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HPg graphing calculator
user’s guide
H
Edition 1
HP part number F2229AA-90006

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Notice
REGISTER YOUR PRODUCT AT: www.register.hp.com
THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE
PROVIDED “AS IS” AND ARE SUBJECT TO CHANGE WITHOUT
NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY
OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT
NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A
PARTICULAR PURPOSE.
HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY ERRORS
OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN
CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE
OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN.
© 2003, 2006 Hewlett-Packard Development Company, L.P.
Reproduction, adaptation, or translation of this manual is prohibited without
prior written permission of Hewlett-Packard Company, except as allowed under
the copyright laws.
Hewlett-Packard Company
16399 West Bernardo Drive
MS 8-600
San Diego, CA 92127-1899
USA
Printing History
Edition 1 April 2006

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Preface
You have in your hands a compact symbolic and numerical computer that will
facilitate calculation and mathematical analysis of problems in a variety of
disciplines, from elementary mathematics to advanced engineering and science
subjects. Although referred to as a calculator, because of its compact format
resembling typical hand-held calculating devices, the HP 50g should be
thought of as a graphics/programmable hand-held computer.
The HP 50g can be operated in two different calculating modes, the Reverse
Polish Notation (RPN) mode and the Algebraic (ALG) mode (see page 1-13 for
additional details). The RPN mode was incorporated into calculators to make
calculations more efficient. In this mode, the operands in an operation (e.g., ‘2’
and ‘3’ in the operation ‘2+3’) are entered into the calculator screen, referred
to as the stack, and then the operator (e.g., ‘+’ in the operation ‘2+3’) is
entered to complete the operation. The ALG mode, on the other hand, mimics
the way you type arithmetic expressions in paper. Thus, the operation ‘2+3’, in
ALG mode, will be entered in the calculator by pressing the keys ‘2’, ‘+’, and
‘3’, in that order. To complete the operation we use the ENTER key. Examples
of applications of the different functions and operations in this calculator are
illustrated in this user’s guide in both modes.
This guide contains examples that illustrate the use of the basic calculator
functions and operations. The chapters are organized by subject in order of
difficulty. Starting with the setting of calculator modes and display options, and
continuing with real and complex number calculations, operations with lists,
vectors, and matrices, detailed examples of graph applications, use of strings,
basic programming, graphics programming, string manipulation, advanced
calculus and multivariate calculus applications, advanced differential equations
applications (including Laplace transform, and Fourier series and transforms),
and probability and statistic applications.

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For symbolic operations the calculator includes a powerful Computer Algebraic
System (CAS) that lets you select different modes of operation, e.g., complex
numbers vs. real numbers, or exact (symbolic) vs. approximate (numerical)
mode. The display can be adjusted to provide textbook-type expressions,
which can be useful when working with matrices, vectors, fractions,
summations, derivatives, and integrals. The high-speed graphics of the
calculator produce complex figures in very little time.
Thanks to the infrared port, the RS232 port, and the USB port and cable
provided with your calculator, you can connect your calculator with other
calculators or computers. This allows for fast and efficient exchange of
programs and data with other calculators or computers. The calculator
provides a flash memory card port to facilitate storage and exchange of data
with other users.
The programming capabilities of the calculator allow you or other users to
develop efficient applications for specific purposes. Whether it is advanced
mathematical applications, specific problem solution, or data logging, the
programming languages available in your calculator make it into a very
versatile computing device.
We hope your calculator will become a faithful companion for your school and
professional applications.

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Page TOC-1
Table of contents
Chapter 1 - Getting started ,1-1
Basic Operations ,1-1
Batteries ,1-1
Turning the calculator on and off ,1-2
Adjusting the display contrast ,1-2
Contents of the calculator’s display ,1-2
Menus ,1-3
SOFT menus vs. CHOOSE boxes ,1-4
Selecting SOFT menus or CHOOSE boxes ,1-5
The TOOL menu ,1-7
Setting time and date ,1-7
Introducing the calculator’s keyboard ,1-11
Selecting calculator modes ,1-12
Operating Mode ,1-13
Number Format and decimal dot or comma ,1-17
Angle Measure ,1-23
Coordinate System ,1-24
Beep, Key Click, and Last Stack ,1-25
Selecting CAS settings ,1-26
Selecting Display modes ,1-27
Selecting the display font ,1-27
Selecting properties of the line editor ,1-28
Selecting properties of the Stack ,1-28
Selecting properties of the equation writer (EQW) ,1-29
Selecting the size of the header ,1-30
Selecting the clock display ,1-30

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Page TOC-2
Chapter 2 - Introducing the calculator ,2-1
Calculator objects ,2-1
Editing expressions on the screen ,2-3
Creating arithmetic expressions ,2-3
Editing arithmetic expressions ,2-6
Creating algebraic expressions ,2-7
Editing algebraic expressions ,2-8
Using the Equation Writer (EQW) to create expressions ,2-10
Creating arithmetic expressions ,2-11
Editing arithmetic expressions ,2-17
Creating algebraic expressions ,2-19
Editing algebraic expressions ,2-21
Creating and editing summations, derivatives, and integrals ,2-29
Organizing data in the calculator ,2-33
Functions for manipulation of variables ,2-34
The HOME directory ,2-35
The CASDIR sub-directory ,2-35
Typing directory and variable names ,2-37
Creating subdirectories ,2-39
Moving among subdirectories ,2-43
Deleting subdirectories ,2-43
Variables ,2-47
Creating variables ,2-47
Checking variables contents ,2-52
Replacing the contents of variables ,2-55
Copying variables ,2-56
Reordering variables in a directory ,2-59
Moving variables using the FILES menu ,2-60
Deleting variables ,2-61
UNDO and CMD functions ,2-62
Flags ,2-64
Example of flag setting: general solutions vs. principal value ,2-65

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Page TOC-3
Other flags of interest ,2-66
CHOOSE boxes vs. Soft MENU ,2-67
Selected CHOOSE boxes ,2-69
Chapter 3 - Calculation with real numbers ,3-1
Checking calculators settings ,3-1
Checking calculator mode ,3-2
Real number calculations ,3-2
Changing sign of a number, variable, or expression ,3-3
The inverse function ,3-3
Addition, subtraction, multiplication, division ,3-3
Using parentheses ,3-4
Absolute value function ,3-4
Squares and square roots ,3-5
Powers and roots ,3-5
Base-10 logarithms and powers of 10 ,3-5
Using powers of 10 in entering data ,3-6
Natural logarithms and exponential function ,3-6
Trigonometric functions ,3-6
Inverse trigonometric functions ,3-6
Differences between functions and operators ,3-7
Real number functions in the MTH menu ,3-7
Hyperbolic functions and their inverses ,3-9
Real number functions ,3-11
Special functions ,3-14
Calculator constants ,3-16
Operations with units ,3-17
The UNITS menu ,3-17
Available units ,3-19
Converting to base units ,3-22
Attaching units to numbers ,3-23
Operations with units ,3-25
Units manipulation tools ,3-27

