User manual HP 48GII

hp 48gII graphing calculator user's guide H Edition 4 HP part number F2226-90020 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. © Copyright 2003 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 4995 Murphy Canyon Rd, Suite 301 San Diego,CA 92123 Printing History Edition 4 April 2004 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 48gII should be thought of as a graphics/programmable hand-held computer. The hp 48gII can be operated in two different calculating modes, the Reverse Polish Notation (RPN) mode and the Algebraic (ALG) mode (see page 1-11 in user's guide 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 in this user's guide 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. 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 are very convenient for producing complex figures in very little time. Thanks to the infrared port and the RS 232 cable available with your calculator, you can connect your calculator with other calculators or computers. The high-speed connection through infrared or RS 232 allows the 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. Table of contents A note about screenshots in this guide, Note-1 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, 1-3 Selecting SOFT menus or CHOOSE boxes, 1-4 The TOOL menu, 1-6 Setting time and date, 1-7 Introducing the calculator's keyboard, 1-10 Setting calculator's mode, 1-11 Operating mode, 1-12 Number format and decimal dot or comma, 1-16 Angle measure, 1-21 Coordinate system, 1-22 Beep, Key Click, and Last Stack, 1-23 Selecting CAS settings, 1-24 Selecting Display modes, 1-24 Selecting the display font, 1-25 Selecting properties of the line editor, 1-26 Selecting properties of the Stack, 1-26 Selecting properties of the Equation Writer (EQW), 1-27 Selecting the size of the header, 1-28 Selecting the clock display, 1-28 Chapter 2 - Introducing the calculator, 2-1 Calculator objects, 2-1 Editing expressions in the screen, 2-3 Creating arithmetic expressions, 2-3 Editing arithmetic expressions, 2-6 Page TOC-1 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, 2-16 Creating algebraic expressions, 2-19 Editing algebraic expressions, 2-20 Creating and editing summations, derivatives, and integrals, 2-28 Organizing data in the calculator, 2-32 Functions for manipulation of variables, 2-33 The HOME directory, 2-34 The CASDIR sub-directory, 2-35 Typing directory and variable names, 2-37 Creating sub-directories, 2-38 Moving among sub-directories, 2-42 Deleting sub-directories, 2-42 Variables, 2-46 Creating variables, 2-46 Checking variable contents, 2-51 Replacing the contents of variables, 2-53 Copying variables, 2-54 Reordering variables in a directory, 2-57 Moving variables using the FILES menu, 2-58 Deleting variables, 2-59 UNDO and CMD functions, 2-61 Flags, 2-62 Example of flag setting: general solution vs. principal value, 2-63 Other flags of interest, 2-64 CHOOSE boxes vs. SOFT menus, 2-65 Selected CHOOSE boxes, 2-66 Chapter 3 - Simple calculations with real numbers, 3-1 Checking calculator settings, 3-1 Checking calculator mode, 3-2 Real number calculations, 3-2 Changing sing of a number, variable, or expression, 3-3 Page TOC-2 The inverse function, 3-3 Addition, subtraction, multiplication, division, 3-3 Using parentheses, 3-4 Absolute value function, 3-4 Squares and square roots, 3-4 Powers and roots, 3-5 Base-10 logarithms and powers of 10, 3-5 Using powers of 10 in entering data, 3-5 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 Operation with units, 3-17 The UNITS menu, 3-17 Available units, 3-18 Converting to base units, 3-21 Attaching units to numbers, 3-22 Operations with units, 3-25 Units manipulation tools, 3-27 Physical constants in the calculator, 3-28 Special physical functions, 3-31 Function ZFACTOR, 3-32 Function F0, 3-32 Function SIDENS, 3-32 Function TDELTA, 3-33 Function TINC, 3-33 Defining and using functions, 3-33 Functions defined by more than one expression, 3-35 The IFTE function, 3-35 Combined IFTE functions, 3-36 Page TOC-3 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, 4-4 Entering the unit imaginary number, 4-5 The CMPLX menus, 4-5 CMPLX menu through the MTH menu, 4-5 CMPLX menu in keyboard, 4-7 Functions applied to complex numbers, 4-8 Functions from the MTH menu, 4-8 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, 5-2 Functions in the ALG menu, 5-3 COLLECT, 5-5 EXPAND, 5-5 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, 5-8 Expansion and factoring using trigonometric functions, 5-8 Functions in the ARITHMETIC menu, 5-9 DIVIS, 5-10 