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Inhaltsangabe
The authors' aim here is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician. They follow a path in the tradition of Ahlfors and Bers by dedicating the book to a very precise goal: the statement and proof of the Fundamental Theorem for functions of one complex variable. They discuss the many equivalent ways of understanding the concept of analyticity, and offer a leisure exploration of interesting consequences and applications. Readers should have had undergraduate courses in advanced calculus, linear algebra, and some abstract algebra. No background in complex analysis is required.
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Über die Autorin bzw. den Autor
Rubí E. Rodríguez is a professor of mathematics at Pontificia Universidad Católica de Chile. Irwin Kra is an emeritus distinguished service professor of mathematics at SUNY, Stony Brook. Jane P. Gilman is a professor II of mathematics at Rutgers University.
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<p>This book is intended for a graduate course in complex analysis, where the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex variables, hyperbolic geometry, two- and three-manifolds, and number theory. Complex analysis has connections and applications to many other subjects in mathematics and to other sciences. Thus this material will also be of interest to computer scientists, physicists, and engineers.</p><p>The book covers most, if not all, of the material contained in Lipman Bers’s courses on first year complex analysis. In addition, topics of current interest, such as zeros of holomorphic functions and the connection between hyperbolic geometry and complex analysis, are explored.</p><p>In addition to many new exercises, this second edition introduces a variety of new and interesting topics. New features include a section on Bers's theorem on isomorphisms between rings of holomorphic functions on plane domains; necessary and sufficient conditions for the existence of a bounded analytic function on the disc with prescribed zeros; sections on subharmonic functions and Perron's principle; and a section on the ring of holomorphic functions on a plane domain. There are three new appendices: the first is a contribution by Ranjan Roy on the history of complex analysis, the second contains background material on exterior differential calculus, and the third appendix includes an alternate approach to the Cauchy theory.</p>
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Complex Analysis: In the Spirit of Lipman Bers (Graduate Texts in Mathematics, 245, Band 245) [Hardcover] Rodríguez, Rubí E.; Kra, Irwin and Gilman, Jane P.
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Complex Analysis
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Complex Analysis
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Springer New York, Springer US Nov 2012, 2012
ISBN 10: 1441973222
ISBN 13: 9781441973221
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Buch. Zustand: Neu. Neuware -This book is intended for a graduate course in complex analysis, where the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex variables, hyperbolic geometry, two- and three-manifolds, and number theory. Complex analysis has connections and applications to many other subjects in mathematics and to other sciences. Thus this material will also be of interest to computer scientists, physicists, and engineers.The book covers most, if not all, of the material contained in Lipman Bers¿s courses on first year complex analysis. In addition, topics of current interest, such as zeros of holomorphic functions and the connection between hyperbolic geometry and complex analysis, are explored.In addition to many new exercises, this second edition introduces a variety of new and interesting topics. New features include a section on Bers's theorem on isomorphisms between rings of holomorphic functions on plane domains; necessary and sufficient conditions for the existence of a bounded analytic function on the disc with prescribed zeros; sections on subharmonic functions and Perron's principle; and a section on the ring of holomorphic functions on a plane domain. There are three new appendices: the first is a contribution by Ranjan Roy on the history of complex analysis, the second contains background material on exterior differential calculus, and the third appendix includes an alternate approach to the Cauchy theory.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 324 pp. Englisch. Artikel-Nr. 9781441973221
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Complex Analysis : In the Spirit of Lipman Bers
Verlag:
Springer New York, Springer US, 2012
ISBN 10: 1441973222
ISBN 13: 9781441973221
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Hardcover
Anbieter: AHA-BUCH GmbH, Einbeck, Deutschland
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book is intended for a graduate course in complex analysis, where the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex variables, hyperbolic geometry, two- and three-manifolds, and number theory. Complex analysis has connections and applications to many other subjects in mathematics and to other sciences. Thus this material will also be of interest to computer scientists, physicists, and engineers.The book covers most, if not all, of the material contained in Lipman Bers's courses on first year complex analysis. In addition, topics of current interest, such as zeros of holomorphic functions and the connection between hyperbolic geometry and complex analysis, are explored.In addition to many new exercises, this second edition introduces a variety of new and interesting topics. New features include a section on Bers's theorem on isomorphisms between rings of holomorphic functions on plane domains; necessary and sufficient conditions for the existence of a bounded analytic function on the disc with prescribed zeros; sections on subharmonic functions and Perron's principle; and a section on the ring of holomorphic functions on a plane domain. There are three new appendices: the first is a contribution by Ranjan Roy on the history of complex analysis, the second contains background material on exterior differential calculus, and the third appendix includes an alternate approach to the Cauchy theory. Artikel-Nr. 9781441973221
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Complex Analysis: In the Spirit of Lipman Bers (Graduate Texts in Mathematics, 245)
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Complex Analysis Graduate Texts in Mathe
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Hardcover. Zustand: Brand New. 324 pages. 9.75x6.50x0.80 inches. In Stock. Artikel-Nr. x-1441973222
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Complex Analysis: In the Spirit of Lipman Bers
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ISBN 10: 1441973222
ISBN 13: 9781441973221
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Zustand: New. Organizing the basic material of complex analysis in a unique manner, the authors of this versatile book aim is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician. Series: Graduate Texts in Mathematics. Num Pages: 324 pages, biography. BIC Classification: PBKD. Category: (P) Professional & Vocational. Dimension: 242 x 163 x 23. Weight in Grams: 612. . 2012. 2nd ed. 2012. Hardcover. . . . . Books ship from the US and Ireland. Artikel-Nr. V9781441973221
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