Transform Methods for Solving Partial Differential Equations

Duffy, Dean G.

ISBN 10: 0849373743 / ISBN 13: 9780849373749

Editore: CRC Press LLC, 1994

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Former library book; may include library markings. Used book that is in excellent condition. May show signs of wear or have minor defects. Codice articolo GRP82647672

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Titolo: Transform Methods for Solving Partial ...

Casa editrice: CRC Press LLC

Data di pubblicazione: 1994

Legatura: Rilegato

Condizione: Very Good

Edizione: 1st Edition.

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Riassunto:

For most scientists and engineers, the only analytic technique for solving linear partial differential equations is separation of variables. In Transform Methods for Solving Partial Differential Equations, the author uses the power of complex variables to demonstrate how Laplace and Fourier transforms can be harnessed to solve many practical, everyday problems experienced by scientists and engineers. Unlike many mathematics texts, this book provides a step-by-step analysis of problems taken from scientific and engineering literature. Detailed solutions are given in the back of the book. This essential text/reference draws from the latest literature on transform methods to provide in-depth discussions on the joint transform problem, the Cagniard-de Hoop method, and the Wiener-Hopf technique. Some 1,500 references are included as well.

Contenuti:

The Fundamentals
Laplace Transforms
Fourier Transforms
Linear Ordinary Differential Equations
Complex Variables
Multivalued Functions, Branch Points, Branch Cuts and Riemann Surfaces
Some Examples of Integration Which Involve Multivalued Functions
Transform Methods with Single-Valued Functions
Inversion of Laplace Transforms by Contour Integration
Inversion of Fourier Transforms by Contour Integration
The Solution of Partial Differential Equations by Laplace Transforms
The Solution of Partial Differential Equations by Fourier Transforms
The Solution of Partial Differential Equations by Hankel Transforms
Transform Methods with Multivalued Functions
Inversion of Laplace Transforms by Contour Integration
Inversion of Fourier Transforms by Contour Integration
The Solution of Partial Differential Equations by Laplace Transforms
The Solution of Partial Differential Equations by Fourier Transforms
The Joint Transform Method
The Solution of Partial Differential Equations Using the Joint Transform Method
Inversion of the Joint Transform by Cagniard's Method
The Modification of Cagniard's Method by De Hoop
Expansions of Terms of Leaky Modes
The Wiener-Hopf Technique
The Wiener-Hopf Technique When the Factorization Contains No Branch Points
The Wiener-Hopf Technique When the Factorization Contains Branch Points
The Wiener-Hopf Technique with a Finite Scatterer
Worked Solutions to Some of the Problems
Index