Complex Analysis

Rubí E. Rodríguez

ISBN 10: 1489999086 / ISBN 13: 9781489999085

Published by Springer New York, Springer US Dez 2014, 2014

About this Item

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.

Seller Inventory # 9781489999085

Bibliographic Details

• Title: Complex Analysis
• Publisher: Springer New York, Springer US Dez 2014
• Publication Date: 2014
• Language: English
• ISBN 10: 1489999086
• ISBN 13: 9781489999085
• Binding: Taschenbuch
• Edition: 2nd Edition
• Condition: Neu
• Dimensions: 235W x 155H x 18D millimeters 235 millimeters width by 155 millimeters height by 18 millimeters depth
• Weight: 493 grams

About this title

Synopsis

Here is a work that breaks with tradition and organizes the basic material of complex analysis in a unique manner. The authors’ aim 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. The first part of the book is a study of the many equivalent ways of understanding the concept of analyticity, and move on to offer a leisurely exploration of interesting consequences and applications. The book covers most, if not all, of the material contained in 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. Readers should have had undergraduate courses in advanced calculus, linear algebra, and some abstract algebra.

About the Author

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.