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Page TOC-4
Physical constants in the calculator ,3-29
Special physical functions ,3-32
Function ZFACTOR ,3-32
Function F0λ ,3-33
Function SIDENS ,3-33
Function TDELTA ,3-33
Function TINC ,3-34
Defining and using functions ,3-34
Functions defined by more than one expression ,3-36
The IFTE function ,3-36
Combined IFTE functions ,3-37
Chapter 4 - Calculations with complex numbers ,4-1
Definitions ,4-1
Setting the calculator to COMPLEX mode ,4-1
Entering complex numbers ,4-2
Polar representation of a complex number ,4-3
Simple operations with complex numbers ,4-4
Changing sign of a complex number ,4-5
Entering the unit imaginary number ,4-5
The CMPLX menus ,4-5
CMPLX menu through the MTH menu ,4-6
CMPLX menu in keyboard ,4-7
Functions applied to complex numbers ,4-8
Functions from the MTH menu ,4-9
Function DROITE: equation of a straight line ,4-9
Chapter 5 - Algebraic and arithmetic operations ,5-1
Entering algebraic objects ,5-1
Simple operations with algebraic objects ,5-1
Functions in the ALG menu ,5-3
COLLECT ,5-4
EXPAND ,5-4

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Page TOC-5
FACTOR ,5-5
LNCOLLECT ,5-5
LIN ,5-5
PARTFRAC ,5-5
SOLVE ,5-5
SUBST ,5-5
TEXPAND ,5-5
Other forms of substitution in algebraic expressions ,5-6
Operations with transcendental functions ,5-7
Expansion and factoring using log-exp functions ,5-7
Expansion and factoring using trigonometric functions ,5-8
Functions in the ARITHMETIC menu ,5-9
DIVIS!,5-9
FACTORS ,5-9
LGCD!,5-10
PROPFRAC ,5-10
SIMP2 ,5-10
INTEGER menu ,5-10
POLYNOMIAL menu ,5-10
MODULO menu ,5-11
Applications of the ARITHMETIC menu ,5-12
Modular arithmetic ,5-12
Finite arithmetic rings in the calculator ,5-14
Polynomials ,5-17
Modular arithmetic with polynomials ,5-17
The CHINREM function ,5-17
The EGCD function ,5-18
The GCD function ,5-18
The HERMITE function ,5-18
The HORNER function ,5-19
The variable VX ,5-19
The LAGRANGE function ,5-19
The LCM function ,5-20
The LEGENDRE function ,5-20
The PCOEF function ,5-21

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Page TOC-6
The PROOT function ,5-21
The PTAYL function ,5-21
The QUOT and REMAINDER functions ,5-21
The EPSX0 function and the CAS variable EPS ,5-22
The PEVAL function ,5-22
The TCHEBYCHEFF function ,5-22
Fractions ,5-23
The SIMP2 function ,5-23
The PROPFRAC function ,5-23
The PARTFRAC function ,5-23
The FCOEF function ,5-24
The FROOTS function ,5-24
Step-by-step operations with polynomials and fractions ,5-25
The CONVERT Menu and algebraic operations ,5-26
UNITS convert menu (Option 1) ,5-26
BASE convert menu (Option 2) ,5-27
TRIGONOMETRIC convert menu (Option 3) ,5-27
MATRICES convert menu (Option 5) ,5-27
REWRITE convert menu (Option 4) ,5-27
Chapter 6 - Solution to single equations ,6-1
Symbolic solution of algebraic equations ,6-1
Function ISOL ,6-1
Function SOLVE ,6-2
Function SOLVEVX ,6-3
Function ZEROS ,6-4
Numerical solver menu ,6-5
Polynomial Equations ,6-6
Financial calculations ,6-9
Solving equations with one unknown through NUM.SLV ,6-13
The SOLVE soft menu ,6-26
The ROOT sub-menu ,6-26
Function ROOT ,6-26

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Page TOC-7
Variable EQ ,6-26
The SOLVR sub-menu ,6-26
The DIFFE sub-menu ,6-29
The POLY sub-menu ,6-29
The SYS sub-menu ,6-30
The TVM sub-menu ,6-30
Chapter 7 - Solving multiple equations ,7-1
Rational equation systems ,7-1
Example 1 – Projectile motion ,7-1
Example 2 – Stresses in a thick wall cylinder ,7-2
Example 3 - System of polynomial equations ,7-4
Solution to simultaneous equations with MSLV ,7-4
Example 1 - Example from the help facility ,7-5
Example 2 - Entrance from a lake into an open channel ,7-5
Using the Multiple Equation Solver (MES) ,7-9
Application 1 - Solution of triangles ,7-9
Application 2 - Velocity and acceleration in polar coordinates ,7-17
Chapter 8 - Operations with lists ,8-1
Definitions ,8-1
Creating and storing lists ,8-1
Composing and decomposing lists ,8-2
Operations with lists of numbers ,8-2
Changing sign ,8-3
Addition, subtraction, multiplication, division ,8-3
Real number functions from the keyboard ,8-4
Real number functions from the MTH menu ,8-5
Examples of functions that use two arguments ,8-6
Lists of complex numbers ,8-7
Lists of algebraic objects ,8-8
The MTH/LIST menu ,8-8
Manipulating elements of a list ,8-10

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Page TOC-8
List size ,8-10
Extracting and inserting elements in a list ,8-10
Element position in the list ,8-11
HEAD and TAIL functions ,8-11
The SEQ function ,8-11
The MAP function ,8-12
Defining functions that use lists ,8-13
Applications of lists ,8-15
Harmonic mean of a list ,8-15
Geometric mean of a list ,8-16
Weighted average ,8-17
Statistics of grouped data ,8-18
Chapter 9 - Vectors ,9-1
Definitions ,9-1
Entering vectors ,9-2
Typing vectors in the stack ,9-2
Storing vectors into variables ,9-3
Using the Matrix Writer (MTRW) to enter vectors ,9-3
Building a vector with ARRY ,9-6
Identifying, extracting, and inserting vector elements ,9-7
Simple operations with vectors ,9-9
Changing sign ,9-9
Addition, subtraction ,9-9
Multiplication by a scalar, and division by a scalar ,9-9
Absolute value function ,9-10
The MTH/VECTOR menu ,9-10
Magnitude ,9-10
Dot product ,9-11
Cross product ,9-11
Decomposing a vector ,9-11
Building a two-dimensional vector ,9-12
Building a three-dimensional vector ,9-12

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Page TOC-9
Changing coordinate system ,9-12
Application of vector operations ,9-15
Resultant of forces ,9-15
Angle between vectors ,9-15
Moment of a force ,9-16
Equation of a plane in space ,9-17
Row vectors, column vectors, and lists ,9-18
Function OBJ ,9-19
Function LIST ,9-20
Function DROP ,9-20
Transforming a row vector into a column vector ,9-20
Transforming a column vector into a row vector ,9-21
Transforming a list into a vector ,9-23
Transforming a vector (or matrix) into a list ,9-24
Chapter 10!- Creating and manipulating matrices ,10-1
Definitions ,10-1
Entering matrices in the stack ,10-2
Using the Matrix Writer ,10-2
Typing in the matrix directly into the stack ,10-3
Creating matrices with calculator functions ,10-3
Functions GET and PUT ,10-6
Functions GETI and PUTI ,10-6
Function SIZE ,10-7
Function TRN ,10-7
Function CON ,10-8
Function IDN ,10-9
Function RDM ,10-9
Function RANM ,10-11
Function SUB ,10-11
Function REPL ,10-12
Function DIAG ,10-12
Function DIAG ,10-13

