Transform Methods For Solving Partial Differential Equations / Edition 2

Transform Methods For Solving Partial Differential Equations / Edition 2

by Dean G. Duffy
     
 

ISBN-10: 1584884517

ISBN-13: 9781584884514

Pub. Date: 07/01/2004

Publisher: Taylor & Francis

Transform Methods for Solving Partial Differential Equations illustrates the use of Laplace, Fourier, and Hankel transforms to solve partial differential equations encountered in science and engineering. This second edition is expanded to provide a broader perspective on the applicability and use of transform methods. It classifies the problems presented in every

Overview

Transform Methods for Solving Partial Differential Equations illustrates the use of Laplace, Fourier, and Hankel transforms to solve partial differential equations encountered in science and engineering. This second edition is expanded to provide a broader perspective on the applicability and use of transform methods. It classifies the problems presented in every chapter by type of region, coordinate system and partial differential equation. Many of the problems included in the book are illustrated to show the reader what they will look like physically. Unlike many mathematics texts, this book provides a step-by-step analysis of problems taken from the actual scientific and engineering literature.

Product Details

ISBN-13:
9781584884514
Publisher:
Taylor & Francis
Publication date:
07/01/2004
Series:
Symbolic & Numeric Computation Series
Edition description:
Revised
Pages:
728
Product dimensions:
6.14(w) x 9.21(h) x 1.56(d)

Table of Contents

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 Technique when the Factorization Contains Branch Points
Papers Using the Wiener-Hopf Technique
WORKED SOLUTIONS TO SOME OF THE PROBLEMS
INDEX

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