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Complex Analysis

  • Serge Lang

Part of the Graduate Texts in Mathematics book series (GTM, volume 103)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Basic Theory

    1. Front Matter
      Pages 1-1
    2. Serge Lang
      Pages 3-36
    3. Serge Lang
      Pages 37-85
    4. Serge Lang
      Pages 86-132
    5. Serge Lang
      Pages 133-154
    6. Serge Lang
      Pages 173-207
    7. Serge Lang
      Pages 208-240
    8. Serge Lang
      Pages 241-290
  3. Geometric Function Theory

    1. Front Matter
      Pages 291-291
    2. Serge Lang
      Pages 293-305
    3. Serge Lang
      Pages 306-321
    4. Serge Lang
      Pages 322-336
  4. Various Analytic Topics

    1. Front Matter
      Pages 337-337
    2. Serge Lang
      Pages 372-390
    3. Serge Lang
      Pages 391-407
    4. Serge Lang
      Pages 408-439
    5. Serge Lang
      Pages 440-452
  5. Back Matter
    Pages 453-489

About this book

Introduction

The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. The first half, more or less, can be used for a one-semester course addressed to undergraduates. The second half can be used for a second semester, at either level. Somewhat more material has been included than can be covered at leisure in one or two terms, to give opportunities for the instructor to exercise individual taste, and to lead the course in whatever directions strikes the instructor's fancy at the time as well as extra read­ ing material for students on their own. A large number of routine exer­ cises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recommend to anyone to look through them. More recent texts have emphasized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex analysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues.

Keywords

Cauchy's integral formula Complex analysis Jensen's formula Meromorphic function calculus differential equation gamma function maximum

Authors and affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3083-8
  • Copyright Information Springer-Verlag New York 1999
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3135-1
  • Online ISBN 978-1-4757-3083-8
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site