Transform Methods for Solving Partial Differential Equations

ISBN-13: 9781584884514 / Angielski / Twarda / 2004 / 728 str.

Laurie Kelly; Dean G. Duffy

Opis

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.

Recenzje

“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

Spis treści

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

O autorze

Dean G. Duffy