Synopses & Reviews
This textbook is an introduction to the classical theory of functions of a complex variable. The author's aim is to explain the basic theory in an easy to understand and careful way. He emphasizes geometrical considerations, and, to avoid topological difficulties associated with complex analysis, begins by deriving Cauchy's integral formula in a topologically simple case and then deduces the basic properties of continuous and differentiable functions. The remainder of the book deals with conformal mappings, analytic continuation, Riemann's mapping theorem, Riemann surfaces and analytic functions on a Riemann surface. The book is profusely illustrated and includes many examples. Problems are collected together at the end of the book. It should be an ideal text for either a first course in complex analysis or more advanced study.
Synopsis
All three volumes of Kodaira's classic text on complex analysis are collected together in English for the first time. The author develops the classical theory of functions of a complex variable in a clear and logical manner. Starting from the basics, students are led on to the study of conformal mappings, Riemann's mapping theorem and analytic functions on a Riemann surface. Caucy's integral formula is first proved in a topologically simple case from which the author deduces the basic properties of holomorphic functions. In general, the approach taken here emphasises geometrical aspects of the theory in order to avoid some of the topological pitfalls associated with this subject. Profusely illustrated and with many problems and examples, this book should be an ideal text for a course in complex analysis.
Synopsis
'Written by a master of the subject, this profusely illustrated textbook, which includes many examples and exercises, will be appreciated by students and experts. The author develops the classical theory of complex functions, emphasising geometrical ideas in order to avoid some of the topological pitfalls associated with this subject.\n
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Synopsis
'Introduction to classical complex analysis; profusely illustrated; written by a master of the subject.'
Table of Contents
1. Holomorphic functions; 2. Cauchyâs theorem; 3. Conformal mappings; 4. Analytic continuation; 5. Riemannâs mapping theorem; 6. Riemann surfaces; 7. The structure of Riemann surfaces; 8. Analytic functions on a closed Riemann surface.