An Introduction to Complex Function Theory - Rilegato

Palka, Bruce P.

Rilegato

ISBN 10: 038797427X ISBN 13: 9780387974279

Casa editrice: Springer Verlag, 1990

Riassunto

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.

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Contenuti

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.

Product Description

Book by Palka Bruce P

Dettagli dell?edizione

• Editore: Springer Verlag
• Data di pubblicazione: 1990
• ISBN 10: 038797427X
• ISBN 13: 9780387974279
• Rilegatura: Copertina rigida
• Lingua: Inglese
• Numero edizione: 1
• Numero di pagine: 577