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Page TOC-10
Function VANDERMONDE ,10-13
Function HILBERT ,10-14
A program to build a matrix out of a number of lists ,10-14
Lists represent columns of the matrix ,10-15
Lists represent rows of the matrix ,10-17
Manipulating matrices by columns ,10-17
Function COL ,10-18
Function COL ,10-19
Function COL+ ,10-19
Function COL- ,10-20
Function CSWP ,10-20
Manipulating matrices by rows ,10-21
Function ROW ,10-22
Function ROW ,10-23
Function ROW+ ,10-23
Function ROW- ,10-24
Function RSWP ,10-24
Function RCI ,10-25
Function RCIJ ,10-25
Chapter 11 - Matrix Operations and Linear Algebra ,11-1
Operations with matrices ,11-1
Addition and subtraction ,11-2
Multiplication ,11-2
Characterizing a matrix (The matrix NORM menu) ,11-7
Function ABS ,11-8
Function SNRM ,11-8
Functions RNRM and CNRM ,11-9
Function SRAD ,11-10
Function COND ,11-10
Function RANK ,11-11
Function DET ,11-12
Function TRACE ,11-14

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Page TOC-11
Function TRAN ,11-15
Additional matrix operations (The matrix OPER menu) ,11-15
Function AXL ,11-16
Function AXM ,11-16
Function LCXM ,11-16
Solution of linear systems ,11-17
Using the numerical solver for linear systems ,11-18
Least-square solution (function LSQ) ,11-24
Solution with the inverse matrix ,11-27
Solution by “division” of matrices ,11-27
Solving multiple set of equations with the same coefficient matrix ,11-28
Gaussian and Gauss-Jordan elimination ,11-29
Step-by-step calculator procedure for solving linear systems ,11-38
Solution to linear systems using calculator functions ,11-41
Residual errors in linear system solutions (Function RSD) ,11-44
Eigenvalues and eigenvectors ,11-45
Function PCAR ,11-45
Function EGVL ,11-46
Function EGV ,11-46
Function JORDAN ,11-47
Function MAD ,11-48
Matrix factorization ,11-49
Function LU ,11-50
Orthogonal matrices and singular value decomposition ,11-50
Function SVD ,11-50
Function SVL ,11-51
Function SCHUR ,11-51
Function LQ ,11-51
Function QR ,11-52
Matrix Quadratic Forms ,11-52
The QUADF menu ,11-52
Function AXQ ,11-53

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Page TOC-12
Function QXA ,11-53
Function SYLVESTER ,11-54
Function GAUSS ,11-54
Linear Applications ,11-54
Function IMAGE ,11-55
Function ISOM ,11-55
Function KER ,11-56
Function MKISOM ,11-56
Chapter 12 - Graphics ,12-1
Graphs options in the calculator ,12-1
Plotting an expression of the form y = f(x) ,12-2
Some useful PLOT operations for FUNCTION plots ,12-5
Saving a graph for future use ,12-7
Graphics of transcendental functions ,12-8
Graph of ln(X) ,12-8
Graph of the exponential function ,12-10
The PPAR variable ,12-11
Inverse functions and their graphs ,12-11
Summary of FUNCTION plot operation ,12-13
Plots of trigonometric and hyperbolic functions ,12-16
Generating a table of values for a function ,12-17
The TPAR variable ,12-17
Plots in polar coordinates ,12-18
Plotting conic curves ,12-20
Parametric plots ,12-22
Generating a table for parametric equations ,12-25
Plotting the solution to simple differential equations ,12-26
Truth plots ,12-28
Plotting histograms, bar plots, and scatter plots ,12-29
Bar plots ,12-29
Scatter plots ,12-31
Slope fields ,12-33

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Page TOC-13
Fast 3D plots ,12-34
Wireframe plots ,12-36
Ps-Contour plots ,12-38
Y-Slice plots ,12-39
Gridmap plots ,12-40
Pr-Surface plots ,12-41
The VPAR variable ,12-42
Interactive drawing ,12-43
DOT+ and DOT- ,12-44
MARK ,12-44
LINE ,12-44
TLINE ,12-45
BOX ,12-45
CIRCL ,12-45
LABEL ,12-45
DEL ,12-46
ERASE ,12-46
MENU ,12-46
SUB ,12-46
REPL ,12-46
PICT ,12-46
X,Y ,12-47
Zooming in and out in the graphics display ,12-47
ZFACT, ZIN, ZOUT, and ZLAST ,12-47
BOXZ ,12-48
ZDFLT, ZAUTO ,12-48
HZIN, HZOUT, VZIN and VZOUT ,12-48
CNTR ,12-48
ZDECI ,12-48
ZINTG ,12-48
ZSQR ,12-49
ZTRIG ,12-49

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Page TOC-14
The SYMBOLIC menu and graphs ,12-49
The SYMB/GRAPH menu ,12-50
Function DRAW3DMATRIX ,12-52
Chapter 13 - Calculus Applications ,13-1
The CALC (Calculus) menu ,13-1
Limits and derivatives ,13-1
Function lim ,13-2
Derivatives ,13-3
Functions DERIV and DERVX ,13-3
The DERIV&INTEG menu ,13-4
Calculating derivatives with ∂ ,13-4
The chain rule ,13-6
Derivatives of equations ,13-7
Implicit derivatives ,13-7
Application of derivatives ,13-7
Analyzing graphics of functions ,13-8
Function DOMAIN ,13-9
Function TABVAL ,13-9
Function SIGNTAB ,13-10
Function TABVAR ,13-10
Using derivatives to calculate extreme points ,13-12
Higher order derivatives ,13-13
Anti-derivatives and integrals ,13-14
Functions INT, INTVX, RISCH, SIGMA and SIGMAVX ,13-14
Definite integrals ,13-15
Step-by-step evaluation of derivatives and integrals ,13-16
Integrating an equation ,13-17
Techniques of integration ,13-18
Substitution or change of variables ,13-18
Integration by parts and differentials ,13-19
Integration by partial fractions ,13-20
Improper integrals ,13-20

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Page TOC-15
Integration with units ,13-21
Infinite series ,13-22
Taylor and Maclaurin’s series ,13-23
Taylor polynomial and reminder ,13-23
Functions TAYLR, TAYLR0, and SERIES ,13-24
Chapter 14 - Multi-variate Calculus Applications ,14-1
Multi-variate functions ,14-1
Partial derivatives ,14-1
Higher-order derivatives ,14-3
The chain rule for partial derivatives ,14-4
Total differential of a function z = z(x,y) ,14-5
Determining extrema in functions of two variables ,14-5
Using function HESS to analyze extrema ,14-6
Multiple integrals ,14-8
Jacobian of coordinate transformation ,14-9
Double integral in polar coordinates ,14-9
Chapter 15 - Vector Analysis Applications ,15-1
Definitions ,15-1
Gradient and directional derivative ,15-1
A program to calculate the gradient ,15-2
Using function HESS to obtain the gradient ,15-2
Potential of a gradient ,15-3
Divergence ,15-4
Laplacian ,15-4
Curl ,15-5
Irrotational fields and potential function ,15-5
Vector potential ,15-6
Chapter 16 - Differential Equations ,16-1
Basic operations with differential equations ,16-1
Entering differential equations ,16-1

