Complex Variables (2nd ed.)

Introduction and Applications

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by Mark Ablowitz and A. S. Fokas

Cambridge University Press

Due/Published May 2003, 650 pages, paper

ISBN 0521534291

Complex variables offer very efficient methods for attacking many difficult problems, and it is the aim of this book to offer a thorough review of these methods and their applications. Part I is an introduction to the subject, including residue calculus and transform methods. Part II advances to conformal mappings, and the study of Riemann-Hilbert problems. An extensive array of examples and exercises are included. This new edition has been improved throughout and is ideal for use in introductory undergraduate and graduate level courses in complex variables.

Contents

Part I: 1. Complex numbers and elementary functions; 2. Analytic functions and integration; 3. Sequences, series and singularities of complex functions; 4. Residue calculus and applications of contour integration;

Part II: 5. Conformal mapping and applications; 6. Asymptotic evaluation of integrals; 7. Riemann-Hilbert problems;

Index.