Page TOC-4 FACTORS, 5-10 LGCD, 5-10 PROPFRAC, 5-10 SIMP2, 5-10 INTEGER menu, 5-10 POLYNOMIAL menu, 5-11 MODULO menu, 5-12 Applications of the ARITHMETIC menu, 5-12 Modular arithmetic, 5-12 Finite arithmetic in the calculator, 5-15 Polynomials, 5-18 Modular arithmetic with polynomials, 5-19 The CHINREM function, 5-19 The EGCD function, 5-19 The GCD function, 5-19 The HERMITE function, 5-20 The HORNER function, 5-20 The variable VX, 5-20 The LAGRANGE function, 5-21 The LCM function, 5-21 The LEGENDRE function, 5-22 The PCOEF function, 5-22 The PROOT function, 5-22 The PTAYL function, 5-22 The QUOTIENT and REMAINDER functions, 5-23 The EPSX0 function and the CAS variable EPS, 5-23 The PEVAL function, 5-23 The TCHEBYCHEFF function, 5-24 Fractions, 5-24 The SIMP2 function, 5-24 The PROPFRAC function, 5-24 The PARTFRAC function, 5-25 The FCOEF function, 5-25 The FROOTS function, 5-26 Step-by-step operations with polynomial fractions, 5-26 The CONVERT menu and algebraic operations, 5-27 Page TOC-5 UNITS convert menu, 5-27 BASE convert menu, 5-28 TRIGONOMETRIC convert menu, 5-28 MATRICES convert menu, 5-28 REWRITE convert menu, 5-28 Chapter 6 - Solution to single equations, 6-1 Symbolic solution of algebraic equations, 6-2 Function ISOL, 6-1 Function SOLVE, 6-2 Function SOLVEVX, 6-4 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, 6-14 The SOLVE soft menu, 6-27 The ROOT sub-menu, 6-27 Function ROOT, 6-27 Variable EQ, 6-28 The SOLVR sub-menu, 6-28 The DIFFE sub-menu, 6-30 The POLY sub-menu, 6-30 The SYS sub-menu, 6-31 The TVM sub-menu, 6-31 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, 7-6 Using the Multiple Equation Solver (MES), 7-10 Application 1 - Solution of triangles, 7-10 Page TOC-6 Application 2 - Velocity and acceleration in polar coordinates, 7-18 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, 8-3 Changing sign, 8-3 Addition, subtraction, multiplication, division, 8-3 Real number functions from the keyboard, 8-5 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 List size, 8-10 Extracting and inserting elements, 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, 8-14 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 Page TOC-7 Using the Matrix Writer (MTWR) 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 and division by a scalar, 9-10 Absolute value function, 9-10 The MTH/VECTOR menu, 9-10 Magnitude, 9-11 Dot product, 9-11 Cross product, 9-11 Decomposing a vector, 9-12 Building a two-dimensional vector, 9-12 Building a three-dimensional vector, 9-13 Changing coordinate system, 9-13 Application of vector operations, 9-16 Resultant of forces, 9-16 Angle between vectors, 9-16 Moment of a force, 9-17 Equation of a plane in space, 9-18 Row vectors, column vectors, and lists, 9-19 Function OBJ , 9-20 Function LIST, 9-20 Function DROP, 9-21 Transforming a row vector into a column vector, 9-21 Transforming a column vector into a row vector, 9-22 Transforming a list into a vector, 9-24 Transforming a vector (or matrix) into a list, 9-25 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 the matrix directly into the stack, 10-3 Creating matrices with calculator functions, 10-3 Page TOC-8 Functions GET and PUT, 10-6 Functions GETI and PUTI, 10-6 Function SIZE, 10-7 Function TRN, 10-8 Function CON, 10-8 Function IDN, 10-9 Function RDM, 10-10 Function RANM, 10-11 Function SUB, 10-11 Function REPL, 10-12 Function DIAG, 10-12 Function DIAG , 10-13 Function VANDERMONDE, 10-14 Function HILBERT, 10-14 A program to build a matrix out of a number of lists, 10-15 Lists represent columns of the matrix, 10-15 Lists represent rows of the matrix, 10-17 Manipulating matrices by columns, 10-18 Function COL, 10-18 Function COL , 10-19 Function COL+, 10-20 Function COL-, 10-20 Function CSWP, 10-21 Manipulating matrices by rows, 10-21 Function ROW, 10-22 Function ROW , 10-23 Function ROW+, 10-24 Function ROW -, 10-24 Function RSWP, 10-25 Function RCI, 10-25 Function RCIJ, 10-26 Chapter 11 - Matrix Operations and Linear Algebra, 11-1 Operations with matrices, 11-1 Addition and subtraction, 11-2 Multiplication, 11-2 Page TOC-9 Characterizing a matrix (the matrix NORM menu), 11-6 Function ABS, 11-7 Function SNRM, 11-7 Functions RNRM and CNRM, 11-8 Function SRAD, 11-9 Function COND, 11-9 Function RANK, 11-10 Function DET, 11-11 Function TRACE, 11-13 Function TRAN, 11-14 Additional matrix operations (the matrix OPER menu), 11-14 Function AXL, 11-15 Function AXM, 11-15 Function LCXM, 11-15 Solution of linear systems, 11-16 Using the numerical solver for linear systems, 11-17 Least-square solution (function LSQ), 