Partial Differential Equations and Mathematica: 2nd Edition (Hardback) book cover

Partial Differential Equations and Mathematica

2nd Edition

By Prem K. Kythe, Michael R. Schäferkotter, Pratap Puri

Chapman and Hall/CRC

440 pages | 74 B/W Illus.

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Hardback: 9781584883142
pub: 2002-11-12
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Description

Early training in the elementary techniques of partial differential equations is invaluable to students in engineering and the sciences as well as mathematics. However, to be effective, an undergraduate introduction must be carefully designed to be challenging, yet still reasonable in its demands. Judging from the first edition's popularity, instructors and students agree that despite the subject's complexity, it can be made fairly easy to understand.

Revised and updated to reflect the latest version of Mathematica, Partial Differential Equations and Boundary Value Problems with Mathematica, Second Edition meets the needs of mathematics, science, and engineering students even better. While retaining systematic coverage of theory and applications, the authors have made extensive changes that improve the text's accessibility, thoroughness, and practicality.

New in this edition:

  • Upgraded and expanded Mathematica sections that include more exercises

  • An entire chapter on boundary value problems

  • More on inverse operators, Legendre functions, and Bessel functions

  • Simplified treatment of Green's functions that make it more accessible to undergraduates

  • A section on the numerical computation of Green's functions

  • Mathemcatica codes for solving most of the problems discussed

  • Boundary value problems from continuum mechanics, particularly on boundary layers and fluctuating flows

  • Wave propagation and dispersion

    With its emphasis firmly on solution methods, this book is ideal for any mathematics curricula. It succeeds not only in preparing readers to meet the challenge of PDEs, but also in imparting the inherent beauty and applicability of the subject.

  • Table of Contents

    INTRODUCTION TO MATHEMATICA

    Introduction

    Conventions

    Getting Started

    File Manipulation

    Differential Equations

    To the Instructor

    To the Student

    MathSource

    INTRODUCTION

    Notation and Definitions

    Initial and Boundary Conditions

    Classification of Second Order Equations

    Some Known Equations

    Superposition Principle

    METHOD OF CHARACTERISTICS

    First Order Equations

    Linear Equations with Constant Coefficients

    Linear Equations with Variable Coefficients

    First Order Quasi-Linear Equations

    First Order Nonlinear Equations

    Geometrical Considerations

    Some Theorems on Characteristics

    Second Order Equations

    Linear and Quasi-linear Equations

    LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS

    Inverse Operators

    Homogeneous Equations

    Nonhomogeneous Equations

    ORTHOGONAL EXPANSIONS

    Orthogonality

    Orthogonal Polynomials

    Series of Orthogonal Functions

    Trigonometric Fourier Series

    Eigenfunction Expansions

    Bessel Functions

    SEPARATION OF VARIABLES

    Introduction

    Hyperbolic Equations

    Parabolic Equations

    Elliptic Equations

    Cylindrical Coordinates

    Spherical Coordinates

    Nonhomogeneous Problems

    INTEGRAL TRANSFORMS

    Laplace Transforms

    Notation

    Basic Laplace Transforms

    Inversion Theorem

    Fourier Transforms

    Fourier Integral Theorems

    Properties of Fourier Transforms

    Fourier Sine and Cosine Transforms

    Finite Fourier Transforms

    GREEN'S FUNCTIONS

    Generalized Functions

    Green's Functions

    Elliptic Equations

    Parabolic Equations

    Hyperbolic Equations

    Applications of Green's Functions

    Computation of Green's Functions

    BOUNDARY VALUE PROBLEMS

    Initial and Boundary Conditions

    Implicit Conditions

    Periodic Conditions

    Wave Propagation and Dispersion

    Boundary Layer Flows

    Miscellaneous Problems

    WEIGHTED RESIDUAL METHODS

    Line Integrals

    Variational Notation

    Multiple Integrals

    Weak Variational Formulation

    Gauss-Jacobi Quadrature

    Rayleigh-Ritz Method

    Choice of Test Functions

    Transient Problems

    Other Methods

    PERTURBATION METHODS

    Perturbation Problem

    Taylor Series Expansions

    Successive Approximations

    Boundary Perturbations

    Fluctuating Flows

    FINITE DIFFERENCE METHODS

    Finite Difference Schemes

    First Order Equations

    Second Order Equations

    Appendix A: Green's Identities

    Appendix B: Orthogonal Polynomials

    Appendix C: Tables of Transform Pairs

    Appendix D: Glossary of Mathematica Functions

    Appendix E: Mathematica Packages and Notebooks

    Bibliography

    Index

    Each chapter also contains sections of Mathematica Projects and Exercises

    Subject Categories

    BISAC Subject Codes/Headings:
    MAT000000
    MATHEMATICS / General
    MAT003000
    MATHEMATICS / Applied
    MAT007000
    MATHEMATICS / Differential Equations
    MAT021000
    MATHEMATICS / Number Systems