Integral Transforms and Their Applications / Edition 3

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Overview

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.

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Editorial Reviews

From the Publisher
From the reviews of the third edition:

B. Davies

Integral Transforms and their Applications

"Extremely well-written and a joy to read . . . Whether the reader is seeking a useful text for a graduate course or a valuable reference on integral transforms, I would highly recommend Brian Davies' book."

—THE AUSTRALIAN MATHEMATICAL SOCIETY

"A testament to the quality and usefulness of this monograph is that a third edition has now appeared. … In addition to the material previously included, there have been significant extensions in some of the topics … . The writing style and the overall structure of the presentation have been modified … and, as a consequence, the current edition is extremely well-written and a joy to read. … I would highly recommend Brian Davies’ book." (W.P. Wood, The Australian Mathematical Society Gazette, Vol. 30 (1), 2003)

"In its present third edition this well known work has undergone considerable reconstruction or augmentation … . Due to the general character of this volume, the many examples worked out or provided, this volume will be of use to readers intending to make actual use of integral transforms." (H. Muthsam, Monatshefte für Mathematik, Vol. 139 (2), 2003)

"Nevertheless that the new edition has less pages, it is now … about 20% longer which can find a seemingly explanation by its more compact and now modern phoomposed copy preparation on the basis of a LaTeX file. … As conclusion … the new edition gained considerably … it can be highly recommended to a broad readership." (J. Synnatzschke, ZAA, Vol. 21 (3), 2002)

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Product Details

  • ISBN-13: 9781441929501
  • Publisher: Springer New York
  • Publication date: 12/6/2010
  • Series: Texts in Applied Mathematics Series , #41
  • Edition description: Softcover reprint of hardcover 3rd ed. 2002
  • Edition number: 3
  • Pages: 367
  • Product dimensions: 0.80 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

Preface 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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