11-23 Solution with the inverse matrix, 11-26 Solution by "division" of matrices, 11-26 Solving multiple set of equations with the same coefficient matrix, 11-27 Gaussian and Gauss-Jordan elimination, 11-28 Step-by-step calculator procedure for solving linear systems, 11-37 Solution to linear systems using calculator functions, 11-46 Residual errors in linear system solutions (function RSD) , 11-43 Eigenvalues and eigenvectors, 11-44 Function PCAR, 11-44 Function EGVL, 11-45 Function EGV, 11-46 Function JORDAN, 11-47 Function MAD, 11-47 Matrix factorization, 11-48 Function LU, 11-49 Orthogonal matrices and singular value decomposition, 11-49 Function SCHUR, 11-50 Function LQ, 11-51 Page TOC-10 Function QR, 11-51 Matrix Quadratic Forms, 11-51 The QUADF menu, 11-52 Linear Applications, 11-54 Function IMAGE, 11-54 Function ISOM, 11-54 Function KER, 11-55 Function MKISOM, 11-55 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, 12-8 Graphics of transcendental functions, 12-10 Graph of ln(X) , 12-8 Graph of the exponential function, 12-10 The PPAR variable, 12-11 Inverse functions and their graphs, 12-12 Summary of FUNCTION plot operation, 12-13 Plots of trigonometric and hyperbolic functions and their inverses, 12-16 Generating a table of values for a function, 12-17 The TPAR variable, 12-18 Plots in polar coordinates, 12-19 Plotting conic curves, 12-21 Parametric plots, 12-23 Generating a table of parametric equations, 12-26 Plotting the solution to simple differential equations, 12-26 Truth plots, 12-29 Plotting histograms, bar plots, and scatterplots, 12-30 Bar plots, 12-30 Scatter plots, 12-32 Slope fields, 12-34 Fast 3D plots, 12-35 Wireframe plots, 12-37 Ps-Contour plots, 12-39 Page TOC-11 Y-Slice plots, 12-41 Gridmap plots, 12-42 Pr-Surface plots, 12-43 The VPAR variable, 12-44 Interactive drawing, 12-44 DOT+ and DOT-, 12-45 MARK, 12-46 LINE, 12-46 TLINE, 12-46 BOX, 12-47 CIRCL, 12-47 LABEL, 12-47 DEL, 12-47 ERASE, 12-48 MENU, 12-48 SUB, 12-48 REPL, 12-48 PICT , 12-48 X,Y , 12-48 Zooming in and out in the graphics display, 12-49 ZFACT, ZIN, ZOUT, and ZLAST, 12-49 BOXZ, 12-50 ZDFLT, ZAUTO, 12-50 HZIN, HZOUT, VZIN, and VZOUT, 12-50 CNTR, 12-50 ZDECI, 12-50 ZINTG, 12-51 ZSQR, 12-51 ZTRIG, 12-51 The SYMBOLIC menu and graphs, 12-51 The SYMB/GRAPH menu, 12-52 Function DRAW3DMATRIX, 12-54 Chapter 13 - Calculus Applications, 13-1 The CALC (Calculus) menu, 13-1 Limits and derivatives, 13-1 Page TOC-12 Function lim, 13-2 Derivatives, 13-3 Function DERIV and DERVX,13-3 The DERIV&INTEG menu, 13-3 Calculating derivatives with ,13-4 The chain rule,13-6 Derivatives of equations,13-6 Implicit derivatives,13-7 Application of derivatives,13-7 Analyzing graphics of functions,13-7 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, 13-18 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,13-21 Integration with units, 13-21 Infinite series,13-23 Taylor and Maclaurin's series,13-23 Taylor polynomial and remainder,13-23 Functions TAYLR, TAYRL0, 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 Page TOC-13 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 Checking solutions in the calculator, 16-2 Slope field visualization of solutions, 16-3 The CALC/DIFF menu, 16-4 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 ODEs, 16-17 Page TOC-14 Fourier series, 16-27 Function FOURIER, 16-28 Fourier series for a quadratic function, 16-29 Fourier series for a triangular wave, 16-35 Fourier series for a square wave, 16-39 Fourier series applications in differential equations, 16-42 Fourier Transforms, 16-43 Definition of Fourier transforms, 16-46 Properties of the Fourier transform, 16-48 Fast Fourier Transform (FFT) , 16-49 Examples of FFT applications, 16-50 Solution to specific second-order differential equations, 16-53 The Cauchy or Euler equation , 16-53 Legendre's equation, 16-54 Bessel's equation, 16-55 Chebyshev or Tchebycheff polynomials, 16-57 Laguerre's equation, 16-58 Weber's equation and Hermite polynomials, 16-59 Numerical and graphical solutions to ODEs, 16-60 Numerical solution of first-order ODE, 16-60 Graphical solution of first-order ODE, 16-62 Numerical solution of second-order ODE, 16-64 Graphical solution for a second-order ODE, 16-66 Numerical solution for stiff first-order ODE, 16-68 Numerical solution to ODEs with the SOLVE/DIFF menu, 16-69 Function RKF, 16-70 Function RRK, 16-71 Function RKFSTEP, 16-72 Function RRKSTEP, 16-73 Function RKFST, 16-72 Function RKFERR, 16-72 Function RSBERR, 16-73 Chapter 17 - Probability Applications, 17-1 The MTH/PROBABILITY.. sub-menu - part 1, 17-1 Factorials, combinations, and