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Complex Function Theory: Second Edition
 
Donald Sarason University of California, Berkeley, Berkeley, CA
Front Cover for Complex Function Theory
SoftcoverISBN:  978-1-4704-6323-6
Product Code:  MBK/49.S
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $36.00
eBookISBN:  978-1-4704-1199-2
Product Code:  MBK/49.E
List Price: $42.00
MAA Member Price: $37.80
AMS Member Price: $33.60
SoftcoverISBN:  978-1-4704-6323-6
eBookISBN:  978-1-4704-1199-2
Product Code:  MBK/49.S.B
List Price: $87.00$66.00
MAA Member Price: $78.30$59.40
AMS Member Price: $69.60$52.80
Front Cover for Complex Function Theory
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  • Front Cover for Complex Function Theory
  • Back Cover for Complex Function Theory
Complex Function Theory: Second Edition
Donald Sarason University of California, Berkeley, Berkeley, CA
Softcover ISBN:  978-1-4704-6323-6
Product Code:  MBK/49.S
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $36.00
eBook ISBN:  978-1-4704-1199-2
Product Code:  MBK/49.E
List Price: $42.00
MAA Member Price: $37.80
AMS Member Price: $33.60
Softcover ISBN:  978-1-4704-6323-6
eBookISBN:  978-1-4704-1199-2
Product Code:  MBK/49.S.B
List Price: $87.00$66.00
MAA Member Price: $78.30$59.40
AMS Member Price: $69.60$52.80
  • Book Details
     
     
    2007; 163 pp
    MSC: Primary 30;

    Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation.

    The first edition was published with the title Notes on Complex Function Theory.

    Readership

    Undergraduate and graduate students interested in complex analysis.

  • Table of Contents
     
     
    • Chapters
    • 1. Complex numbers
    • 2. Complex differentiation
    • 3. Linear-fractional transformations
    • 4. Elementary functions
    • 5. Power series
    • 6. Complex integration
    • 7. Core versions of Cauchy’s theorem, and consequences
    • 8. Laurent series and isolated singularities
    • 9. Cauchy’s theorem
    • 10. 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
  • Reviews
     
     
    • From a review of the previous edition …

      The exposition is clear, rigorous, and friendly.

      Zentralblatt MATH
  • Requests
     
     
    Review Copy – for reviewers who would like to review an AMS book
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
2007; 163 pp
MSC: Primary 30;

Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation.

The first edition was published with the title Notes on Complex Function Theory.

Readership

Undergraduate and graduate students interested in complex analysis.

  • Chapters
  • 1. Complex numbers
  • 2. Complex differentiation
  • 3. Linear-fractional transformations
  • 4. Elementary functions
  • 5. Power series
  • 6. Complex integration
  • 7. Core versions of Cauchy’s theorem, and consequences
  • 8. Laurent series and isolated singularities
  • 9. Cauchy’s theorem
  • 10. 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
  • From a review of the previous edition …

    The exposition is clear, rigorous, and friendly.

    Zentralblatt MATH
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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