Complex Analysis

  • Theodore W. Gamelin

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. First Part

    1. Theodore W. Gamelin
      Pages 1-32
    2. Theodore W. Gamelin
      Pages 33-69
    3. Theodore W. Gamelin
      Pages 70-101
    4. Theodore W. Gamelin
      Pages 102-129
    5. Theodore W. Gamelin
      Pages 130-164
    6. Theodore W. Gamelin
      Pages 165-194
    7. Theodore W. Gamelin
      Pages 195-223
  3. Second Part

    1. Theodore W. Gamelin
      Pages 224-259
    2. Theodore W. Gamelin
      Pages 260-273
    3. Theodore W. Gamelin
      Pages 274-288
    4. Theodore W. Gamelin
      Pages 289-314
  4. Third Part

    1. Theodore W. Gamelin
      Pages 315-341
    2. Theodore W. Gamelin
      Pages 342-360
    3. Theodore W. Gamelin
      Pages 361-389
    4. Theodore W. Gamelin
      Pages 390-417
    5. Theodore W. Gamelin
      Pages 418-446
  5. Back Matter
    Pages 447-480

About this book

Introduction

The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. It conists of sixteen chapters. The first eleven chapters are aimed at an Upper Division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied in the book include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces. The three geometries, spherical, euclidean, and hyperbolic, are stressed. Exercises range from the very simple to the quite challenging, in all chapters. The book is based on lectures given over the years by the author at several places, including UCLA, Brown University, the universities at La Plata and Buenos Aires, Argentina; and the Universidad Autonomo de Valencia, Spain.

Keywords

analytic function Argument principle Complex analysis complex number conformal map functional analysis integral integration logarithm Meromorphic function residue Riemann surface Schwarz lemma special function

Authors and affiliations

  • Theodore W. Gamelin
    • 1
  1. 1.Department of MathematicsUCLALos AngelesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-21607-2
  • Copyright Information Springer-Verlag New York 2001
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-95069-3
  • Online ISBN 978-0-387-21607-2
  • Series Print ISSN 0172-6056
  • About this book