Integral Transforms and Their Applications

Brian Davies

368 pages, parution le 24/01/2002 (3^eme édition)

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Résumé

This book is an introduction and reference for the applications of integral transforms to a wide range of common mathematical problems. Emphasis is placed on the development of techniques and on the connection between properties of transforms and the kinds of problems for which they provide tools. Over 400 problems accompany the text, illustrating areas of applications. This third edition has been substantially updated, extended, and reorganized. Chapter one is largely new, covering introductory aspects of complex variable theory. Chapters 2-6 are devoted to the Laplace transform and include material on ordinary differential equations and partial differential equations. Chapters 7-11 cover the Fourier transform by exposition and application. Chapters 12-13 discuss techniques of the Mellin transform, and the final chapter on the numerical inversion of the Laplace transform brings up to date the enormous progress in the area. Graduate students and researchers working in mathematics and physics will find this book useful.

Contents

Functions of a Complex Variable.
The Laplace Transform.
The Inversion Integral.
Ordinary Differential Equations.
Partial Differential Equations I.
Integral Equations.
The Fourier Transform.
Partial Differential Equations II.
Generalized Functions.
Green's Functions.
Transforms in Several Variables.
The Mellin Transform.
Application to Sums and Integrals.
Hankel Transforms.
Integral Transforms Generated by Green's Functions.
The Wiener-Hopf Technique.
Methods Based on Cauchy Integrals.
Laplace's Method for Ordinary Differential Equations.
Numerical Inversion of Laplace Transforms.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Brian Davies
Parution	24/01/2002
Édition	3^eme édition
Nb. de pages	368
Format	16 x 24
Couverture	Relié
Poids	691g
Intérieur	Noir et Blanc
EAN13	9780387953144
ISBN13	978-0-387-95314-4