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Page TOC-16
Checking solutions in the calculator ,16-2
Slope field visualization of solutions ,16-3
The CALC/DIFF menu ,16-3
Solution to linear and non-linear equations ,16-4
Function LDEC ,16-4
Function DESOLVE ,16-7
The variable ODETYPE ,16-8
Laplace Transforms ,16-10
Definitions ,16-10
Laplace transform and inverses in the calculator ,16-11
Laplace transform theorems ,16-12
Dirac’s delta function and Heaviside’s step function ,16-15
Applications of Laplace transform in the solution of linear ODEs ,16-17
Fourier series ,16-26
Function FOURIER ,16-28
Fourier series for a quadratic function ,16-28
Fourier series for a triangular wave ,16-34
Fourier series for a square wave ,16-38
Fourier series applications in differential equations ,16-40
Fourier Transforms ,16-42
Definition of Fourier transforms ,16-45
Properties of the Fourier transform ,16-47
Fast Fourier Transform (FFT) ,16-47
Examples of FFT applications ,16-48
Solution to specific second-order differential equations ,16-51
The Cauchy or Euler equation ,16-51
Legendre’s equation ,16-51
Bessel’s equation ,16-52
Chebyshev or Tchebycheff polynomials ,16-55
Laguerre’s equation ,16-56
Weber’s equation and Hermite polynomials ,16-57
Numerical and graphical solutions to ODEs ,16-57

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Page TOC-17
Numerical solution of first-order ODE ,16-57
Graphical solution of first-order ODE ,16-59
Numerical solution of second-order ODE ,16-61
Graphical solution for a second-order ODE ,16-63
Numerical solution for stiff first-order ODE ,16-65
Numerical solution to ODEs with the SOLVE/DIFF menu ,16-67
Function RKF ,16-67
Function RRK ,16-68
Function RKFSTEP ,16-69
Function RRKSTEP ,16-70
Function RKFERR ,16-71
Function RSBERR ,16-71
Chapter 17 - Probability Applications ,17-1
The MTH/PROBABILITY.. sub-menu - part 1 ,17-1
Factorials, combinations, and permutations ,17-1
Random numbers ,17-2
Discrete probability distributions ,17-3
Binomial distribution ,17-4
Poisson distribution ,17-5
Continuous probability distributions ,17-6
The gamma distribution ,17-6
The exponential distribution ,17-6
The beta distribution ,17-7
The Weibull distribution ,17-7
Functions for continuous distributions ,17-7
Continuous distributions for statistical inference ,17-9
Normal distribution pdf ,17-9
Normal distribution cdf ,17-10
The Student-t distribution ,17-10
The Chi-square distribution ,17-11
The F distribution ,17-12
Inverse cumulative distribution functions ,17-13

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Page TOC-18
Chapter 18 - Statistical Applications ,18-1
Pre-programmed statistical features ,18-1
Entering data ,18-1
Calculating single-variable statistics ,18-2
Obtaining frequency distributions ,18-5
Fitting data to a function y = f(x) ,18-10
Obtaining additional summary statistics ,18-13
Calculation of percentiles ,18-14
The STAT soft menu ,18-15
The DATA sub-menu ,18-16
The ΣPAR sub-menu ,18-16
The 1VAR sub menu ,18-17
The PLOT sub-menu ,18-17
The FIT sub-menu ,18-18
The SUMS sub-menu ,18-18
Example of STAT menu operations ,18-19
Confidence intervals ,18-22
Estimation of Confidence Intervals ,18-23
Definitions ,18-23
Confidence intervals for the population mean when the population vari-
ance is known ,18-24
Confidence intervals for the population mean when the population vari-
ance is unknown ,18-24
Confidence interval for a proportion ,18-25
Sampling distribution of differences and sums of statistics ,18-25
Confidence intervals for sums and differences of mean values ,18-26
Determining confidence intervals ,18-27
Confidence intervals for the variance ,18-33
Hypothesis testing ,18-35
Procedure for testing hypotheses ,18-35
Errors in hypothesis testing ,18-36
Inferences concerning one mean ,18-37
Inferences concerning two means ,18-39

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Page TOC-19
Paired sample tests ,18-41
Inferences concerning one proportion ,18-41
Testing the difference between two proportions ,18-42
Hypothesis testing using pre-programmed features ,18-43
Inferences concerning one variance ,18-47
Inferences concerning two variances ,18-48
Additional notes on linear regression ,18-50
The method of least squares ,18-50
Additional equations for linear regression ,18-51
Prediction error ,18-52
Confidence intervals and hypothesis testing in linear regression ,18-52
Procedure for inference statistics for linear regression using the calcula-
tor ,18-54
Multiple linear fitting ,18-57
Polynomial fitting ,18-59
Selecting the best fitting ,18-62
Chapter 19 - Numbers in Different Bases ,19-1
Definitions ,19-1
The BASE menu ,19-1
Functions HEX, DEC, OCT, and BIN ,19-2
Conversion between number systems ,19-3
Wordsize ,19-4
Operations with binary integers ,19-4
The LOGIC menu ,19-5
The BIT menu ,19-6
The BYTE menu ,19-7
Hexadecimal numbers for pixel references ,19-7
Chapter 20 - Customizing menus and keyboard ,20-1
Customizing menus ,20-1
The PRG/MODES/MENU menu ,20-1
Menu numbers (RCLMENU and MENU functions) ,20-2

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Page TOC-20
Custom menus (MENU and TMENU functions) ,20-2
Menu specification and CST variable ,20-4
Customizing the keyboard ,20-5
The PRG/MODES/KEYS sub-menu ,20-5
Recall current user-defined key list ,20-6
Assign an object to a user-defined key ,20-6
Operating user-defined keys ,20-7
Un-assigning a user-defined key ,20-7
Assigning multiple user-defined keys ,20-7
Chapter 21 - Programming in User RPL language ,21-1
An example of programming ,21-1
Global and local variables and subprograms ,21-2
Global Variable Scope ,21-4
Local Variable Scope ,21-5
The PRG menu ,21-5
Navigating through RPN sub-menus ,21-6
Functions listed by sub-menu ,21-7
Shortcuts in the PRG menu ,21-9
Keystroke sequence for commonly used commands ,21-10
Programs for generating lists of numbers ,21-13
Examples of sequential programming ,21-15
Programs generated by defining a function ,21-15
Programs that simulate a sequence of stack operations ,21-17
Interactive input in programs ,21-19
Prompt with an input string ,21-21
A function with an input string ,21-22
Input string for two or three input values ,21-24
Input through input forms ,21-27
Creating a choose box ,21-31
Identifying output in programs ,21-33
Tagging a numerical result ,21-33
Decomposing a tagged numerical result into a number and a tag ,21-33

