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.
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Partial Differential Equations-Mathematics
Partial Differential Equations-Mechanical Engineering
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.
Represents the only complete reference on the eigenfunction
Emphasizes the universality of the separation-of-variables
technique, thereby demystifying it and providing a step-by-step
Contains tabulations and derivations of all known eigenfunction
Reviews elementary but infrequently-used calculus
techniques from a fresh perspective.
Expostulates advanced mathematical concepts and theorems
through physical and geometrical reasoning.
- Thus, even mature students returning from industrial
practice will find the text user-friendly.
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
Explores the special functions of mathematics via their
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 presented without
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.
Contains approximately 500 figures making this
the most visual and geometric text on the market.
- Analyzes the problem of heat flow in a cylindrical
wedge where the flat sides are heated (entailing the obscure
Includes over 200 worked-out examples and an abundance
Comments of a historical, digressive, or abstract nature
are set off by the indentation scheme.
- Some demonstrate the computational procedures, some illustrate
the physical significance, some explore the mathematical generalizations.
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.