Complex Analysis in One Variable - Rilegato

Narasimhan, Raghavan; Nievergelt, Yves

Rilegato

ISBN 10: 0817641645 ISBN 13: 9780817641641

Casa editrice: Springer Basel AG, 2000

Riassunto

This volume presents complex analysis in one variable in the context of modern mathematics, with connections to several complex variables, de Rham theory, real analysis, and other branches of mathematics. Covering spaces are used in dealing with Cauchy's theorem, real variable methods are illustrated in the Loman-Menchoff theorem and in the corona theorem, and the algebraic structure of the ring of holomorphic functions on a domain in C is studied. The book illustrates mathematical ideas and tools. Cohomological methods are introduced, in connection with the existence of primatives and in the study of meromorphic funtion as on a compact Riemann surface. This second edition has exercises, problems and examples for students, so they can consolidate their command of complex analysis and its relations to other branches of mathematics.

Su questo libro

Dalla quarta di copertina

This book presents complex analysis in one variable in the context of modern mathematics, with clear connections to several complex variables, de Rham theory, real analysis, and other branches of mathematics. Thus, covering spaces are used explicitly in dealing with Cauchy's theorem, real variable methods are illustrated in the Loman-Menchoff theorem and in the corona theorem, and the algebraic structure of the ring of holomorphic functions is studied.

Using the unique position of complex analysis, a field drawing on many disciplines, the book also illustrates powerful mathematical ideas and tools, and requires minimal background material. Cohomological methods are introduced, both in connection with the existence of primitives and in the study of meromorphic functionas on a compact Riemann surface. The proof of Picard's theorem given here illustrates the strong restrictions on holomorphic mappings imposed by curvature conditions.

New to this second edition, a collection of over 100 pages worth of exercises, problems, and examples gives students an opportunity to consolidate their command of complex analysis and its relations to other branches of mathematics, including advanced calculus, topology, and real applications.

Dettagli dell'edizione

• Editore: Springer Basel AG
• Data di pubblicazione: 2000
• Lingua: Inglese
• ISBN 10: 0817641645
• ISBN 13: 9780817641641
• Rilegatura: Copertina rigida
• Numero edizione: 2
• Numero di pagine: 404
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