Skip to main content
  • Textbook
  • © 1991

Theory of Complex Functions

Authors:

Part of the book series: Graduate Texts in Mathematics (GTM, volume 122)

Part of the book sub series: Readings in Mathematics (READMATH)

Buy it now

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

This is a preview of subscription content, log in via an institution to check for access.

Table of contents (16 chapters)

  1. Front Matter

    Pages i-xix
  2. Historical Introduction

    1. Historical Introduction

      • Reinhold Remmert
      Pages 1-7
  3. Elements of Function Theory

    1. Complex Numbers and Continuous Functions

      • Reinhold Remmert
      Pages 9-44
    2. Complex-Differential Calculus

      • Reinhold Remmert
      Pages 45-70
    3. Modes of Convergence in Function Theory

      • Reinhold Remmert
      Pages 91-107
    4. Power Series

      • Reinhold Remmert
      Pages 109-132
    5. Elementary Transcendental Functions

      • Reinhold Remmert
      Pages 133-165
  4. The Cauchy Theory

    1. Complex Integral Calculus

      • Reinhold Remmert
      Pages 167-189
  5. Cauchy-Weierstrass-Rieman Function Theory

    1. Fundamental Theorems about Holomorphic Functions

      • Reinhold Remmert
      Pages 227-263
    2. Miscellany

      • Reinhold Remmert
      Pages 265-301
    3. Isolated Singularities. Meromorphic Functions

      • Reinhold Remmert
      Pages 303-320
    4. Convergent Series of Meromorphic Functions

      • Reinhold Remmert
      Pages 321-341
    5. Laurent Series and Fourier Series

      • Reinhold Remmert
      Pages 343-375
    6. The Residue Calculus

      • Reinhold Remmert
      Pages 377-393
    7. Definite Integrals and the Residue Calculus

      • Reinhold Remmert
      Pages 395-415
  6. Back Matter

    Pages 417-453

Reviews

R. Remmert and R.B. Burckel

Theory of Complex Functions

"Its accessibility makes it very useful for a first graduate course on complex function theory, especially where there is an opportunity for developing an interest on the part of motivated students in the history of the subject. Historical remarks abound throughout the text. Short biographies of Abel, Cauchy, Eisenstein, Euler, Riemann and Weierstrass are given. There is an extensive bibliography of classical works on complex function theory with comments on some of them. In addition, a list of modern complex function theory texts and books on the history of the subject and of mathematics is given. Throughout the book there are numerous interesting quotations. In brief, the book affords splendid opportunities for a rich treatment of the subject."—MATHEMATICAL REVIEWS

Authors and Affiliations

  • Mathematisches Institut, Universität Münster, Münster, Germany

    Reinhold Remmert

Bibliographic Information

  • Book Title: Theory of Complex Functions

  • Authors: Reinhold Remmert

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0939-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1991

  • Hardcover ISBN: 978-0-387-97195-7Published: 30 April 1990

  • Softcover ISBN: 978-1-4612-6953-3Published: 30 September 2012

  • eBook ISBN: 978-1-4612-0939-3Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XIX, 458

  • Topics: Analysis

Buy it now

Buying options

eBook USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access