SIMPSON'S RULE WHEN f(x) IS KNOWN The specific f(x) is programmed into the calculator by the user and is then used by the general solution to evaluate the integral. Execution time is dependent on the number of panels. Note f(x) should not have any singularities in the integration interval. AI x 70410 - INTEGRAL OF THE FORM: F(x) = f (u) du WITH PLOT This program calculates the integral of a known function f(u) between any lower limit A and a successively incremented upper limit X. Simpson's rule is used to perform the integration. A special application of this program is when f(u) is a probability denSity function. F(x) then represents the cumulative distribution function. 70411 - MAX - MIN OF Z = Z(X, Y) This program determines the approximate range of a function Z of two independent variables X and Y given a range for X and Y. This program can be used in conjunction with Program 09100-70412, PLOT OF Z = Z(X, Y). o 70412 - PLOT OF Z = Z(X, Y) Given a function Z of two independent variables X and Y, this program creates a three dimensional plot over a prescribed range of X and Y. STATISTICS 09100-70800 70801 - MEAN AND STANDARD DEVIATION Calculates the mean and standard deviation of n data points. 70802 - STANDARD DE VIA TION AND MEAN OF GROUPED DATA Calculates the mean and standard deviation of data points of certain frequencies. 70803 - LINEAR REGRESSION Calculates the best fit of a set of data pOints to the line y = ax + b, i. e., the program computes the estimates ~ and b. It also gives the correlation coefficient r. 70804 - NORMAL PROBABILITY INTEGRAL Evaluates the integral under the normal density function. 70805 - X2 - CHI SQUARE DISTRIBUTION Calculates the integral of the Chi Square distribution from 0 up to a value of given number of degrees of freedom. X 2 for a 2 70806 - X - CHI SQUARE EVALUATION EXPECTED VALUES EQUAL (Ei = E) Chi square calculation where the expected value of each observation is equal. 70808 - X2 - CHI SQUARE EVALUATION EXPECTED VALUES UNEQUAL (Ei f Ej) Chi square calculation where the expected values of the observations are not necessarily equal. o 70811 - LEAST SQUARES FIT-POWER CURVE Calculates coefficients fitting data pOints (xb Yi) to an equation of the form: y = ax b 3 _:.:W&I«"; m A, P4 '" i ,;;iAiWMlf1" STATISTICS (CON'T) 70812 - LEAST SQUARES FIT-EXPONENTIAL Calculates coefficients fitting data points (xi, Yi) to an equation of the form: y = aebx 70813 - POISSON DENSITY CalCulates the various summations associated with the Poisson density to give a probability based on an input parameter and summation endpoints. 70816 - RANDOM NUMBER GENERATOR Random numbers (RN) in the range 0 ~ RN ~ 1 are calculated; more than 10,000 random numbers may be generated before any previous value is repeated. 70901 - MULTIPLE LINEAR REGRESSIONS Given a set of data points (Xi' Yi , Zi), this program determines the coefficients of the linear equation 70902 - WEIBULL DISTRIBUTION PARAMETER CALCULATION FOR FAILURE DATA Calculates the parameters for the Weibull distribution and thus estimates of times to failure percentages may be made. 70903 - NON-LINEAR REGRESSION - LEAST SQUARES PARABOLA Calculates coefficients fitting data points (xb Yi) to an equation of the form: y = a O + a 1x + a2 x2 70904 - NORMAL (GAUSSIAN) CURVE PLOT Given mean (M) and variance (J" '2 , this program generates a normal curve given by 1 y = (J",.f2-iT e -(X - M) 2 (J" 2 2 This program can be used with Program 70905, Histogram Generation. 