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Applied Integral Transforms
M. Ya. Antimirov and A. A. Kolyshkin, Riga Technical University, Latvia, and Rémi Vaillancourt, University of Ottawa, ON, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques.
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CRM Monograph Series
1993; 265 pp; softcover
Volume: 2
ISBN-10: 0-8218-4314-1
ISBN-13: 978-0-8218-4314-7
List Price: US$33 Member Price: US$26.40
Order Code: CRMM/2.S

This book does what few books on integral transforms do: it constructs the kernels of the integral transforms by solving the generalized Sturm-Liouville problems associated with the partial differential equations at hand. In the first part of the book, the authors construct the kernels and then use them to solve elementary problems of mathematical physics. This section, which proceeds mainly by examples and includes exercises, requires little mathematical background and provides an introduction to the subject of integral transforms.

In the second part of the book, the method of integral transforms is used to solve modern applied problems in convective stability, temperature fields in oil strata, and eddy current testing. The choice of topics reflects the authors' research experience and involvement in industrial applications. The first part of the book is accessible to undergraduates, while the second part is aimed more at graduate students and researchers. Because of the applications it discusses, the book will interest engineers (especially petroleum engineers) and physicists.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Undergraduates, graduate students and research mathematicians interested in applications of integral transforms.

Reviews

"Well written and may be recommended to all who are interested in applications of integral transforms."

-- Zentralblatt MATH

Part 1: General Methods
• Introduction
• Basic integral transforms
• Kernels of integral transforms
• Hyperbolic equations
• Parabolic equations
• The three-dimensional wave equation
Part 2: Applications
• Convective stability problems
• Temperature fields in oil strata
• Eddy-current testing problems