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  • Textbook
  • © 1993

Complex Analysis

Authors:

  1. Serge Lang

    1. Department of Mathematics, Yale University, New Haven, USA

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

Sections

Table of contents (16 chapters)

  1. Front Matter

    Pages i-xiv
    PDF

  2. Basic Theory

    1. Front Matter

      Pages 1-1
      PDF

    2. Complex Numbers and Functions

      • Serge Lang
      Pages 3-36
      PDF

    3. Power Series

      • Serge Lang
      Pages 37-85
      PDF

    4. Cauchy’s Theorem, First Part

      • Serge Lang
      Pages 86-132
      PDF
    5. PDF
    6. PDF

    7. Calculus of Residues

      • Serge Lang
      Pages 173-207
      PDF

    8. Conformal Mappings

      • Serge Lang
      Pages 208-236
      PDF

    9. Harmonic Functions

      • Serge Lang
      Pages 237-275
      PDF

  3. Geometric Function Theory

    1. Front Matter

      Pages 277-277
      PDF

    2. Schwarz Reflection

      • Serge Lang
      Pages 279-290
      PDF

    3. The Riemann Mapping Theorem

      • Serge Lang
      Pages 291-306
      PDF

    4. Analytic Continuation Along Curves

      • Serge Lang
      Pages 307-320
      PDF

  4. Various Analytic Topics

    1. Front Matter

      Pages 321-321
      PDF
    2. PDF

    3. Entire and Meromorphic Functions

      • Serge Lang
      Pages 356-373
      PDF

    4. Elliptic Functions

      • Serge Lang
      Pages 374-390
      PDF

    5. The Gamma and Zeta Functions

      • Serge Lang
      Pages 391-421
      PDF

    6. The Prime Number Theorem

      • Serge Lang
      Pages 422-434
      PDF
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About this book

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 lookthrough 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.
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Keywords

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Authors and Affiliations

  • Department of Mathematics, Yale University, New Haven, USA

    Serge Lang

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Bibliographic Information

  • Book Title: Complex Analysis

  • Authors: Serge Lang

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-59273-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 1993

  • eBook ISBN: 978-3-642-59273-7Published: 14 March 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 3

  • Number of Pages: XIV, 458

  • Topics: Functions of a Complex Variable, Analysis

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