70905 - HISTOGRAM GENERATION WITH PLOT This program generates and RIots a histogram of ten windows given a set of positive numbers. The mean M and variance (J" 2 of the data set are computed and stored for use by Program 70904, NORMAL CURVE PLOT. 70906 - HISTOGRAM GENERATION This program generates a histogram table of ten windows given a data set of positive numbers. In addition it determines the mean M and the variance (J" 2 of the data set. 70907 - ONE WAY ANALYSIS OF VARIANCE This program separates the total variance in a table of data into that due to chance and that due to differences between the population means underlying each column of sample data. 70908 - F DISTRIBUTION This program evaluates the F distribution density function for given values of F, V 1, and V2' 70909 - TWO WAY ANALYSIS OF VARIANCE (m X 4) This program analyses the total statistical variance in a table of data by separating the total variance into two parts, the variance among rows, and the variance between columns. These variances are then compared to the variance due to random influence. 70910 - TWO WAY ANALYSIS OF VARIANCE WITH REPLICATES This program analyses the total statistical variance of a table of data by separating the total variance into three parts; the variance among rows, the variance between columns, and the variance due to interaction. 4 / ELECTRONICS o 09100-71000 71001 - TCHEBYSHEFF FILTER DESIGN Calculates component values for Tchebysheff low pass filters with equal terminations. 71003 - BUTTERWORTH FILTER DESIGN Calculates component values for Butterworth low pass filters between equal terminations. 71004 - MINIMUM LOSS PADS Calculates resistive minimum loss pad and gives resistor values and loss in dB. 71005 - TCHEBYSHEFF EVALUATION Used to determine filter order or the frequency response of a particular Tchebysheff filter. 71006 - A TTENUATOR PADS T OR IT Calculates resistor values for either T or IT pads. 71007 - BAND PASS FILTER DESIGN Calculates ideal component values and evaluates the frequency response by the image parameter method for a band pass filter. 71008 - STUB MATCHED TRANSMISSION LINE Calculates the distance from a load to a point where a shorted stub is to be placed and the length of the stub to match a transmission line. 71009 - TRANSM1SSION LINE Calculates the impedance at any point on a transmission line either toward the generator or toward the load, the voltage reflection (magnitude and phase) and the VSWR on the line. 71010 - WYE -+DELTA AND/OR DELTA-+WYE CONVERSION Transforms impedances wired in delta configuration to the equivalent wye configuration and vice-versa. Loop and nodal analyses are used to perform the transformations. 71501 - TCHEBYSHEFF FILTER DESIGN - FINITE TERMINATIONS Calculates component values for Tchebysheff low pass filters with finite terminations (equal or unequal). c 71502 - S PARAMETER TO Y PARAMETER CONVERSION Converts S parameters for linear (active or passive) circuits to Y parameters. 