Complex analysis
著者
書誌事項
Complex analysis
（Cambridge studies in advanced mathematics, 107）
Cambridge University Press, c2007
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注記
Includes bibliographical references and index
Originally published in Japanese as Complex analysis, vols. I, II and III, by Iwanami Shoten, Publishers, Tokyo, 1977 and 1978
Volumes I and II published in English in 1984 as Introduction to complex analysis. Combined three-volume edition first published in English 2007
内容説明・目次
内容説明
Written by a master of the subject, this text will be appreciated by students and experts for the way it develops the classical theory of functions of a complex variable in a clear and straightforward manner. 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. Thus, Cauchy's integral formula is first proved in a topologically simple case from which the author deduces the basic properties of holomorphic functions. Starting from the basics, students are led on to the study of conformal mappings, Riemann's mapping theorem, analytic functions on a Riemann surface, and ultimately the Riemann-Roch and Abel theorems. Profusely illustrated, and with plenty of examples, and problems (solutions to many of which are included), this book should be a stimulating text for advanced courses in complex analysis.
目次
- 1. Holomorphic functions
- 2. Cauchy's theorem
- 3. Conformal mappings
- 4. Analytic continuation
- 5. Riemann's mapping theorem
- 6. Riemann surfaces
- 7. The structure of Riemann surfaces
- 8. Analytic functions on a closed Riemann surface.
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