permutations, 17-1 Page TOC-15 Random numbers, 17-2 Discrete probability distributions, 17-4 Binomial distribution, 17-4 Poisson distribution, 17-5 Continuous probability distributions, 17-6 The gamma distribution, 17-6 The exponential distribution, 17-7 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 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, 18-15 The PAR sub-menu, 18-16 The 1VAR sub-menu, 18-16 The PLOT sub-menu, 18-17 The FIT sub-menu, 18-18 Example of STAT menu operations, 18-18 Confidence intervals, 18-22 Estimation of Confidence Intervals, 18-23 Definitions, 18-23 Page TOC-16 Confidence intervals for the population mean when the population variance is known, 18-23 Confidence intervals for the population mean when the population variance is unknown, 18-24 Confidence interval for a proportion, 18-24 Sampling distributions 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, 18-34 Procedure for testing hypotheses, 18-35 Errors in hypothesis testing, 18-35 Inferences concerning one mean, 18-36 Inferences concerning two means, 18-39 Paired sample tests, 18-40 Inferences concerning one proportion, 18-41 Testing the difference between two proportions, 18-41 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, 18-49 The method of least squares, 18-49 Additional equations for linear regression, 18-51 Prediction error, 18-51 Confidence intervals and hypothesis testing in linear regression, 18-52 Procedure for inference statistics for linear regression using the calculator, 18-53 Multiple linear fitting, 18-56 Polynomial fitting, 18-58 Selecting the best fitting, 18-62 Chapter 19 - Numbers in Different Bases, 19-1 Definitions, 19-1 The BASE menu, 19-1 Functions HEC, DEC, OCT and BIN, 19-2 Page TOC-17 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, 19-6 Hexadecimal numbers for pixel references, 19-7 Chapter 20 - Customizing menus and keyboard, 20-1 Customizing menus, 20-1 The PRG/MODES/MENU, 20-1 Menu numbers (RCLMENU and MENU functions), 20-2 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, 20-6 Un-assigning a user-defined key, 20-7 Assigning multiple user-defined key, 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, 21-6 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 Page TOC-18 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 number and tag, 21-33 "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, 21-44 Program branching, 21-46 Branching with IF, 21-46 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, 21-62 Errors and error trapping, 21-64 DOERR, 21-64 ERRN, 21-64 ERRM, 21-65 ERR0, 21-65 LASTARG, 21-65 Sub-menu IFERR, 21-65 User RPL programming in algebraic mode, 21-66 Chapter 22 - Programs for graphics manipulation, 22-1 The PLOT menu, 22-1 User-defined key for the PLOT menu, 22-1 Page TOC-19 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 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, 22-22 PVIEW, 22-22 PX C, 22-22 C PX, 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), 22-30 The GROB menu, 22-31 A program with plotting and drawing functions, 22-33 Modular programming, 22-36 Running the program, 22-36 A program to calculate principal stresses, 22-38 Ordering the variables in the sub-directory, 22-39 A second example of Mohr's circle calculations, 22-39 An input form for the Mohr's circle program, 22-40 Chapter 23 - Character strings, 23-1 String-related functions in the TYPE sub-menu, 23-1 String concatenation, 23-2 Page TOC-20 The CHARS menu, 23-2 The characters list, 23-3 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 Calculations 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, 26-2 Backup objects, 26-3 Backing up objects in port memory, 26-3 Backing up and restoring HOME, 26-4 Storing, deleting, and restoring backup objects, 26-5 Using data in backup objects, 26-5 Using libraries, 26-6 Installing and attaching a library, 26-6 Library numbers, 26-7 Deleting a library, 26-7 Page TOC-21 Creating libraries, 26-7 Backup battery, 26-7 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 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 - The MATHS menu, J-1 Appendix K - The MAIN menu, K-1 Appendix L - Line editor commands, L-1 Appendix M ­ Index, M-1 Limited Warranty ­ W-1 Service, W-2 Regulatory information, W-4 Page TOC-22 A note about screenshots in this guide A screenshot is a representation of the calculator screen. For example, the first time the calculator is turned on you get the following screen (calculator screens are shown with a thick border in this section): The top two lines represent the screen header