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Complex Analysis

  • Textbook
  • © 2001

Overview

Authors:
  1. Theodore W. Gamelin

    1. Department of Mathematics, UCLA, Los Angeles, USA

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

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xviii
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  2. First Part

    1. The Complex Plane and Elementary Functions

      • Theodore W. Gamelin
      Pages 1-32

    2. Analytic Functions

      • Theodore W. Gamelin
      Pages 33-69

    3. Line Integrals and Harmonic Functions

      • Theodore W. Gamelin
      Pages 70-101

    4. Complex Integration and Analyticity

      • Theodore W. Gamelin
      Pages 102-129

    5. Power Series

      • Theodore W. Gamelin
      Pages 130-164

    6. Laurent Series and Isolated Singularities

      • Theodore W. Gamelin
      Pages 165-194

    7. The Residue Calculus

      • Theodore W. Gamelin
      Pages 195-223

  3. Second Part

    1. The Logarithmic Integral

      • Theodore W. Gamelin
      Pages 224-259

    2. The Schwarz Lemma and Hyperbolic Geometry

      • Theodore W. Gamelin
      Pages 260-273

    3. Harmonic Functions and the Reflection Principle

      • Theodore W. Gamelin
      Pages 274-288

    4. Conformal Mapping

      • Theodore W. Gamelin
      Pages 289-314

  4. Third Part

    1. Compact Families of Meromorphic Functions

      • Theodore W. Gamelin
      Pages 315-341

    2. Approximation Theorems

      • Theodore W. Gamelin
      Pages 342-360

    3. Some Special Functions

      • Theodore W. Gamelin
      Pages 361-389

    4. The Dirichlet Problem

      • Theodore W. Gamelin
      Pages 390-417

    5. Riemann Surfaces

      • Theodore W. Gamelin
      Pages 418-446

  5. Back Matter

    Pages 447-480
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, UCLA, Los Angeles, USA

    Theodore W. Gamelin

About the author



Bibliographic Information

  • Book Title: Complex Analysis

  • Authors: Theodore W. Gamelin

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-0-387-21607-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2001

  • Hardcover ISBN: 978-0-387-95093-8Published: 18 May 2001

  • Softcover ISBN: 978-0-387-95069-3Published: 18 May 2001

  • eBook ISBN: 978-0-387-21607-2Published: 01 November 2013

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XVIII, 480

  • Topics: Analysis

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