An introduction to complex function theory
著者
書誌事項
An introduction to complex function theory
（Undergraduate texts in mathematics）
Springer-Verlag, c1991
- : us
- : gw
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注記
Includes index
内容説明・目次
- 巻冊次
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: us ISBN 9780387974279
内容説明
This book provides a rigorous yet elementary introduction to the theory of analytic functions of a single complex variable. While presupposing in its readership a degree of mathematical maturity, it insists on no formal prerequisites beyond a sound knowledge of calculus. Starting from basic definitions, the text slowly and carefully develops the ideas of complex analysis to the point where such landmarks of the subject as Cauchy's theorem, the Riemann mapping theorem, and the theorem of Mittag-Leffler can be treated without sidestepping any issues of rigor. The emphasis throughout is a geometric one, most pronounced in the extensive chapter dealing with conformal mapping, which amounts essentially to a "short course" in that important area of complex function theory. Each chapter concludes with a wide selection of exercises, ranging from straightforward computations to problems of a more conceptual and thought-provoking nature.
目次
Contents: The Complex Number System.- The Rudiments of Plane Topology.- Analytic Functions.- Complex Integration.- Cauchy's Theorem and its Consequences.- Harmonic Functions.- Sequences and Series of Analytic Functions.- Isolated Singularities of Analytic Functions.- Conformal Mapping.- Constructing Analytic Functions.- Appendix A: Background on Fields.- Appendix B: Winding Numbers Revisited.- Index.
- 巻冊次
-
: gw ISBN 9783540974277
内容説明
This book provides an introduction to the theory of analytic functions of a single complex variable. While presupposing in its readership a degree of mathematical maturity, it insists on no formal prerequisites beyond a sound knowledge of calculus. Starting from basic definitions, the text develops the ideas of complex analysis to the point where such landmarks of the subject as Cauchy's theorem of Mittag-Leffler can be treated without side-stepping any issues of rigor. The emphasis throughout is a geometric one, most pronounced in the extensive chapter dealing with conformal mapping, which amounts essentially to a "short course" in that important area of complex function theory. Each chapter concludes with a selection of exercises, ranging from straightforward computations to problems of a more conceptual and thought-provoking nature.
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