Complex analysis : in the spirit of Lipman Bers
 Author/Creator
 Gilman, Jane, 1945
 Language
 English.
 Imprint
 New York : Springer, c2007.
 Physical description
 xiii, 220 p. : ill. ; 25 cm.
 Series
 Graduate texts in mathematics 245.
Access
Available online
 www.springerlink.com SpringerLink
 www.myilibrary.com MyiLibrary
 site.ebrary.com ebrary
 dx.doi.org SpringerLink

Stacks

Unknown
QA331.7 .G55 2007

Unknown
QA331.7 .G55 2007
Related
Contributors
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Preface. Standard Notation and Commonly used Symbols. The Fundamental Theorem in Complex Function Theory. Foundations. Power Series. The Cauchy TheoryA Fundamental Theorem. The Cauchy TheoryKey Consequences. Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions. Sequences and Series of Holomorphic Functions. Conformal Equivalence. Harmonic Functions. Zeros of Holomorphic Functions. Bibliographical Notes. Bibliography. Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 This book organizes the basic material of complex analysis in a unique manner. The first part of the book is a study of the many equivalent ways of understanding the concept of analyticity. The many ways of formulating the concept of an analytic function are summarized in what we term the Fundamental Theorem for functions of a complex variable. The organization of these conditions into a single unifying theorem is a hallmark of Bers' mathematical style with an emphasis on clarity and elegance. Here, it provides a conceptual framework for results that are highly technical and often computational. The framework comes from an insight that, once articulated, will drive the subsequent mathematics and lead to new results.In the second part, the text proceeds to a leisurely exploration of interesting ramifications of the main concepts. The book covers most, if not all, of the material contained in Bers' 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. The organization of material in this book allows for an elegant and economical treatment of many important topics.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2007
 Responsibility
 Jane P. Gilman, Irwin Kra, Rubi E. Rodriguez.
 Series
 Graduate texts in mathematics ; 245
 ISBN
 9780387747149
 0387747141
 038774715X
 9780387747156