Integral Transforms and Their Applications

ISBN-13: 9781441929501 / Angielski / Miękka / 2010 / 370 str.

Brian Davies

Opis

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.

Recenzje

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 photocomposed 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)

Spis treści

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