##### Page: 24

Page TOC-21
“De-tagging” a tagged quantity ,21-33
Examples of tagged output ,21-34
Using a message box ,21-37
Relational and logical operators ,21-43
Relational operators ,21-43
Logical operators ,21-45
Program branching ,21-46
Branching with IF ,21-47
The IF…THEN…END construct ,21-47
The CASE construct ,21-51
Program loops ,21-53
The START construct ,21-53
The FOR construct ,21-59
The DO construct ,21-61
The WHILE construct ,21-63
Errors and error trapping ,21-64
DOERR ,21-64
ERRN ,21-65
ERRM ,21-65
ERR0 ,21-65
LASTARG ,21-65
Sub-menu IFERR ,21-65
User RPL programming in algebraic mode ,21-67
Chapter 22 - Programs for graphics manipulation ,22-1
The PLOT menu ,22-1
User-defined key for the PLOT menu ,22-1
Description of the PLOT menu ,22-2
Generating plots with programs ,22-14
Two-dimensional graphics ,22-14
Three-dimensional graphics ,22-15
The variable EQ ,22-15
Examples of interactive plots using the PLOT menu ,22-15

##### Page: 25

Page TOC-22
Examples of program-generated plots ,22-17
Drawing commands for use in programming ,22-19
PICT ,22-20
PDIM ,22-20
LINE ,22-20
TLINE ,22-20
BOX ,22-21
ARC ,22-21
PIX?, PIXON, and PIXOFF ,22-21
PVIEW ,22-22
PXC ,22-22
CPX ,22-22
Programming examples using drawing functions ,22-22
Pixel coordinates ,22-25
Animating graphics ,22-26
Animating a collection of graphics ,22-27
More information on the ANIMATE function ,22-29
Graphic objects (GROBs) ,22-29
The GROB menu ,22-31
A program with plotting and drawing functions ,22-33
Modular programming ,22-35
Running the program ,22-36
A program to calculate principal stresses ,22-38
Ordering the variables in the sub-directory ,22-38
A second example of Mohr’s circle calculations ,22-39
An input form for the Mohr’s circle program ,22-40
Chapter 23 - Charactor strings ,23-1
String-related functions in the TYPE sub-menu ,23-1
String concatenation ,23-2
The CHARS menu ,23-2
The characters list ,23-3

##### Page: 26

Page TOC-23
Chapter 24 - Calculator objects and flags ,24-1
Description of calculator objects ,24-1
Function TYPE ,24-2
Function VTYPE ,24-2
Calculator flags ,24-3
System flags ,24-3
Functions for setting and changing flags ,24-3
User flags ,24-4
Chapter 25 - Date and Time Functions ,25-1
The TIME menu ,25-1
Setting an alarm ,25-1
Browsing alarms ,25-2
Setting time and date ,25-2
TIME Tools ,25-2
Calculations with dates ,25-3
Calculating with times ,25-4
Alarm functions ,25-4
Chapter 26 - Managing memory ,26-1
Memory Structure ,26-1
The HOME directory ,26-2
Port memory ,26-2
Checking objects in memory ,26-3
Backup objects ,26-4
Backing up objects in port memory ,26-4
Backing up and restoring HOME ,26-5
Storing, deleting, and restoring backup objects ,26-6
Using data in backup objects ,26-7
Using SD cards ,26-7
Inserting and removing an SD card ,26-7
Formatting an SD card ,26-8
Accessing objects on an SD card ,26-9

##### Page: 27

Page TOC-24
Storing objects on an SD card ,26-9
Recalling an object from an SD card ,26-10
Evaluating an object on an SD card ,26-10
Purging an object from the SD card ,26-11
Purging all objects on the SD card (by reformatting) ,26-11
Specifying a directory on an SD card ,26-11
Using libraries ,26-12
Installing and attaching a library ,26-12
Library numbers ,26-13
Deleting a library ,26-13
Creating libraries ,26-13
Backup battery ,26-13
Chapter 27 - The Equation Library ,27-1
Solving a Problem with the Equation Library ,27-1
Using the Solver ,27-2
Using the menu keys ,27-3
Browsing in the Equation Library ,27-4
Viewing equations ,27-4
Viewing variables and selecting units ,27-5
Viewing the picture ,27-5
Using the Multiple-Equation Solver ,27-6
Defining a set of equations ,27-8
Interpreting results from the Multiple-Equation Solver ,27-10
Checking solutions ,27-11
Appendices
Appendix A - Using input forms ,A-1
Appendix B - The calculator’s keyboard ,B-1
Appendix C - CAS settings ,C-1
Appendix D - Additional character set ,D-1
Appendix E - The Selection Tree in the Equation Writer ,E-1

##### Page: 28

Page TOC-25
Appendix F - The Applications (APPS) menu ,F-1
Appendix G - Useful shortcuts ,G-1
Appendix H - The CAS help facility ,H-1
Appendix I - Command catalog list ,I-1
Appendix J - MATHS menu ,J-1
Appendix K - MAIN menu ,K-1
Appendix L - Line editor commands ,L-1
Appendix M - Table of Built-In Equations ,M-1
Appendix N - Index ,N-1
Limited Warranty ,LW-1
Service! ,LW-2
Regulatory information ,LW-4
Disposal of Waste Equipment by Users in Private Household in the European
Union ,LW-6

##### Page: 29

Page 1-1
Chapter 1
Getting started
This chapter provides basic information about the operation of your calculator.
It is designed to familiarize you with the basic operations and settings before
you perform a calculation.
Basic Operations
The following sections are designed to get you acquainted with the hardware of
your calculator.
Batteries
The calculator uses 4 AAA (LR03) batteries as main power and a CR2032
lithium battery for memory backup.
Before using the calculator, please install the batteries according to the
following procedure.
To install the main batteries
a. Make sure the calculator is OFF. Slide up the battery compartment cover as
illustrated.
b. Insert 4 new AAA (LR03) batteries into the main compartment. Make sure
each battery is inserted in the indicated direction.
To install the backup battery
a. Make sure the calculator is OFF. Press down the holder. Push the plate to the
shown direction and lift it.

##### Page: 30

Page 1-2
b. Insert a new CR2032 lithium battery. Make sure its positive (+) side is facing
up.
c. Replace the plate and push it to the original place.
After installing the batteries, press [ON] to turn the power on.
Warning: When the low battery icon is displayed, you need to replace the
batteries as soon as possible. However, avoid removing the backup battery and
main batteries at the same time to avoid data lost.
Turning the calculator on and off
The $ key is located at the lower left corner of the keyboard. Press it once to
turn your calculator on. To turn the calculator off, press the right-shift key @
(first key in the second row from the bottom of the keyboard), followed by the
$ key. Notice that the $ key has a OFF label printed in the upper right
corner as a reminder of the OFF command.
Adjusting the display contrast
You can adjust the display contrast by holding the $ key while pressing the
+ or - keys. The $(hold) + key combination produces a darker
display. The $(hold) - key combination produces a lighter display
Contents of the calculator’s display
Turn your calculator on once more. The display should look as indicated
below.