and the remaining area in the screen is used for calculator output. Most screenshots in this guide were generated using a computer-based emulator (a program that simulates the operation of the calculator in a computer), and are missing the screen header lines. Instead, they will show additional screen output area in the location of the header lines, as shown below: This additional screen output area in many screen shots in this guide will not show when you try those guide's example in your calculator. Thus, while in the guide you may see a screenshot as the following: the calculator will actually show the following screen: Page Note-1 Notice that the header lines cover the top first and a half lines of output in the calculator's screen. Nevertheless, the lines of output not visible are still available for you to use. You can access those lines in your calculator by pressing the up-arrow key (--), which will allow you to scroll down the screen contents. Also, as you perform the three operations listed in the screenshot, in the order shown, your screen will show them occupying higher levels in the display as shown next: The keystrokes required to complete these exercises are the following: S2.5` R,,Ü5.5+,¹2.5` The next operation, 2.3+5*,,Ê\2.3` will force the lines corresponding to the operation SIN(2.5) to move upwards and be hidden by the header lines. Many screenshots in this guide have also been modified to show only the operation of interest. For example, the screenshot for the operation SIN(2.5), shown above, may be simplified in this guide to look as: Page Note-2 These simplifications of the screenshots are aimed at economizing output space in the guide. Be aware of the differences between the guide's screenshots and the actual screen display, and you should have no problem reproducing the exercises in this guide. Page Note-3 Chapter 1 Getting started This chapter is aimed at providing basic information in the operation of your calculator. The exercises are aimed at familiarizing yourself with the basic operations and settings before actually performing a calculation. Basic Operations The following exercises are aimed at getting you acquainted with the hardware of your calculator. Batteries The calculator uses 3 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 3 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 1-1 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 red 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 red 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. below. The display should look as indicated Page 1-2 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: RAD XYZ HEX R= 'X' For details on the meaning of these specifications 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. 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 Page 1-3 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: This CHOOSE box is labeled BASE MENU and provides a list of numbered functions, from 1. HEX x to 6. B R. 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 Page 1-4 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 R B (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. 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: Page 1-5 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. 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: To revert to the CHOOSE boxes setting, use: H @)FLAGS --,, --~@ @CHK@@ @@@OK@@@ @@@OK@@@. 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. 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) Page 1-6 @VIEW @@ RCL @@ @@STO@ ! PURGE CLEAR B C D E F VIEW the contents of a variable ReCaLl the contents of a variable STOre the contents of a variable PURGE a variable 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 red right-shift button, ,, with the 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: Page 1-7 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#@ F 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#@ F 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 1-8 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). · If using the W key, the setting in the time format field will change to either of the following options: o o o AM : indicates that displayed time is AM time PM : indicates that displayed time is PM time 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. · 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#@ F soft menu key to make the selection. Setting the date After setting the time format option, the SET TIME AND DATE input form will look as follows: Page 1-9 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 ( B), to see the options for the date format: Highlight your choice by using the up and down arrow keys,-- ~, and press the !!