71503 - FREQUENCY RESPONSE FROM POLES AND ZEROES WITH PLOT Given the zeroes and poles of a complex function f(s), the magnitude and phase response is computed over a specified frequency range. The program can consider any combination of six poles and zeroes of the form ri + jw. MECHANICS 09100-72000 72002 - TRANSCENDENTAL EQUATION (ARC INVOLUTE IN GEAR DESIGN) Solves for the angle c:P in radians in the following expression INV (c:p) = TAN c:p - cp where the INV (cp) is given. 1x10-17 < c:p < 1x10 6 (cp is in radians). 72003 - SPRING DESIGN - COMPRESSION AND EXTENSION SPRINGS This program calculates one of three variables (d - diameter of Wire, N - number of turns of wire, and D - mean coil diameter), the remaining two being set, and calculates the maximum allowable stress. Other inputs are set to predetermined values. 72004 - STRESS AND STRAIN FROM A RECTANGULAR ROSETTE Calculates the principal strains and stresses given rectangular rosette and strain gauge inputs. 72501 - PROPERTIES OF AREAS This program determines the properties of any area which can be approximated by a set of rectangles. The properties determined are: o 1. Area 2. Moments of inertia 3. Distances from axes to the centroid 40 Products of inertia about the centroid 5 &&llR••AMalle.lNaC ,.; au. M=*".saars Ott e, M W4¥A ij ; \ 4444M!( 4.14 W) AI 1.4.% q; $4M;;;:; .. BUSINESS 09100-73000 73001 - ANNUAL INTEREST Calculates i that satisfies the equation: P i(1 + i)n R (1 + i)n - 1 73008 - AMORTIZED LOAN Calculates the monthly payment on the principal of a loan for a specified term, the amount of payments toward principal and interest, and a running total of the amount of payments toward principal and interest to date. 73101 - RETURN ON INVESTMENT FOR UP TO 16 VARYING CASH FLOWS This program solves for the value of interest per period for up to sixteen varying cash flows. The program solves the equation: 16 PV (Present Value) = L k =1 (1 + i)k where C k represents a cash flow per period. PHYSICS 09100-73200 73202 - FLUX DENSITY Calculates the flux density along an axis of a circular loop for a specified radius r, current I, and distance d. ~d 73203 - VENTURI METER Calculates flow Q by using Bernoulli's equation. 73204 - ORBITAL MECHANICS Calculates the velocity of a satellite at apogee and perigee and the orbital time in seconds of a satellite orbiting a body in space. THERMODYNAMICS 09100-73700 73851 - HEAT TRANSFER THROUGH A MULTILAYERED CYLINDER This program calculates the rate of heat flow through a multilayered cylinder. Both convective and conductive layers are considered. 73852 - TRANSIENT CONDUCTION IN A SLAB Given the initial temperature of a sUtb and a fluid, this program determines the temperature (as a function of time and distance) of the slab as it is immersed into the fluid. SURVEYING 09100-74000 74003 - INVERSE TRAVERSE FROM COORDINA TES Calculates bearing, distance, and quadrant code from end-point coordinates. 6 o ", " ' tt !"1m? tit SURVEYING (CON'T) 74004 - THREE POINT PROBLEM Calculates the coordinates of an observer's position given coordinates of three other points and two reference angles to the observer's position. o 74101 - TRAVERSE WITH COMPASS RULE ADJUSTMENT OPTION Traverses by bearing and distance, calculates coordinates, closure error, total traverse distance and precision ratio. The program may then be used to distribute the closure error by the Compass Rule. 74102 - COORDINATE GEOMETRY AND ENCLOSED AREA Traverses by bearing and distance and calculates coordinates, enclosed area, and the following curve data: 1. Arc length 2. Chord length STRUCTURES 3. Central angle in decimal degrees 4. Coordinates of tangent points 09100-74200 74203 - CANTILEVER BEAM - INTERMEDIATE LOAD Calculates shear, moment, and deflection. 