Items related to Partial Differential Equations: Sources and Solutions
Synopsis
The author strikes a balance between rigor and ease of comprehension, while bravely confronting some mathematically untidy applications such as heat flow in a cylindrical wedge where the flat sides (rather than the cylindrical side) are heated externally. Topics include Fourier methods, differential equations of physics and engineering, methodology for the Sturm-Liouville sub-problems, Green's functions for non-homogeneous partial differential equations, and perturbation methods and their use in applied mathematics. Annotation c. by Book News, Inc., Portland, Or.
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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.
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Partial Differential Equations: Sources and Solutions
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Partial Differential Equations: Sources and Solutions
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Partial Differential Equations: Sources and Solutions
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Partial Differential Equations: Sources and Solutions
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Partial Differential Equations: Sources and Solutions
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