The MAPLE BOOK FRANK GARVAN CHAPMAN & HALL/CRC. A CRC Press Company Boca Raton London New York Washington, D.C.

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1 The MAPLE BOOK FRANK GARVAN CHAPMAN & HALL/CRC A CRC Press Company Boca Raton London New York Washington, D.C.

2 CONTENTS 1. Getting Started Starting a MAPLE session Different versions of MAPLE Basic syntax Editing mistakes Help A sample session and context menus Palettes Spreadsheets Quitting MAPLE MAPLE as a Calculator Exact arithmetic and basic functions Floating-point arithmetic High School Algebra Polynomials and rational functions Factoring a polynomial Expanding an expression Collecting like terms Simplifying an expression Simplifying radicals 22, Working in the real domain Simplifying rational functions Degree and coefficients of a polynomial Substituting into an expression Restoring variable status Equations Left- and right-hand sides Finding exact solutions Finding approximate solutions Assigning solutions Fun with integers Complete integer factorization Quotient and remainder Gcd and lcm Primes Integer solutions Reduction mod p Unit conversion Trigonometry Degrees and radians Trigonometric functions Simplifying trigonometric functions 38

3 4. Data Types Sequences Sets Lists Tables Arrays.... J Data conversions Other data types Calculus Defining functions Composition of functions Summation and product i Limits Differentiation Ext rema Integration Techniques of integration Substitution Integration by parts Partial fractions Taylor and series expansions The student package Graphics Two-dimensional plotting Restricting domain and range Parametric plots Multiple plots Polar plots Plotting implicit functions Plotting points Title and text in a plot Plotting options Saving and printing a plot Other plot functions Three-dimensional plotting Parametric plots Multiple plots Space curves Contour plots Plotting surfaces defined implicitly Title and text in a plot Three-dimensional plotting options Other three-dimensional plot functions Animation 99

4 7. MAPLE Programming The MAPLE procedure Local and global variables Conditional statements Boolean expressions The "for" loop Type declaration Ill 7.5 The "while" loop Recursive procedures Explicit return Error statement args and nargs : Input and output Formatted output Interactive input Reading commands from a file Reading data from a file Writing data to a file Writing and saving to a file Generating C and Fortran code Viewing built-in MAPLE code The MAPLE interactive debugger Writing your own packages Packages as tables Modules for packages Answers to programming exercises Differential Equations Solving ordinary differential equations Implicit solutions Initial conditions Systems of differential equations First-order differential equations odeadvisor Integrating factors Direction fields Numerical solutions Second- and higher order linear DEs Constant coefficients Variation of parameters Reduction of order Series solutions The method of Frobenius The Laplace transform The Heaviside function 165

5 8.6.2 The Dirac delta function The DEtools package DE plotting functions Dynamical systems DE manipulation Lie symmetry methods Differential operators Closed form solutions Simplifying DEs and rifsimp Linear Algebra Vectors, Arrays, and Matrices Matrix and Vector entry assignment The Matrix and Vector palettes Matrix operations Matrix and vector construction shortcuts Viewing large Matrices and Vectors Matrix context menu ^The Export As submenu The Norm submenu The Select Element submenu The Solvers submenu The Conversions submenu The In-place Options submenu Elementary row and column operations Gaussian elimination Inverses, determinants, minors, and the adjoint Special matrices and vectors Band matrix Constant matrices and vectors Diagonal matrices Givens rotation matrices Hankel matrices Hilbert matrices Householder matrices Identity matrix Jordan block matrices Random matrices and vectors Toeplitz matrices Vandermonde matrices Zero matrices and vectors Systems of linear equations Row space, column space, and nullspace Eigenvectors and diagonalization Jordan form Inner products, and Vector and matrix norms 209

6 The dot product and bilinear forms Vector norms Matrix norms Least squares problems QR-factorization and the Gram-Schmidt process LU-factorization Other LinearAlgebra functions The linalg package Matrices and vectors Conversion between linalg and LinearAlgebra Matrix operations in linalg The functions in the linalg package Multivariable and Vector Calculus Vectors Vector operations Length, dot product, and cross product Plotting vectors Lines and planes Lines Planes Vector-valued functions Differentiation and integration of vector functions Space curves Tangents and normals to curves Curvature The gradient and directional derivatives Extrema Local extrema and saddle points Lagrange multipliers Multiple integrals Double integrals Triple integrals The Jacobian Vector field Plotting a vector field Divergence and curl Potential functions Line integrals Green's theorem Surface integrals Flux of a vector field Stoke's theorem The divergence theorem Complex Analysis Arithmetic of complex numbers 271

7 11.2 Polar form ' nth roots? The Cauchy-Riemann equations and harmonic functions Elementary functions Conformal mapping Taylor series and Laurent series Contour integrals Residues and poles Opening, Saving, and Exporting Worksheets Opening ah existing worksheet Saving a worksheet Opening a MAPLE text file Exporting worksheets and LaTeX Document Preparation Adding text Inserting math into text Adding titles and headings Creating a subsection Cutting and pasting Bookmarks and hypertext More Graphics The plottools package Two-dimensional plot objects Three-dimensional plot objects Transformation of plots The geometry package The geomsd package Regular polyhedra Quasi-regular polyhedra The Archimedean solids Special Functions Overview of mathematical functions Bessel functions The Gamma function Hypergeometric functions Elliptic integrals The AGM Jacobi's theta functions Elliptic functions The Riemann zeta-function Orthogonal polynomials Integral transforms Fourier transforms Hilbert transform Mellin transform 350

8 15.12 Fast Fourier transform Asymptotic expansion Statistics Introduction Data sets Numerical methods for describing data Describing the center of a data set Describing the dispersion of a data set Describing characteristics of a data set Transforming data Graphical methods for describing data Histogram Box plot Scatter plot Linear regression ANOVA Distributions , Evaluating distributions Generating random distributions Overview of Other Packages Finite fields Polynomials Group theory Combinatorics The combinat package The networks package The combstruct package Number theory The numtheory package The Gausslnt package p-adic numbers Numerical approximation Miscellaneous packages ' The algcurves package The codegen package The diffalg package The difforms package The Domains package The finance package The genfunc package The geometry package The geomsd package The Groebner package The liesymm package The LREtools package 431

9 The Ore.algebra package The PDEtools package The powseries package The process package The simplex package The Slode package The Spread package The sumtools package The tensor package New packages The CurveFitting package The ExternalCailing package The LinearFunctionalSystemspa.cka.ge The LinearOperators package The ListTools package The MathML package The OrthogonalSeries package The RandomTools package The RationalNormalForms package The RealDomain package The Sockets package The SolveTools package The StringTools package The Units package The XMLTools package 443 Appendix A MAPLE Resources 445 The MAPLE Application Center 445 The MAPLE Student Center 448 The MAPLE Share Library 448 Interesting URLs 448 Appendix B Glossary of Commands 451 Appendix C Further Reading 461 References 463 Index '. 465

Honors Precalculus: Solving equations and inequalities graphically and algebraically. Page 1

Honors Precalculus: Solving equations and inequalities graphically and algebraically. Page 1 Solving equations and inequalities graphically and algebraically 1. Plot points on the Cartesian coordinate plane. P.1 2. Represent data graphically using scatter plots, bar graphs, & line graphs. P.1