74204 - CANTILEVER BEAM - TRIANGULAR LOAD Calculates shear, moment, and deflection. 74205 - COORDINATES OF EQUALLY SPACED POINTS ON A CIRCLE Computes the rectangular coordinates of equally spaced points on a circle given the center point coordinates, radius and offset angle of the circle, and the number of coordinate points desired on the circle. FLUID MECHANICS o 09100-75000 75001 - CHEZY -MANNING EQUATION Finds channel flow when channel is circular pipe and flowing full. 75003 - RECTANGULAR WEIR Calculates the rate of fluid flow over a rectangular weir. 75004 - WATER FLOW IN PIPE Calculates the loss factor (f) and the head loss for a pipe of specified dimensions with a known flow rate a LIFE SCIENCES 09100-75200 75201 - RADIOACTIVE DECAY Calculates the mass loss between any two times given the half-life, initial mass and present mass; displays the decay curve; or calculates the age of the mass based upon the present mass. CHEMICAL 09100-75500 75502 - ELEMENTAL PERCENTAGE AND MOLECULAR WEIGHT - 6 ELEMENT Calculates percentages and molecular weight of compounds containing 6 elements or less. 75503 - CHN ANALYSIS [K VALUES] Calculates K values given C, Hand N, blank values, and percentages for a known standard. 75504 - CHN PERCENTAGES Given C, H, and N values and using previously calculated K values and known blank values, calculates C, Hand N percentages. 0 '" , ' 7 &aaa_MaG.;.' "anitA 4:"5" 4.;:;; Ail;; , i a( &WI T44«M44 CHEMICAL (CON'T) 75505 - MOLECULAR WEIGHT BY VPO Calculates molecular weight for an unknown based on a series of vapor pressure osmometer (VPO) readings at various dilutions by extrapolating a least squares curve fit to infinite dilution. 75506 - MEMBRANE OSMOMETER Determines the number-average molecular weight by extrapolating a least squares curve fit to infinite dilution. SECONDARY EDUCATION 09100-75800 75802 - PRIME NUMBERS Calculates all prime numbers between any two numbers. 75901 - CONIC SECTION DETERMINATION WITH PLOT Given the generating angle of a cone, /3 , and the intersection angle with a plane, a , this program determines and plots the conic section. MISCELLANEOUS 09100-76000 76003 - NA VIGA TIONAL COURSE CALCULATION Calculates course settings for one or more adjoining legs of a proposed journey, the length of each leg, and the total distance covered on completion of the journey. 76004 - CIRCLE DETERMINED BY THREE POINTS Calculates the radius and center point (in rectangular coordinates) of the circle defined by three given points. 76005 - AREA OF A RECTILINEAR SURFACE POLYGON Calculates the area of any rectilinear polygon given the rectangular coordinates of the vertices. 76501 - DIAGNOSTIC (EXERCISER) The program exercises each calculator operation and memory location with the exception of the FMT, PRINT, and error conditions. 