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Complex Analysis

In the Spirit of Lipman Bers

  • Textbook
  • © 2007

Overview

Authors:
  1. Jane P. Gilman

    1. Department of Mathematics and Computer Science, Rutgers University, Newark, USA

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  2. Irwin Kra

    1. Math for America, New York, USA
      Department of Mathematics, State University of New York at Stony Brook, Stony Brook, USA

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    You can also search for this author in PubMed   Google Scholar

  3. Rubí E. Rodríguez

    1. Pontificia Universidad Católica de Chile, Santiago, Chile

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  • Covers vast majority of the material needed for a beginning graduate level course on complex analysis
  • Elegant and economical treatment of complex analysis
  • Provides many ways of understanding the concept of analyticity
  • Material of interest to computer scientists, physicists and engineers
  • Includes supplementary material: sn.pub/extras

Part of the book series: Graduate Texts in Mathematics (GTM, volume 245)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XIII
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  2. The Fundamental Theorem in Complex Function Theory

    • Jane P. Gilman, Irwin Kra, Rubí E. Rodríguez
    Pages 1-5

  3. Foundations

    • Jane P. Gilman, Irwin Kra, Rubí E. Rodríguez
    Pages 7-21

  4. Power Series

    • Jane P. Gilman, Irwin Kra, Rubí E. Rodríguez
    Pages 23-57

  5. The Cauchy Theory–A Fundamental Theorem

    • Jane P. Gilman, Irwin Kra, Rubí E. Rodríguez
    Pages 59-82

  6. The Cauchy Theory–Key Consequences

    • Jane P. Gilman, Irwin Kra, Rubí E. Rodríguez
    Pages 83-99

  7. Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions

    • Jane P. Gilman, Irwin Kra, Rubí E. Rodríguez
    Pages 101-121

  8. Sequences and Series of Holomorphic Functions

    • Jane P. Gilman, Irwin Kra, Rubí E. Rodríguez
    Pages 123-146

  9. Conformal Equivalence

    • Jane P. Gilman, Irwin Kra, Rubí E. Rodríguez
    Pages 147-172

  10. Harmonic Functions

    • Jane P. Gilman, Irwin Kra, Rubí E. Rodríguez
    Pages 173-190

  11. Zeros of Holomorphic Functions

    • Jane P. Gilman, Irwin Kra, Rubí E. Rodríguez
    Pages 191-211

  12. Back Matter

    Pages 213-223
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Keywords

About this book

This bookpresents fundamental material that should be part of the education of every practicing mathematician. This material will also be of interest to computer scientists, physicists, and engineers. Complex analysis is also known as function theory. In this text we address the theory of complex-valued functions of a single complex variable. This is a prerequisite for the study of many current and rapidlydevelopingareasofmathematics, includingthetheoryofseveral andin?nitely many complex variables, thetheoryofgroups, hyperbolic geometry and three-manifolds, and number theory. Complex analysis has connections and applications to many other many other subjects in mathematics, and also to other sciences as an area where the classic and the modern techniques meet and bene?t from each other. We will try to illustrate this in the applications we give. Because function theory has been used by generations of practicing mathematicians working in a number of di?erent ?elds, the basic - sults have been developed and redeveloped from a number of di?erent perspectives. We are not wedded to any one viewpoint. Rather we will try to exploit the richness of the subject and explain and interpret standard de?nitions and results using the most convenient tools from analysis, geometry, and algebra.

Reviews

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 good exercises … . It is nominally a graduate text (it is in Springer’s series of Graduate Texts in Mathematics) … . The book covers all the usual topics for a first course and includes a lot of advanced topics … ." (Allen Stenger, MathDL, February, 2008)

"This book is based on the original courses of Complex Analysis that was delivered by the well-known American specialist and lecturer in Analysis, Professor Lipman Bers. … the book is written in a clear and easily readable manner. … this book is useful for all specialists and lecturers in Complex Analysis … and also all specialists who deal with applications of Complex Analysis. I also recommend this book to beginners who want to study Complex Analysis … ." (Peter Zabreiko, Zentralblatt MATH, Vol. 1139 (17), 2008)

“An introduction to complex analysis based on original lectures by Lipman Bers … . the whole text is clearly suitable as a first course in complex analysis. … In addition, it contains many exercises and a brief guide to the literature.” (G. Teschl, Monatshefte für Mathematik, Vol. 156 (4), April, 2009)

Authors and Affiliations

  • Department of Mathematics and Computer Science, Rutgers University, Newark, USA

    Jane P. Gilman

  • Math for America, New York, USA

    Irwin Kra

  • Department of Mathematics, State University of New York at Stony Brook, Stony Brook, USA

    Irwin Kra

  • Pontificia Universidad Católica de Chile, Santiago, Chile

    Rubí E. Rodríguez

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