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 Equations Fun with Integers Unit Conversion Trigonometry DATA TYPES Sequences Sets Lists Tables Arrays Data Conversions Other Data Types CALCULUS Defining Functions Composition of Functions Summation and Product Limits Differentiation Extrema Integration Taylor and Series Expansions The Student Package GRAPHICS 2-Dimensional Plotting 3-Dimensional Plotting Animation MAPLE PROGRAMMING The MAPLE Procedure Conditional Statements The "for" loop Type Declaration The "while" Loop Recursive Procedures Explicit Return Error Statement args and nargs Input and Output Benerating C and Fortran Code Viewing Built-in MAPLE Code The MAPLE Interactive Debugger Writing your own Packages Answers to Programming Exercises DIFFERENTIAL EQUATIONS Solving Ordinary Differential Equations First-Order Differential Equation Numerical Solutions Second- and Higher-Order Des Series Solutions The Laplace Transform The Detools Package Solving Systems of Ordinary Differential Equations Plotting Solutions to Ordinary Differential Equations Partial Differential Equations LINEAR ALGEBRA Vectors, Arrays, and Matrices Matrix Context Menu Elementary Row and Colum Operations Gaussian Elimination Inverses, Determinants, Minors, and the Adjoint Special 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 Least Squares Problems QR-Factorization and the Gram-Schmidt Process LU-Factorization Other Linear Algebra Functions The linalg Package MULTIVARIABLE AND VECTOR CALCULUS Vectors Lines and Planes Vector-Valued Functions The Gradient and Directional Derivatives Extrema Multiple Integrals Vector Field Line Integrals Green''s Theorem Surface Integrals COMPLEX ANALYSIS Arithmetic of Complex Numbers 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 and Existing Worksheet Saving a Worksheet Opening a MAPLE Text Fle 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 plottoos Package The geometry Package The geom3d Package 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 Fast Fourier Transform Asymptotic Expansion STATISTICS Introduction Data Sets Numerical Methods for Describing Data Transforming Data Graphical Methods for Describing Data Linear Regression ANOVA Distributions OVERVIEW OF OTHER PACKAGES Finite Fields Polynomials Group Theory Combinatorics Number Theory Numerical Approximation Miscellaneous Packages New Packages APPENDICES MAPLE Resources Glossary of Commands Further Reading REFERENCES INDEXlotting 3-Dimensional Plotting Animation MAPLE PROGRAMMING The MAPLE Procedure Conditional Statements The "for" loop Type Declaration The "while" Loop Recursive Procedures Explicit Return Error Statement args and nargs Input and Output Benerating C and Fortran Code Viewing Built-in MAPLE Code The MAPLE Interactive Debugger Writing your own Packages Answers to Programming Exercises DIFFERENTIAL EQUATIONS Solving Ordinary Differential Equations First-Order Differential Equation Numerical Solutions Second- and Higher-Order Des Series Solutions The Laplace Transform The Detools Package Solving Systems of Ordinary Differential Equations Plotting Solutions to Ordinary Differential Equations Partial Differential Equations LINEAR ALGEBRA Vectors, Arrays, and Matrices Matrix Context Menu Elementary Row and Colum Operations Gaussian Elimination Inverses, Determinants, Minors, and the Adjoint Special 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 Least Squares Problems QR-Factorization and the Gram-Schmidt Process LU-Factorization Other Linear Algebra Functions The linalg Package MULTIVARIABLE AND VECTOR CALCULUS Vectors Lines and Planes Vector-Valued Functions The Gradient and Directional Derivatives Extrema Multiple Integrals Vector Field Line Integrals Green''s Theorem Surface Integrals COMPLEX ANALYSIS Arithmetic of Complex Numbers 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 and Existing Worksheet Saving a Worksheet Opening a MAPLE Text Fle 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 plottoos Package The geometry Package The geom3d Package 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 Fast Fourier Transform Asymptotic Expansion STATISTICS Introduction Data Sets Numerical Methods for Describing Data Transforming Data Graphical Methods for Describing Data Linear Regression ANOVA Distributions OVERVIEW OF OTHER PACKAGES Finite Fields Polynomials Group Theory Combinatorics Number Theory Numerical Approximation Miscellaneous Packages New Packages APPENDICES MAPLE Resources Glossary of Commands Further Reading REFERENCES INDEX>LINEAR ALGEBRA Vectors, Arrays, and Matrices Matrix Context Menu Elementary Row and Colum Operations Gaussian Elimination Inverses, Determinants, Minors, and the Adjoint Special 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 Least Squares Problems QR-Factorization and the Gram-Schmidt Process LU-Factorization Other Linear Algebra Functions The linalg Package MULTIVARIABLE AND VECTOR CALCULUS Vectors Lines and Planes Vector-Valued Functions The Gradient and Directional Derivatives Extrema Multiple Integrals Vector Field Line Integrals Green''s Theorem Surface Integrals COMPLEX ANALYSIS Arithmetic of Complex Numbers 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 and Existing Worksheet Saving a Worksheet Opening a MAPLE Text Fle 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 plottoos Package The geometry Package The geom3d Package 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 Fast Fourier Transform Asymptotic Expansion STATISTICS Introduction Data Sets Numerical Methods for Describing Data Transforming Data Graphical Methods for Describing Data Linear Regression ANOVA