8 ~~~-~-~-~~- ----------------- - - - - t t 'dH tt&Irl'rit!' ,,"liP .Wlt!!' "'IIW,.,HfY'"Jt filM rY,,"IIU"'IIflfrge 11m i"' '\lHtl'hw Hit'!",. I ,"r Q c::: <C ~ u d w ....J 3: w :c ~ 70001 - n! Calculates n! for positive integer n. (n < 70) Q 70002 - POLYNOMIAL EVALUATION Evaluates polynomials of the form: t::1 c::: <C ~ U <C a.. lIW f( Z ) = Cnzn + C _ z n-1 + . • . + C 1z + Co n 1 for complex Ci , i=1, . . w :c ~ t::1 , n and complex z. 70003 - NUMERICAL INTEGRATION USING SIMPSON'S ONE-THIRD RULE Uses Simpson's rule to obtain the area under a curve. The equation used is: ....J 3: 0 h A = "3 (YO + 4Y 1 + Y2) 70006 - 1st ORDER DIFFERENTIAL EQUATIONS Solves differential equations of the form: YI = f(x, y) Q c::: <C ~ u d 70007 - RAISING A NUMBER TO A POWER Solves the equation: Z3 IW ....J 3: w :c ~ = Z1 Z2 h were Zi = Xi + .JYi i = 1, 2 , 3 70008 - 2nd ORDER DIFFERENTIAL EQUATIONS Solves differential equations of the form: y II = f(x, y, y I) 70009 - QUADRATIC EQUATION E:1 Solves ax 2 + bx + c = 0 for the roots. Q c::: <C ~ U <C a.. 1-. IW ....J 3: w :c 70010 - FINITE DIFFERENCE INTERPOLATION USING GAUSS'S BACKWARD FORMULA Uses Gauss's backward formula for interpolation in tabular data with equal abscissa spacing. The program fits a cubic equation through the tabular data. 70011 - CUBIC EQUATION Solves x 3 + px2 + qx + r = 0 for the real and complex roots. 70013 - FACTORS OF n Gives all factors of an integer n. ~ 70014 - REAL ROOTS OF f(x) Calculates real roots of f(x) by starting from Xo and incrementing until f(x) changes sign, then converges on the root. f(x) is programmed in by the user. Q 70016 - SIMULTANEOUS SOLUTION OF TWO EQUATIONS IN TWO UNKNOWNS The program solves two independent equations of the form: t::1 c::: <C ~ q U I- ax+by = e cx + dy = f x and yare the unknowns to be found. W ....J 3: w :c ~ t::1 1 MATHEMATICS (CON'T) 70017 - n! (n < 10 12 ) Calculates n! for positive integer n. c 70021 - POLYNOMIAL EVALUATION (1 $ n ~ 10) Repeatedly evaluates for a given x, a real polynomial of the form: n n-1 f(x) = Anx + A n _ 1x ••• A1x + AO for 1 $ n $ 10 70022 - 3 X 3 MATRIX INVERSION OR SIMULTANEOUS SOLUTION OF THREE EQUATIONS IN THREE UNKNOWNS Solves three linear independent equations in three unknowns simultaneously or inverts a 3 x 3 matrix. 70023 - FOURIER SERIES Calculates the Fourier Series coefficients that represent a periodic time function f(t) with period T. The specific f(t) is programmed into the calculator by the user. 70024 - GAMMA FUNCTION Evaluates the gamma function r(lI) for 0 $ II $ 10 9 where r (II) = of co e-tt 1I- 1dt 70025 - BESSEL FUNCTION Calculates the value of the Bessel function In(x) of the first kind of integer order n where x In(x) n =(-2 ) ~2 )k co (_ L k =0 k! (n + k) ! 9100B ONLY 70401 - HYPERGEOMETRIC SERIES EXPANSION Given a, b, and c, this program determines the coefficients of the hypergeometric series F(a, b, c; X). This program is useful in solving Gauss's differential equation. \. 70402 - (3 X 3) MATRIX MULTIPLICATION Given two (3 x 3) matrices A and B, this program determines the product matrix C ;; A· B • 70403 - ROOTS OF A 4th DEGREE POLYNOMIAL This program determines the roots (real and complex) of a 4th degree polynomial of the form X4 + a1 x3 + a2x2 + a3X + a4 where ai is real. 70404 - NUMERICAL SOLUTION OF TWO FmST ORDER DIFFERENTIAL EQUATIONS This program may be used to solve a wide variety of pairs of first order differential equations of the form dy dx f(X, Y, Z) , az dx = g(X,Y,Z). 