Partial Differential Equations and Mathematica

Partial Differential Equations and Mathematica

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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 more

Product details

  • Hardback | 440 pages
  • 132.6 x 265.2 x 28.2mm | 757.51g
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • Revised
  • 2nd Revised edition
  • 74 black & white illustrations, 7 black & white tables
  • 1584883146
  • 9781584883142

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 Exercisesshow more

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