Integral Transforms and Their Applications / Edition 2by Brian Davies
Pub. Date: 11/28/1993
Publisher: Springer-Verlag New York, LLC
This book is an introduction to and a reference for the applications of integral problems 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. Graduate students and researchers working in mathematics and physics will find this book useful.
The author is Reader in Mathematics at the Australian National University, with interests in applied mathematics, mathematical physics, scientific computation, nonlinear dynamics, and chaos. He has also held posts in physics and theoretical physics, and in private and government research organizations. He is the author of a recent book chaotic systems, as well as of numerous research articles in many areas.
Table of ContentsPreface to the Third Edition * Preface to the Second Edition * Preface to the Frist Edition * 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 * Bibliography * Index
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