70405 - ROOTS OF A 6th DEGREE POLYNOMIAL The program determines the roots (real and complex) of a 6th degree polynomial of the form X6 + a1 x5 + a2 x4 + a3 x3 + a4x2 + a5X + a6 where ~ is real. 2 () c MATHEMATICS (CON'T) 9100B ONLY 70406 - CHARACTERISTIC EQUATION OF A (3 X 3) MATRIX AND EIGENVALUE DETERMINATION Given a (3 x 3) matrix A, this program computes the characteristic equation A3 + p A2 + q A + r = 0 and then determines the eigenvalues by using Program 09100-70011 as a Sub Program. 70407 - SIMULTANEOUS SOLUTION OF FOUR LINEAR EQUATIONS IN FOUR UNKNOWNS Given a system of four linear equations in four unlmowns defined by the matrix equation [Aij] [XiJ = [Pi], this program uses Cholewski's method to determine the Xi's. 70408 - CONVOLUTION INTEGRAL WITH PLOT This program evaluates and plots y(t), the convolution of e(t) and h(t). Mathematically t y(t) = J e( o T) h(t - T ) d T • 70409 - NUMERICAL INTEGRATION USING SIMPSON'S RULE WHEN f(x) IS KNOWN The specific f(x) is programmed into the calculator by the user and is then used by the general solution to evaluate the integral. Execution time is dependent on the number of panels. Note f(x) should not have any singularities in the integration interval. x c 70410 - INTEGRAL OF THE FORM: F(x) = AI f (u) du WITH PLOT This program calculates the integral of a known function f(u) between any lower limit A and a successively incremented upper limit X. Simpson's rule is used to perform the integration. A special application of this program is when f(u) is a probability density function. F(x) then represents the cumulative distribution function. 70411 - MAX - MIN OF Z = Z(X, Y) This program determines the approximate range of a function Z of two independent variables X and Y given a range for X and Y. This program can be used in conjunction with Program 09100-70412, PLOT OF Z = Z(X, Y)o l 70412 - PLOT OF Z = Z(X, Y) Given a function Z of two independent variables X and Y, this program creates a three dimensional plot over a prescribed range of X and Y. -- o 3 o b' N,t t t t rldftttNftWN't",Wff#¥WWW mrS!! II 'tt"WfwwfflftrdltMW" 'W''''' Im',"'rr:nrrn'NVtW)!P ttt!! !, 'UfI"U f "!I"[,ftj " lfI"W"'''ffi8!!fllft)'$''fL'', Cl 0::: « ~ u d I- w ....I 3: w :c ~ E:1 This program calculates n~ for integer n where 0 ~ n ~ 69. Cl 0::: « G « a.. l- IW ....I 3: w :c ~ ~ Cl 0::: « ~ u d I- w ....I 3: w :c ~ ~ Cl 0::: « ~ u « a.. l- I- W ....I 3: w :c ~ ~ Cl 0::: « ~ d. lI- W ....I 3: w :c ~ ~ n!=n(n-1)···3·2·1 "IC"II "{tHe W"I"W"Wbw '¥±ti+'!' I'JI'P'I" I"'" W'RnW H I' 'P'If'!'f""P'[ I' ",,"5' 09100-70001 EXAMPLES USER INSTRUCTIONS O~ =1 ENTER PROGRAM (Starting Address is 0-0) 6! = 720 PRESS: GO TO (0) (0) ~PRESS: [or END] c CONTINUE ENTER DATA: n ---- X PRESS: CONTINUE DISPLAY 0-- Z n~-- Y n --X o JULY, 1969 PART NO. PAGE 1 c N o o ENTER 1 0 a 0 ROLL '" F END N N! Denotes Revisionli c 0 09100-70001 / o c::: « ~ u d w ....I ~ W :::c ~ t:::l o c::: « ~ u « a.. I-I-- W ....I ~ W :::c ~ t:::l o c::: « ~ u d I-- W ....I ~ W :::c ~ t:::l o c::: « ~ u « a.. I-I-- W ....I ~ W :::c ~ t:::l o c::: « ~ a u I-- w ....I ~ W :::c ~ t::J This program evaluates polynomials of the form n n-1 f(Z)=C n Z + Cn-1Z + ... + C1 Z + Co for complex C i , =0,1; .. , n and complex Z. 09100-70002 USER INSTRUCTIONS EXAMPLES P(Z) = (3 + 4i)Z2 + (-2 + i)Z1 + (1 - i) for Z = 2 + i ReZ = 2 IrnZ = 1 P(2 + i) = - 11 + 23i P(Z) = 49. 