@@OK#@ F soft menu key to make the selection. Introducing the calculator's keyboard The figure below shows a diagram of the calculator's keyboard with the numbering of its rows and columns. Page 1-10 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 green left-shift key, key (8,1), the red right-shift key, key (9,1), and the blue ALPHA key, key (7,1), can be Page 1-11 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), rightshift ... (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 1-12 Press the !!@@OK#@ F 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 ( B). 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: 3 5 - 23 3 33 2.5 +e 1 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,OsTM~--` Page 1-13 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*!Ü51/3*3 -------------- /23Q3TMTM+!¸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.TMTM /23.Q3+!¸2.5` to obtain the same result. 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#@ F soft menu key to complete the operation. The display, for the RPN mode looks as follows: Page 1-14 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. Basically, what RPN means is that, instead of writing an operation such as 3 + 2, in the calculator by using 3+2`, we write first the operands, 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 2`pushes 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. A simpler way to calculate this operation is by using: 3`2+. Let's try some other simple operations before trying the more complicated expression used earlier for the algebraic operating mode: 123/32 123`32/ 2 4 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: 3 5 - 23 3 33 2.5 +e 1 Page 1-15 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.Q3TMTM+!¸2.5` The resulting expression is shown in stack level 1 as follows: 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 Page 1-16 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 --,,--,,--,, -- @ @CHK@@ @@OK@@ @@OK@@ Alternatively, you can use one of the following shortcuts: · In ALG mode, CF(-95) selects RPN mode · 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 more about reals, see Chapter 2. To illustrate this and other number formats try the following exercises: · 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. Page 1-17 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: · 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 ( B), and select the option Fixed with the arrow down key ~. 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. Page 1-18 · 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 ( B), and select the option Fixed with the arrow down key ~. Press the right arrow key, TM, 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. Press the !!@@OK#@ soft menu key to complete the selection: Press the !!@@OK#@ soft menu key return to the calculator display. number now is shown as: The 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 Page 1-19 · 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 ( B), 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 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. number now is shown as: The This result, 1.23E2, is the calculator's version of powers-of-ten notation, i.e., 1.235 × 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. · 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 ( B), 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). Page 1-20 Press the !!@@OK#@ soft menu key return to the calculator display. number now is shown as: The Because this number has three figures in the integer part, it is shown with four significative figures and a zero power of ten, while using the Engineering format. For example, the number 0.00256, will be shown as: · · Decimal comma vs. decimal point Decimal points in floating-point numbers can be replaced by commas, if the user is more familiar with such notation. To replace decimal points for commas, change the FM option in the CALCULATOR MODES input form to commas, as follows (Notice that we have changed the Number Format to Std): Press the H button. Next, use the down arrow key, ~, once, and the right arrow key, TM, highlighting the option __FM,. To select commas, press the @ @CHK@@ soft menu key (i.e., the B key). The input form will look as follows: · Press the !!@@OK#@ soft menu key return to the calculator display. number 123.456789012, entered earlier, now is shown as: The Page 1-21