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Functions of a Complex Variable: Theory and Technique

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By George F. Carrier, Max Krook, and Carl E. Pearson


2005 / xiv + 438 pages / Softcover / ISBN: 978-0-898715-95-8 / List Price $71.00 / SIAM Member Price $49.70 / Order Code CL49

[This volume] is a classic textbook and reference on the subject of complex variables. It established a gold standard against which all other texts in applied mathematics should be judged…. As the authors intended, the theory part is concise and quickly leads the reader from an introduction to complex numbers to useful and powerful techniques, with applications to integral representation of special functions, transform and asymptotic methods in the complex plane, and integral equations, just to name a few. It is in the application of these techniques where the authors devoted most of the efforts. These were done masterfully. This book remains a relevant and must-read book for applied mathematicians today. — K.K. Tung, Professor and Chair of Applied Mathematics, University of Washington.

[This] is a book for those looking for applications of complex variables above and beyond what is found in standard elementary texts. I know of no single source where one finds such advanced topics as asymptotics, transforms, the Wiener-Hopf method, and dual and singular integral equations treated with such insight, thoroughness, and flair or where one finds such a rich, non-trivial collection of examples and exercises. Here is the power of complex variables as a practical tool on full display. — Jim Simmonds, Emeritus Professor of Civil Engineering, University of Virginia.

Functions of a complex variable are used to solve applications in various branches of mathematics, science, and engineering. Functions of a Complex Variable: Theory and Technique is a book in a special category of influential classics because it is based on the authorsÕ extensive experience in modeling complicated situations and providing analytic solutions. The book makes available to readers a comprehensive range of these analytical techniques based upon complex variable theory.

Proficiency in these techniques requires practice. The authors provide many exercises, incorporating them into the body of the text. By completing a substantial number of these exercises, the reader will more fully benefit from this book.

Based on graduate courses in applied mathematics, Functions of a Complex Variable: Theory and Technique is intended for applied mathematicians, scientists, engineers, and senior or graduate-level students who have advanced knowledge in calculus and are interested in such subjects as complex variable theory, function theory, mathematical methods, advanced engineering mathematics, and mathematical physics.

Preface; Erratum; Chapter 1: Complex Numbers And Their Elementary Properties; Chapter 2: Analytic Functions; Chapter 3: Contour Integration; Chapter 4: Conformal Mapping; Chapter 5: Special Functions; Chapter 6: Asymptotic Methods; Chapter 7: Transform Methods; Chapter 8: Special Techniques; Index.

ISBN: 9780898715958

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