Partial Differential Equations: Sources and Solutions (Dover Books on Mathematics)

Snider, Arthur David

ISBN 10: 0486453405 / ISBN 13: 9780486453408

Published by Dover Publications, 2006

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Bibliographic Details

• Title: Partial Differential Equations: Sources and Solutions (Dover Books on Mathematics)
• Publisher: Dover Publications
• Publication Date: 2006
• Language: English
• ISBN 10: 0486453405
• ISBN 13: 9780486453408
• Binding: Paperback
• Condition: new

About this title

Synopsis

Newly updated by the author, this text explores the solution of partial differential equations by separating variables, rather than by conducting qualitative theoretical analyses of their properties. These qualitative features--uniqueness, existence, elegance of composition, and convergence modes--are substantiated by physical reasoning, rather than rigorous arguments. Geared toward applied mathematicians, physicists, engineers, and others seeking explicit solutions, the book offers heuristic justifications for each construction.
The first three chapters review the necessary tools for understanding the separation of variables technique: basics of ordinary differential equations, Frobenius-series construction and properties of Bessel functions, and Fourier analysis. Subsequent chapters explore the exposition of the algorithmic nature of the separation of variables process, based on a sequence of steps that infallibly leads to the solution expansion, regardless of the nature of the boundary conditions.

From the Back Cover

Offering a welcome balance between rigor and ease of comprehension, this book presents full coverage of the analytic (and accurate) method for solving PDEs -- in a manner that is both decipherable to engineers and physically insightful for mathematicians. By exploring the eigenfunction expansion method based on physical principles instead of abstract analyses, it makes the analytic approach understandable, visualizable, and straightforward to implement. Contains tabulations and derivations of all known eigenfunction expansions. Offers demystifying coverage of the separation of variables technique and presents a novel approach to FFT and its utilization. Presents a fast, automatic algorithmic procedure for solving wave, heat, and Laplace equation in rectangular, cylindrical, and spherical coordinates. Discusses Sturm-Liouville Theory; Green's functions and transform methods; and perturbation methods, small wave analysis, and dispersion laws. Motivates every technique presented --without exception -- by a heuristic discussion demonstrating the plausibility or inevitability of the procedure, and includes an abundance of figures and worked-out examples. For engineers, applied mathematicians, computer specialists, and analysts.