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Complex analysis : in the spirit of Lipman Bers

Author: Jane Gilman; Lipman Bers; Irwin Kra; Rubí E Rodríguez
Publisher: New York, NY : Springer, ©2007.
Series: Graduate texts in mathematics, 245.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
"This book is intended for a graduate course on complex analysis, also known as function theory. 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 current and rapidly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Gilman, Jane, 1945-
Complex analysis.
New York, NY : Springer, c2007
(DLC) 2007940048
(OCoLC)173498966
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jane Gilman; Lipman Bers; Irwin Kra; Rubí E Rodríguez
ISBN: 9780387747156 038774715X 0387747141 9780387747149
OCLC Number: 209985106
Description: 1 online resource (xiii, 220 p.) : ill.
Contents: Preface --
Standard Notation and Commonly used Symbols --
The Fundamental Theorem in Complex Function Theory --
Foundations --
Power Series --
The Cauchy Theory-A Fundamental Theorem --
The Cauchy Theory-Key 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
Series Title: Graduate texts in mathematics, 245.
Responsibility: Jane P. Gilman, Irwin Kra, Rubí E. Rodríguez.

Abstract:

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  Read more...

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From the reviews: "This is a fairly conventional text for a first course in complex analysis. It is an interesting mix of the concrete and the abstract, and of the formulaic and the geometric. It has Read more...

 
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schema:reviewBody""This book is intended for a graduate course on complex analysis, also known as function theory. 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 current and rapidly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and three-manifolds, and number theory. Complex analysis has connections and applications to many other subjects in mathematics and to other sciences. It is an area where the classic and the modern techniques meet and benefit from each other. This material should be part of the education of every practicing mathematician, and it will also be of interest to computer scientists, physicists, and engineers." "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."--Jacket."
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