Description

Book Synopsis
Provides a concise and rigorous introduction to the theory of functions of a complex variable. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. The book is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation.

Trade Review
From a review of the previous edition: ""The exposition is clear, rigorous, and friendly."" —Zentralblatt MATH

Table of Contents
  • Complex numbers
  • Complex differentiation
  • Linear-fractional transformations
  • Elementary functions
  • Power series
  • Complex integration
  • Core versions of Cauchy's theorem, and consequences
  • Laurent series and isolated singularities
  • Cauchy's theorem
  • Further development of basic complex function theory
  • Appendix 1: Sufficient condition for differentiability
  • Appendix 2: Two instances of the chain rule
  • Appendix 3: Groups, and linear-fractional transformations
  • Appendix 4: Differentiation under the integral sign
  • References
  • Index

Complex Function Theory

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    A Paperback by Donald Sarason

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      Publisher: MP-AMM American Mathematical
      Publication Date: Publication Date: 12/30/2007 12:00:00 AM
      ISBN13: 9781470463236, 978-1470463236
      ISBN10: 1470463237
      Also in:
      Calculus and mathematical analysis

      Description

      Book Synopsis
      Provides a concise and rigorous introduction to the theory of functions of a complex variable. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. The book is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation.

      Trade Review
      From a review of the previous edition: ""The exposition is clear, rigorous, and friendly."" —Zentralblatt MATH

      Table of Contents
      • Complex numbers
      • Complex differentiation
      • Linear-fractional transformations
      • Elementary functions
      • Power series
      • Complex integration
      • Core versions of Cauchy's theorem, and consequences
      • Laurent series and isolated singularities
      • Cauchy's theorem
      • Further development of basic complex function theory
      • Appendix 1: Sufficient condition for differentiability
      • Appendix 2: Two instances of the chain rule
      • Appendix 3: Groups, and linear-fractional transformations
      • Appendix 4: Differentiation under the integral sign
      • References
      • Index

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