##### Page: 31

Page 1-3
At the top of the display you will have two lines of information that describe the
settings of the calculator. The first line shows the characters:
R D XYZ HEX R= 'X'
For details on the meaning of these symbols see Chapter 2.
The second line shows the characters: { HOME } indicating that the HOME
directory is the current file directory in the calculator’s memory. In Chapter 2
you will learn that you can save data in your calculator by storing them in files
or variables. Variables can be organized into directories and sub-directories.
Eventually, you may create a branching tree of file directories, similar to those in
a computer hard drive. You can then navigate through the file directory tree to
select any directory of interest. As you navigate through the file directory the
second line of the display will change to reflect the proper file directory and
sub-directory.
At the bottom of the display you will find a number of labels, namely,
@EDIT @VIEW @@RCL@@ @@STO@ !PURGE !CLEAR
associated with the six soft menu keys, F1 through F6:
ABCDEF
The six labels displayed in the lower part of the screen will change depending
on which menu is displayed. But A will always be associated with the first
displayed label, B with the second displayed label, and so on.
Menus
The six labels associated with the keys A through F form part of a menu
of functions. Since the calculator has only six soft menu keys, it only display 6
labels at any point in time. However, a menu can have more than six entries.

##### Page: 32

Page 1-4
Each group of 6 entries is called a Menu page. The current menu, known as
the TOOL menu (see below), has eight entries arranged in two pages. The next
page, containing the next two entries of the menu is available by pressing the
L (NeXT menu) key. This key is the third key from the left in the third row of
keys in the keyboard. Press L once more to return to the main TOOL menu,
or press the I key (third key in second row of keys from the top of the
keyboard).
The TOOL menu is described in detain in the next section. At this point we will
illustrate some properties of menus that you will find useful while using your
calculator.
SOFT menus vs. CHOOSE boxes
Menus, or SOFT menus, associate labels in the lower part of the screen with the
six soft menu keys (Athrough F). By pressing the appropriate soft menu
key, the function shown in the associated label gets activated. For example,
with the TOOL menu active, pressing the @CLEAR key (F) activates function
CLEAR, which erases (clears up) the contents of the screen. To see this function
in action, type a number, say 123`, and then press the F key.
SOFT menus are typically used to select from among a number of related
functions. However, SOFT menus are not the only way to access collections of
related functions in the calculator. The alternative way will be referred to as
CHOOSE boxes. To see an example of a choose box, activate the TOOL menu
(press I), and then press the keystroke combination ‚ã(associated with
the 3 key). This will provide the following CHOOSE box:

##### Page: 33

Page 1-5
This CHOOSE box is labeled BASE MENU and provides a list of numbered
functions, from 1. HEX x to 6. BR. This display will constitute the first page of
this CHOOSE box menu showing six menu functions. You can navigate through
the menu by using the up and down arrow keys, —˜, located in the upper
right side of the keyboard, right under the E and Fsoft menu keys. To
activate any given function, first, highlight the function name by using the up
and down arrow keys, —˜, or by pressing the number corresponding to
the function in the CHOOSE box. After the function name is selected, press the
@@@OK@@@ soft menu key (F). Thus, if you wanted to use function RB (Real to
Binary), you could press 6F.
If you want to move to the top of the current menu page in a CHOOSE box, use
„—. To move to the bottom of the current page, use „˜. To move to
the top of the entire menu, use ‚—. To move to the bottom of the entire
menu, use ‚˜.
Selecting SOFT menus or CHOOSE boxes
You can select the format in which your menus will be displayed by changing a
setting in the calculator system flags (A system flag is a calculator variable that
controls a certain calculator operation or mode. For more information about
flags, see Chapter 24). System flag 117 can be set to produce either SOFT
menus or CHOOSE boxes. To access this flag use:
H @)FLAGS —„ —˜
Your calculator will show the following screen, highlighting the line starting with
the number 117:
By default, the line will look as shown above. The highlighted line (117
CHOOSE boxes) indicates that CHOOSE boxes are the current menu display
setting. If you prefer to use SOFT menu keys, press the @@CHK@@ soft menu key
(C), followed by @@@OK@@@ (F). Press @@@OK@@@ (F) once more to return to
normal calculator display.

##### Page: 34

Page 1-6
If you now press ‚ã, instead of the CHOOSE box that you saw earlier,
the display will now show six soft menu labels as the first page of the STACK
menu:
To navigate through the functions of this menu, press the L key to move to the
next page, or „«(associated with the L key) to move to the previous
page. The following figures show the different pages of the BASE menu
accessed by pressing the L key twice:
Pressing the L key once more will takes us back to the first menu page.
To revert to the CHOOSE boxes setting, use:
H @)FLAGS —„ —˜@@CHK@@ @@@OK@@@ @@@OK@@@.
Note: With the SOFT menu setting for system flag 117, the keystroke
combination ‚(hold) ˜, will show a list of the functions in the current soft
menu. For example, for the two first pages in the BASE menu, you will get:
Notes:
1. The TOOL menu, obtained by pressing I, will always produce a SOFT
menu.
2. Most of the examples in this User’s Manual are shown using both SOFT
menus and CHOOSE boxes. Programming applications (Chapters 21 and
22) use exclusively SOFT menus.
3. Additional information on SOFT menus vs. CHOOSE boxes is presented in
Chapter 2 o f this guide.

##### Page: 35

Page 1-7
The TOOL menu
The soft menu keys for the menu currently displayed, known as the TOOL menu,
are associated with operations related to manipulation of variables (see pages
for more information on variables):
@EDIT A EDIT the contents of a variable (see Chapter 2 and Appendix
L for more information on editing)
@VIEW B VIEW the contents of a variable
@@RCL@@ C ReCaLl the contents of a variable
@@STO@ D STOre the contents of a variable
!PURGE E PURGE a variable
CLEAR F CLEAR the display or stack
The calculator has only six soft menu keys, and can only display 6 labels at any
point in time. However, a menu can have more than six entries. Each group of
6 entries is called a Menu page. The TOOL menu has eight entries arranged
in two pages. The next page, containing the next two entries of the menu are
available by pressing the L (NeXT menu) key. This key is the third key from
the left in the third row of keys in the keyboard.
In this case, only the first two soft menu keys have commands associated with
them. These commands are:
@CASCM A CASCMD: CAS CoMmanD, used to launch a command from
the CAS by selecting from a list
@HELP B HELP facility describing the commands available
Pressing the L key will show the original TOOL menu. Another way to
recover the TOOL menu is to press the I key (third key from the left in the
second row of keys from the top of the keyboard).
Setting time and date
The calculator has an internal real time clock. This clock can be continuously
displayed on the screen and be used for alarms as well as running scheduled
tasks. This section will show not only how to set time and date, but also the
basics of using CHOOSE boxes and entering data in a dialog box. Dialog
boxes on your calculator are similar to a computer dialog box.
To set time and date we use the TIME choose box available as an alternative
function for the 9 key. By combining the right-shift button, ‚, with the

