Kunihiko Kodaira: Complex Analysis | Buch

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Cover: 9780521809375 | Complex Analysis | Kunihiko Kodaira | Buch | Englisch | 2007

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Kunihiko Kodaira (1915-97) worked in many areas including harmonic integrals, algebraic geometry and the classification of compact complex analytic surfaces. He held faculty positions at many universities including the University of Tokyo, Harvard University, Massachusetts, Stanford University, California, and The Johns Hopkins University, and the Institute for Advanced Study in Princeton. He was awarded a Fields medal in 1954 and a Wolf Prize in 1984.

Zusammenfassung

Written by a master of the subject, this profusely illustrated textbook, which includes many examples and exercises, will be welcomed by students and appreciated by experts. The author develops the classical theory of functions of a complex variable, emphasising geometrical ideas in order to avoid some of the topological pitfalls associated with this subject. Readers are led from the basics to the study of conformal mappings, Riemann’s mapping theorem, analytic functions on a Riemann surface, and ultimately the Riemann-Roch and Abel theorems.

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2007
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	418
ISBN-13:	9780521809375
ISBN-10:	0521809371
Sprache:	Englisch
Ausstattung / Beilage:	HC gerader Rücken kaschiert
Einband:	Gebunden
Autor:	Kodaira, Kunihiko
Hersteller:	Cambridge University Press
Maße:	235 x 157 x 29 mm
Von/Mit:	Kunihiko Kodaira
Erscheinungsdatum:	23.08.2007
Gewicht:	0,828 kg

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