Complex Analysis in One Variable

Raghavan Narasimhan

ISBN 10: 0817641645 / ISBN 13: 9780817641641

Editore: Birkhäuser, Birkhäuser, 2000

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Druck auf Anfrage Neuware - Printed after ordering - The original edition of this book has been out of print for some years. The appear ance of the present second edition owes much to the initiative of Yves Nievergelt at Eastern Washington University, and the support of Ann Kostant, Mathematics Editor at Birkhauser. Since the book was first published, several people have remarked on the absence of exercises and expressed the opinion that the book would have been more useful had exercises been included. In 1997, Yves Nievergelt informed me that, for a decade, he had regularly taught a course at Eastern Washington based on the book, and that he had systematically compiled exercises for his course. He kindly put his work at my disposal. Thus, the present edition appears in two parts. The first is essentially just a reprint of the original edition. I have corrected the misprints of which I have become aware (including those pointed out to me by others), and have made a small number of other minor changes.

Codice articolo 9780817641641

Dati bibliografici

• Titolo: Complex Analysis in One Variable
• Editore: Birkhäuser, Birkhäuser
• Data di pubblicazione: 2000
• Lingua: Inglese
• ISBN 10: 0817641645
• ISBN 13: 9780817641641
• Rilegatura: Buch
• Edizione: seconda edizione
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 27 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 27 millimetri di profondità
• Peso: 770 grammi

Descrizione articolo

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.

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.