6Z 4 + 18Z 3 + 52. 4Z2 + 8Z + 12.8 for Z = i ReZ = 0 ENTER PROGRAM (Starting Address is 0 - 0) PRESS: GO TO (0) (0) .-----i__ PRESS: [or ENDl CONTINUE c DISPLAY IrnZ = 1 P(i) = 10 - 10i 0-- Z o --Y 1 --X GENERAL FORM ENTER DATA: n --... Z, Irn Z --. Y, Re Z --... X ~PRESS: CONTINUE DISPLAY 0 -- Z 0 --Y ni -- Z ni is an indicator or coefficient entry number. When ni = 0 enter Co. ' - -ENTER DATA: 1m Cni --. Y, ReCni --+ X PRESS: CONTINUE DISPLAY '----------4 o Z IrnP(Z) Y ReP(Z) X o PART NO. c Sf:0iP K0iY 0 0 CLEAR 20 I "1 1 01 DISPLAY STOP 41 ReZ 1 13 4 5 X y ImZ n ImCnj o TO POLAR X-+( J d STORE DA A BRANCH ReCnj c 09100-70002 PART NO. PAGE 2 x RECALL ReP(Z) y (Z) ImP(Z) o 09100-70002 .b e• iHifhM'fllt'l"i!i"!"'@U!1g,!!!!·wl M'W!ItIt ""f! ru w ""V"""'II" 'ff! t iH •• te'OCt' o a:::: « ~ u C~ IW ..J 3: w I ~ ~ o a:::: « ~ This program evaluates the area under a curve represented by discrete points. The equation used is Simpson's One-Third Rule ie., X2 f f(x)dx = ~ (YO+ 4Y1+ Y2 ) - ~O h5 f(4l(e-) Xo u « a.. where X0 < e- < X2 lIW ..J Graphically the integration is performed over two panels (each of width h) as shown below 3: w Y I f(x) ~ ~ o a:::: « ~ u d ~--------~~~,~~------~X I Xo W ..J w I ~ ~ I The application of Simpson's Rule over 2n panels between Xo= a ,and X2n = b I b « ~ lIW ..J 3: w h I~O (b-a) h4 f(4l(e-) a:::: « a.. where a<~ < band f(4)(t) is the fourth derivative of f(x) evaluated at t . Thus to use the program divide the abscissa into 2n panels. (The method requires an even number of panels of width h.) Since the error term is neglected, choose h (the distance between points) such that the error term is small. Usually h« 1 when f(4)(t) is unknown. I ~ ~ o a:::: « ~ u a IW ..J 3: w I ~ ~ gives a f(x)dx = 3 (Yo+ 4 Y1+2Y2+4 Y3+2Y4 + "'+4 Yn- I + Yn ) o u X2 --':h:'I I- 3: XI Reference: Numerical Analysis by Kaiser S. Kunz McGraw - Hill Book Co., Inc. 1957 09100-70003 EXAMPLES USER INSTRUCTIONS INCREMENT CONSTANT ENTER PROGRAM (Starting Address is 0 - 0) PRESS: GO TO (0) (0) [or END] PRESS: CONTINUE DISPLAY o o o 2 .25 2.8 .50 3.8 5.2 .75 z 1. 00 Y 1. 25 1 --x 1. 50 1. 75 ENTER DATA: h - + X c Y X 2.00 h = .25 2 J f(x)dx 16. 7.0 9.2 12.1 15.6 20 = 58 o PRESS: CONTINUE INCREMENT CHANGE DISPLAY Y X o o z o 2 Y .25 2.8 2 X .50 3.8 .75 5.2 ENTER DATA: Xo - - + X 1. 00 7.0 PRESS: CONTINUE 1. 50 12.1l DISPLAY 2.00 ~ h = .25 h = .5 Io f(x )dx 16.62 2 z Y X Note: Subsequent Xi's are calculated from Xo and hand are not entered. = A - the area shows every other time starting after third y entry (Corresponds to calcuENTER DATA: Yi ---. X latedXi displayed in Y) PRESS: CONTINUE (To restart a new problem PRESS: END, PRESS: CONTINUE) To Change Increment (new h) This can only be done if area or Z register is blank ENTER DATA: Yi --. X PRESS: SET FLAG PRESS: CONTINUE DISPLAY ---------------o Z o Y 1 X ENTER DATA: new h--. X PRESS: CONTINUE (Program branches to area display and ordinate entry. Proceed as before. ) o PAGE 1 c PART NO. y z Tel> INDICATE F RST DATA o o 1 BRANCH WiHEN T CHANGE h INDICATE Xo 0 Yo Xo o c CALCULA E Xi = X i-I h AREA i-I Xi Xi+ h o 09100-70003 PAGE 2 x SUM A T PART NO. 09100-70003 z y PREVIOUS AREA \ BRANCH ;/ ORDINATE -·.. ·······-AT·--··SAM~~tf"1:~tt:"t\tT-r-------·-·-~-·····l····--···t---- ~ ...... -... + .. _._.......................................