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Zusatztext "This book provides a detailed account of the application of transform methods to solving linear PDEs in science and engineering. The main techniques studied are the Fourier and Laplace transform! Hankel transforms! and the Wiener-Hopf technique. In this second edition the references have been extended and numerical and asymptotic techniques are included. It provides a valuable source of concrete examples from diverse fields of applications with detailed solutions." - M. Kunzinger "The discussed solutions typically involve quite difficult algebra! while non-trivial mathematical steps! such as a change of order of integration or expansion into infinite series (product) are not justified. This gives the book more of an 'engineering' flavour; nonetheless it is certainly of interest to a wider interest." -EMS Newsletter! Sept. 2005 "The book contains many examples and exercises taken from a wide variety of scientific and engineering sources. Also numerical examples are presented using Matlab to help readers for better understanding of the physical problems." -Studia Univ. "Babes-Bolyai" Mathematica! Sept. 2005 Informationen zum Autor Dean G. Duffy Klappentext Illustrates the use of Laplace! Fourier! and Hankel transforms to solve partial differential equations encountered in science and engineering. This edition provides a broader perspective on the applicability and use of transform methods. It offers a step-by-step analysis of problems taken from the actual scientific and engineering literature. Zusammenfassung Illustrates the use of Laplace, Fourier, and Hankel transforms to solve partial differential equations encountered in science and engineering. This edition provides a broader perspective on the applicability and use of transform methods. It offers a step-by-step analysis of problems taken from the actual scientific and engineering literature. Inhaltsverzeichnis THE FUNDAMENTALS Fourier Transforms Laplace Transforms Linear Ordinary Differential Equations Complex Variables Multivalued Functions! Branch Points! Branch Cuts! and Riemann Surfaces Some Examples of Integration which Involve Multivalued Functions Bessel Functions What are Transform Methods? METHODS INVOLVING SINGLE-VALUED LAPLACE TRANSFORMS Inversion of Laplace Transforms by Contour Integration The Heat Equation The Wave Equation Laplace's and Poisson's Equations Papers Using Laplace Transforms to Solve Partial Differential Equations METHODS INVOLVING SINGLE-VALUED FOURIER AND HANKEL TRANSFORMS Inversion of Fourier Transforms by Contour Integration The Wave Equation The Heat Equation Laplace's Equation The Solution of Partial Differential Equations by Hankel Transforms Numerical Inversion of Hankel Transforms Papers Using Fourier Transforms to Solve Partial Differential Equations Papers Using Hankel Transforms to Solve Partial Differential Equations METHODS INVOLVING MULTIVALUED LAPLACE TRANSFORMS Inversion of Laplace Transforms by Contour Integration Numerical Inversion of Laplace Transforms The Wave Equation The Heat Equation Papers Using Laplace Transforms to Solve Partial Differential Equations METHODS INVOLVING MULTIVALUED FOURIER TRANSFORMS Inversion of Fourier Transforms by Contour Integration Numerical Inversion of Fourier Transforms The Solution of Partial Differential Equations by Fourier Transforms Papers Using Fourier Transforms to Solve Partial Differential Equations THE JOINT TRANSFORM METHOD The Wave Equation The Heat and Other Partial Differential Equations Inversion of the Joint Transform by Cagniard's Method The Modification of Cagniard's Method by De Hoop Papers Using the Joint Transform Technique Papers Using the Cagniard Technique Papers Using the Cagniard-De Hoop Technique THE WIENER-HOPF TECHNIQUE The Wiener-Hopf Technique When the Factorization Contains No Branch Points The Wiener-Hopf Techni...
