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Partial Differential Equations: Sources and Solutions, 1/e

Arthur David Snider, University of South Florida

Published February, 1999 by Prentice Hall Engineering/Science/Mathematics

Copyright 1999, 658 pp.
Cloth
ISBN 0-13-674359-5


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Summary

For courses in Partial Differential Equations taken by mathematics and engineering majors. An alternative to the obscure, jargon-heavy tomes on PDEs for math specialists and the cookbook, numerics-based “user manuals” (which provide little insight and questionable accuracy), this text presents full coverage of the analytic (and accurate) method for solving PDEs — in a manner that is both decipherable to engineering students and physically insightful for math students. The exposition is based on physical principles instead of abstract analyses, making the presentation accessible to a larger audience.

Features


Represents the only complete reference on the eigenfunction expansion method.
Emphasizes the universality of the separation-of-variables technique, thereby demystifying it and providing a step-by-step implementation.
Contains tabulations and derivations of all known eigenfunction expansions.
Reviews elementary but infrequently-used calculus techniques from a fresh perspective.

  • Thus, even mature students returning from industrial practice will find the text user-friendly.
Expostulates advanced mathematical concepts and theorems through physical and geometrical reasoning.

Explains the physical origins of the equations and the physical basis for their mathematical properties.
The Fourier analysis chapter unifies the mathematical, engineering, and computational aspects. Offers a novel approach to FFT and its utilization.
Explores the special functions of mathematics via their physical origins.
Presents a fast, automatic algorithmic procedure for solving wave, heat, and Laplace equation in rectangular, cylindrical, and spherical coordinates.
Extends the methodology to nonlinear situations by qualitative analysis and perturbative techniques.
Motivates every technique presentedwithout exception
— by a heuristic discussion demonstrating the plausibility or inevitability of the procedure.
Presents derivations for virtually all of the classical Sturm-Liouville expansions — even the singular ones which usually appear only as cookbook formulas in tabulations or as formidable examples in ponderous tomes on the subject.
  • Analyzes the problem of heat flow in a cylindrical wedge where the flat sides are heated (entailing the obscure Lebedev expansions).
Contains approximately 500 figures — making this the most visual and geometric text on the market.
Includes over 200 worked-out examples and an abundance of exercises.
  • Some demonstrate the computational procedures, some illustrate the physical significance, some explore the mathematical generalizations.
Comments of a historical, digressive, or abstract nature are set off by the indentation scheme.


Table of Contents
    1. Basics of Differential Equations.
    2. Series Solutions for Ordinary Differential Equations.
    3. Fourier Methods.
    4. The Differential Equations of Physics and Engineering.
    5. The Separation of Variables Technique.
    6. Eigenfunction Expansions.
    7. Applications of Eigenfunctions to Partial Differential Equations.
    8. Green's Functions and Transform Methods.
    9. Perturbation Methods, Small Wave Analysis, and Dispersion.
    Appendix A. Some Numerical Techniques.
    Appendix B. Evaluation of Certain Bromwich Integrals.
    References.
    Index.


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