+,. _,."".,'.'...·.·l·.·.·..··--.. ------t--------+-~,-"..-~ . "'·,. . . ····-,-- 2 '--· ......·,···-_············.. -········· ...... ..;.· ...•..••·••.. ·.. ,...1·.. • ....................- - - - - - - + - - - - - - f - - - - - , - + - - + - - - - - - - 1 - - - - - t - - - - - - , - - - I .....,.......,.-...-----------1-------I--..................' -------t---~-~ . . ".".'". . .,..... t - - - - - - - - - - - - - - f - - - - - . , -. .-.,. . -......-....-. - - + - - - - - - c o c::: <C :::.::: U d w ..j 3: w :::c ~ t:J o This program may be used to solve a wide variety of first order (homogenous or non-homogenous, linear or nonlinear) differential equations of the form y/ = f(X,Y) c::: <C :::.::: U <C a.. The solution is a numerical solution which calculates Yi for Xi' The X values are closely spaced with increment h over the desired range. Specifically the solution used in this program is a Runge-Kutta Method (thirdorder) which uses the equations, Yi+1 =Yj + I-I-- k(p+2q+2r+s) W ..j 3: w :::c where p = hf (Xj,Yj) ~ q = hf ( X j + ~ , Y j + ~) o r= hf( Xj + 2" ' Yj + 2") <C :::.::: U s=hf(Xj+h, Yj +r) t:J h c::: d h= X j+1-Xj w ..j 3: w :::c ~ t:J Reference: Numerical Analysis by Kaiser S. Kunz McGraw-Hill Book Co. Inc. o c::: <C :::.::: U <C a.. I-I-W ..j 3: w :::c ~ t:J o c::: <C :::.::: U d I-W ..j 3: w :::c [§} t:J 1957 q 09100-70006 USER INSTRUCTIONS EXAMPLES ENTER PROGRAM (Starting Address is 0 - 0) PRESS: (GO TO) (4) (a) Place mode switch to PROGRAM Starting at 4-a, enter the program steps which take the independent variable from the X register, the dependent variable from the Y register and calculate f(X, Y). Place f(X, Y) in the Y register and exit to location 8-b. Note there is a maximum of 57 steps (4-a through 8-a) available for storingandpositioningf(X, Y). R 'V'V'v f(t)~ T ~:) Vo(O) = 0 C to = 0 0 h = .01 f(t) ~ Vo Place mode switch to RUN PRESS: GO TO (0) (0) [ or END] t1 PRESS: CONTINUE ENTER DATA: (Initial conditions and increment) h - . Z, Yo - . Y, Xo - . X PRESS: CONTINUE The Calculator will display answers at every increment of the independent variable in the form h --Z i1 f~)~ i3 ~ Ii~. t c f(t) _ Vo(t) _ C dVo(t) = 0 R R dt Yi - - Y dVo(t) _ Xi - - X (It- - Vo(t) f(t) CR + CR :0:) Initial } to = 0 Conditions V0(0) = 0 Increment h = .01 LetV o =1V, C=lF,R=lnandt1=4sec. To stop the solution at the next increment depress PAUSE until display. To restart press CONTINUE. The equation becomes To start from a new set of initial conditions dVo(t) = _ Vo(t) + 1; dt "I t < 4 PRESS: STOP PRESS: GO TO (0) (0) [or END] dVo(t) dt - Vo(t); t > 4 PRESS: CONTINUE Enter initial conditions and increment as before. The program steps that form V6 = f(t, Yo) appear on Page 1. See User Instructions. Vo (Volts) 1.0 o ...i; ! w·! .hle"W'jI l.tL·4tLJLj#*IItJwlHW.+<fhidHW. . . .!tH!I'ty.".wHlld"l"AALJi#i4:.lWH 1I4lwihIJWYUUtH.wKW+ib "IMUlti!)]" II I. j I'I! 9' 1M h IIIH'!!"!!!!1 ~J It' " .\~ • I 'ij"II'II'PM'.' ''i'm Oil"",.! • PAGE 1 x