Ebook: Integral Transforms and Their Applications

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in re­ search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numeri­ cal and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe­ matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Pasadena, California J.E. Marsden Providence, Rhode Island L. Sirovich Houston, Texas M. Golubitsky College Park, Maryland S.S. Antman Preface to the Third Edition It is more than 25 years since I finished the manuscript of the first edition of this volume, and it is indeed gratifying that the book has been in use over such a long period and that the publishers have requested a third edition.

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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.