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Functions of One Complex Variable I

  • Textbook
  • © 1978

Overview

Authors:
  1. John B. Conway

    1. Mathematics Department, University of Tennessee, Knoxville, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 11)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xiii
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  2. The Complex Number System

    • John B. Conway
    Pages 1-10

  3. Metric Spaces and the Topology of ℂ

    • John B. Conway
    Pages 11-29

  4. Elementary Properties and Examples of Analytic Functions

    • John B. Conway
    Pages 30-57

  5. Complex Integration

    • John B. Conway
    Pages 58-102

  6. Singularities

    • John B. Conway
    Pages 103-127

  7. The Maximum Modulus Theorem

    • John B. Conway
    Pages 128-141

  8. Compactness and Convergence in the Space of Analytic Functions

    • John B. Conway
    Pages 142-194

  9. Runge’s Theorem

    • John B. Conway
    Pages 195-209

  10. Analytic Continuation and Riemann Surfaces

    • John B. Conway
    Pages 210-251

  11. Harmonic Functions

    • John B. Conway
    Pages 252-278

  12. Entire Functions

    • John B. Conway
    Pages 279-291

  13. The Range of an Analytic Function

    • John B. Conway
    Pages 292-301

  14. Back Matter

    Pages 303-321
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Keywords

About this book

This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - 8 arguments. The actual pre­ requisites for reading this book are quite minimal; not much more than a stiff course in basic calculus and a few facts about partial derivatives. The topics from advanced calculus that are used (e.g., Leibniz's rule for differ­ entiating under the integral sign) are proved in detail. Complex Variables is a subject which has something for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics (e.g., homotopy theory, manifolds). This view of Complex Analysis as "An Introduction to Mathe­ matics" has influenced the writing and selection of subject matter for this book. The other guiding principle followed is that all definitions, theorems, etc.

Reviews

"This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis. The approach to each topic appears to be carefully thought out both as to mathematical treatment and pedagogical presentation, and the end result is a very satisfactory book for classroom use or self-study."   --MathSciNet

Authors and Affiliations

  • Mathematics Department, University of Tennessee, Knoxville, USA

    John B. Conway

Bibliographic Information

  • Book Title: Functions of One Complex Variable I

  • Authors: John B. Conway

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-6313-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media, Inc. 1978

  • Hardcover ISBN: 978-0-387-90328-6Published: 24 August 1978

  • Softcover ISBN: 978-0-387-94234-6Published: 14 January 1994

  • eBook ISBN: 978-1-4612-6313-5Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: XIV, 322

  • Topics: Calculus of Variations and Optimal Control; Optimization, Analysis

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