A Complex Analysis Problem Book

  • Daniel Alpay

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Complex Numbers

    1. Front Matter
      Pages 9-9
    2. Daniel Alpay
      Pages 11-60
    3. Daniel Alpay
      Pages 61-86
    4. Daniel Alpay
      Pages 87-140
  3. Functions of a Complex Variable

  4. Applications and More Advanced Topics

    1. Front Matter
      Pages 393-393
    2. Daniel Alpay
      Pages 395-419
    3. Daniel Alpay
      Pages 421-430
  5. Appendix

    1. Front Matter
      Pages 447-447
    2. Daniel Alpay
      Pages 449-461
    3. Daniel Alpay
      Pages 463-477
    4. Daniel Alpay
      Pages 479-494
    5. Daniel Alpay
      Pages 495-511

About this book


This is a collection of exercises in the theory of analytic functions, with completed and detailed solutions. We wish to introduce the student to applications and aspects of the theory of analytic functions not always touched upon in a first course. Using appropriate exercises show the students some aspects of what lies beyond a first course in complex variables. We also discuss topics of interest for electrical engineering students (for instance, the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). Examples of  important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space) are given. The book also includes a part where relevant facts from topology, functional analysis and Lebesgue integration are reviewed.


Cauchy formula analytic function complex variables conformal mapping holomorphic function

Authors and affiliations

  • Daniel Alpay
    • 1
  1. 1.Dept. Mathematics & Computer ScienceBen-Gurion University of the NegevBeer ShevaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0078-5
  • Copyright Information Springer Basel AG 2011
  • Publisher Name Springer, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0077-8
  • Online ISBN 978-3-0348-0078-5
  • About this book