##### Page: 36

Page 1-8
9 key the TIME choose box is activated. This operation can also be
represented as ‚Ó. The TIME choose box is shown in the figure below:
As indicated above, the TIME menu provides four different options, numbered 1
through 4. Of interest to us as this point is option 3. Set time, date... Using the
down arrow key, ˜, highlight this option and press the !!@@OK#@ soft menu key.
The following input form (see Appendix 1-A) for adjusting time and date is
shown:
Setting the time of the day
Using the number keys, 1234567890, start by
adjusting the hour of the day. Suppose that we change the hour to 11, by
pressing 11 as the hour field in the SET TIME AND DATE input form is
highlighted. This results in the number 11 being entered in the lower line of the
input form:
Press the !!@@OK#@ soft menu key to effect the change. The value of 11 is now
shown in the hour field, and the minute field is automatically highlighted:

##### Page: 37

Page 1-9
Let’s change the minute field to 25, by pressing: 25 !!@@OK#@ . The seconds
field is now highlighted. Suppose that you want to change the seconds field to
45, use: 45 !!@@OK#@
The time format field is now highlighted. To change this field from its current
setting you can either press the W key (the second key from the left in the fifth
row of keys from the bottom of the keyboard), or press the @CHOOS soft menu key
( B).
Θ If using the W key, the setting in the time format field will change to either
of the following options:
o AM : indicates that displayed time is AM time
o PM : indicates that displayed time is PM time
o 24-hr : indicates that that the time displayed uses a 24 hour
format where18:00, for example, represents 6pm
The last selected option will become the set option for the time format by
using this procedure.
Θ If using the @CHOOS soft menu key, the following options are available.
Use the up and down arrow keys,— ˜, to select among these three
options (AM, PM, 24-hour time). Press the !!@@OK#@ soft menu key to make the
selection.

##### Page: 38

Page 1-10
Setting the date
After setting the time format option, the SET TIME AND DATE input form will
look as follows:
To set the date, first set the date format. The default format is M/D/Y (month/
day/year). To modify this format, press the down arrow key. This will highlight
the date format as shown below:
Use the @CHOOS soft menu key to see the options for the date format:
Highlight your choice by using the up and down arrow keys,— ˜, and
press the !!@@OK#@ soft menu key to make the selection.

##### Page: 39

Page 1-11
Introducing the calculator’s keyboard
The figure below shows a diagram of the calculator’s keyboard with the
numbering of its rows and columns.
The figure shows 10 rows of keys combined with 3, 5, or 6 columns. Row 1
has 6 keys, rows 2 and 3 have 3 keys each, and rows 4 through 10 have 5
keys each. There are 4 arrow keys located on the right-hand side of the
keyboard in the space occupied by rows 2 and 3.
Each key has three, four, or five functions. The main key function correspond to
the most prominent label in the key. Also, the left-shift key, key (8,1), the right-

##### Page: 40

Page 1-12
shift key, key (9,1), and the ALPHA key, key (7,1), can be combined with some
of the other keys to activate the alternative functions shown in the keyboard.
For example, the P key, key(4,4), has the following six functions associated
with it:
P Main function, to activate the SYMBolic menu
„´ Left-shift function, to activate the MTH (Math) menu
… N Right-shift function, to activate the CATalog function
~p ALPHA function, to enter the upper-case letter P
~„p ALPHA-Left-Shift function, to enter the lower-case letter p
~…p ALPHA-Right-Shift function, to enter the symbol P
Of the six functions associated with the key only the first four are shown in the
keyboard itself. This is the way that the key looks in the keyboard:
Notice that the color and the position of the labels in the key, namely, SYMB,
MTH, CAT and P, indicate which is the main function (SYMB), and which of
the other three functions is associated with the left-shift „(MTH), right-shift
… (CAT ) , and ~ (P) keys.
For detailed information on the calculator keyboard operation referee to
Appendix B .
Selecting calculator modes
This section assumes that you are now at least partially familiar with the use of
choose and dialog boxes (if you are not, please refer to Chapter 2).
Press the H button (second key from the left on the second row of keys from
the top) to show the following CALCULATOR MODES input form:

##### Page: 41

Page 1-13
Press the !!@@OK#@ soft menu key to return to normal display. Examples of selecting
different calculator modes are shown next.
Operating Mode
The calculator offers two operating modes: the Algebraic mode, and the
Reverse Polish Notation (RPN) mode. The default mode is the Algebraic mode
(as indicated in the figure above), however, users of earlier HP calculators may
be more familiar with the RPN mode.
To select an operating mode, first open the CALCULATOR MODES input form
by pressing the H button. The Operating Mode field will be highlighted.
Select the Algebraic or RPN operating mode by either using the \ key
(second from left in the fifth row from the keyboard bottom), or pressing the
@CHOOS soft menu key. If using the latter approach, use up and down arrow
keys, — ˜, to select the mode, and press the !!@@OK#@ soft menu key to
complete the operation.
To illustrate the difference between these two operating modes we will calculate
the following expression in both modes:
5
.
2
3
23
3
3
1
5
3
e
+
⋅
−
⋅ ⎟
⎠
⎞
⎜
⎝
⎛

##### Page: 42

Page 1-14
To enter this expression in the calculator we will first use the equation writer,
‚O. Please identify the following keys in the keyboard, besides the
numeric keypad keys:
!@.#*+-/R
Q¸Ü‚Oš™˜—`
The equation writer is a display mode in which you can build mathematical
expressions using explicit mathematical notation including fractions, derivatives,
integrals, roots, etc. To use the equation writer for writing the expression
shown above, use the following keystrokes:
‚OR3*!Ü5-
1/3*3
———————
/23Q3™™+!¸2.5`
After pressing `the calculator displays the expression:
√ (3*(5-1/(3*3))/23^3+EXP(2.5))
Pressing `again will provide the following value. Accept Approx. mode on,
if asked, by pressing !!@@OK#@. [Note: The integer values used above, e.g., 3, 5,
1, represent exact values. The EXP(2.5), however, cannot be expressed as an
exact value, therefore, a switch to Approx mode is required]:
You could also type the expression directly into the display without using the
equation writer, as follows:
R!Ü3.*!Ü5.-1./
!Ü3.*3.™™
/23.Q3+!¸2.5`
to obtain the same result.

##### Page: 43

Page 1-15
Change the operating mode to RPN by first pressing the H button. Select the
RPN operating mode by either using the \key, or pressing the @CHOOS soft
menu key. Press the !!@@OK#@ soft menu key to complete the operation. The
display, for the RPN mode looks as follows:
Notice that the display shows several levels of output labeled, from bottom to
top, as 1, 2, 3, etc. This is referred to as the stack of the calculator. The
different levels are referred to as the stack levels, i.e., stack level 1, stack level 2,
etc.
In RPN mode, instead of writing an operation such as 3 + 2 by pressing
3+2`, we write the operands first , in the proper order, and then
the operator, i.e., 3`2+. As you enter the operands, they occupy
different stack levels. Entering 3`puts the number 3 in stack level 1.
Next, entering 2pushes the 3 upwards to occupy stack level 2. Finally, by
pressing +, we are telling the calculator to apply the operator, or program,
+ to the objects occupying levels 1 and 2. The result, 5, is then placed in
level 1.
Let's try some other simple operations before trying the more complicated
expression used earlier for the algebraic operating mode:
123/32 123`32/
42
4`2Q
3√27 27`3@»
Notice the position of the y and the x in the last two operations. The base in
the exponential operation is y (stack level 2) while the exponent is x (stack level
1) before the key Q is pressed. Similarly, in the cubic root operation, y (stack
level 2) is the quantity under the root sign, and x (stack level 1) is the root.
Try the following exercise involving 3 factors: (5 + 3) × 2
5`3+ Calculates (5 + 3) first.
2X Completes the calculation.
Let's try now the expression proposed earlier:

##### Page: 44

Page 1-16
3.` Enter 3 in level 1
5.` Enter 5 in level 1, 3 moves to y
3.` Enter 3 in level 1, 5 moves to level 2, 3 to level 3
3.* Place 3 and multiply, 9 appears in level 1
Y 1/(3×3), last value in lev. 1; 5 in level 2; 3 in level 3
- 5 - 1/(3×3) , occupies level 1 now; 3 in level 2
* 3× (5 - 1/(3×3)), occupies level 1 now.
23.`Enter 23 in level 1, 14.66666 moves to level 2.
3.Q Enter 3, calculate 233
into level 1. 14.666 in lev. 2.
/ (3× (5-1/(3×3)))/233 into level 1
2.5 Enter 2.5 level 1
!¸ e2.5, goes into level 1, level 2 shows previous value.
+ (3× (5 - 1/(3×3)))/233
+ e2.5
= 12.18369, into lev. 1.
R √((3× (5 - 1/(3×3)))/233
+ e2.5) = 3.4905156, into 1.
Although RPN requires a little bit more thought than the algebraic (ALG) mode,
there are multiple advantages in using RPN. For example, in RPN mode you
can see the equation unfolding step by step. This is extremely useful to detect a
possible input error. Also, as you become more efficient in this mode and learn
more of the tricks, you will be able to calculate expression faster and will much
less keystrokes. Consider, for example the calculation of (4×6 - 5)/(1+4×6 - 5).
In RPN mode you can write:
4 ` 6 * 5 - ` 1 + /
obviously, even In RPN mode, you can enter an expression in the same order as
the algebraic mode by using the Equation writer. For example,
‚OR3.*!Ü5.-
1/3.*3.
———————
/23.Q3™™+!¸2.5`
The resulting expression is shown in stack level 1 as follows:
5
.
2
3
23
3
3
1
5
3
e
+
⋅
−
⋅ ⎟
⎠
⎞
⎜
⎝
⎛

##### Page: 45

Page 1-17
Notice how the expression is placed in stack level 1 after pressing `.
Pressing the EVAL key at this point will evaluate the numerical value of that
expression Note: In RPN mode, pressing ENTER when there is no command
line will execute the DUP function which copies the contents of stack level 1 of
the stack onto level 2 (and pushes all the other stack levels one level up). This is
extremely useful as showed in the previous example.
To select between the ALG vs. RPN operating mode, you can also set/clear
system flag 95 through the following keystroke sequence:
H@FLAGS 9 ˜ ˜ ˜ ˜ @CHK@@ `
Alternatively, you can use one of the following shortcuts:
Θ In ALG mode,
CF(-95) selects RPN mode
Θ In RPN mode,
95 \` SF selects ALG mode
For more information on calculator’s system flags see Chapter 2.
Number Format and decimal dot or comma
Changing the number format allows you to customize the way real numbers are
displayed by the calculator. You will find this feature extremely useful in
operations with powers of tens or to limit the number of decimals in a result.
To select a number format, first open the CALCULATOR MODES input form by
pressing the H button. Then, use the down arrow key, ˜, to select the
option Number format. The default value is Std, or Standard format. In the
standard format, the calculator will show floating-point numbers with the
maximum precision allowed by the calculator (12 significant digits). To learn

##### Page: 46

Page 1-18
more about reals, see Chapter 2. To illustrate this and other number formats try
the following exercises:
Θ Standard format:
This mode is the most used mode as it shows numbers in the most familiar
notation.
Press the !!@@OK#@ soft menu key, with the Number format set to Std, to return
to the calculator display. Enter the number 123.4567890123456. Notice
that this number has 16 significant figures. Press the ` key. The number
is rounded to the maximum 12 significant figures, and is displayed as
follows:
In the standard format of decimal display, integer numbers are shown with
no decimal zeros whatsoever. Numbers with different decimal figures will
be adjusted in the display so that only those decimal figures that are
necessary will be shown. More examples of numbers in standard format
are shown next:
Θ Fixed format with no decimals: Press the H button. Next, use the down
arrow key, ˜, to select the option Number format. Press the @CHOOS soft
menu key, and select the option Fixed with the arrow down key ˜.

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Notice that the Number Format mode is set to Fix followed by a zero (0).
This number indicates the number of decimals to be shown after the
decimal point in the calculator’s display. Press the !!@@OK#@ soft menu key to
return to the calculator display. The number now is shown as:
This setting will force all results to be rounded to the closest integer (0 digit
displayed after the comma). However, the number is still stored by the
calculator with its full 12 significant digit precision. As we change the
number of decimals to be displayed, you will see the additional digits
being shown again.
Θ Fixed format with decimals:
This mode is mainly used when working with limited precision. For
example, if you are doing financial calculation, using a FIX 2 mode is
convenient as it can easily represent monetary units to a 1/100 precision.
Press the H button. Next, use the down arrow key, ˜, to select the
option Number format. Press the @CHOOS soft menu key, and select the
option Fixed with the arrow down key ˜.
Press the right arrow key, ™, to highlight the zero in front of the option
Fix. Press the @CHOOS soft menu key and, using the up and down arrow
keys, —˜, select, say, 3 decimals.

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Press the !!@@OK#@ soft menu key to complete the selection:
Press the !!@@OK#@ soft menu key return to the calculator display. The number
now is shown as:
Notice how the number is rounded, not truncated. Thus, the number
123.4567890123456, for this setting, is displayed as 123.457, and not
as 123.456 because the digit after 6 is > 5
Θ Scientific format
The scientific format is mainly used when solving problems in the physical
sciences where numbers are usually represented as a number with limited
precision multiplied by a power of ten.
To set this format, start by pressing the H button. Next, use the down
arrow key, ˜, to select the option Number format. Press the @CHOOS soft
menu key and select the option Scientific with the arrow down key ˜.
Keep the number 3 in front of the Sci. (This number can be changed in the

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same fashion that we changed the Fixed number of decimals in the
example above).
Press the !!@@OK#@ soft menu key return to the calculator display. The number
now is shown as:
This result, 1.23E2, is the calculator’s version of powers-of-ten notation,
i.e., 1.235 x 102
. In this, so-called, scientific notation, the number 3 in
front of the Sci number format (shown earlier) represents the number of
significant figures after the decimal point. Scientific notation always
includes one integer figure as shown above. For this case, therefore, the
number of significant figures is four.
Θ Engineering format
The engineering format is very similar to the scientific format, except that
the powers of ten are multiples of three.
To set this format, start by pressing the H button. Next, use the down
arrow key, ˜, to select the option Number format. Press the @CHOOS soft
menu key and select the option Engineering with the arrow down key ˜.
Keep the number 3 in front of the Eng. (This number can be changed in
the same fashion that we changed the Fixed number of decimals in an
earlier example).

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