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Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A
 
Barry Simon California Institute of Technology, Pasadena, CA
Basic Complex Analysis
Hardcover ISBN:  978-1-4704-1100-8
Product Code:  SIMON/2.1
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-2757-3
Product Code:  SIMON/2.1.E
List Price: $95.00
MAA Member Price: $85.50
AMS Member Price: $76.00
Hardcover ISBN:  978-1-4704-1100-8
eBook: ISBN:  978-1-4704-2757-3
Product Code:  SIMON/2.1.B
List Price: $194.00 $146.50
MAA Member Price: $174.60 $131.85
AMS Member Price: $155.20 $117.20
Basic Complex Analysis
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Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A
Barry Simon California Institute of Technology, Pasadena, CA
Hardcover ISBN:  978-1-4704-1100-8
Product Code:  SIMON/2.1
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-2757-3
Product Code:  SIMON/2.1.E
List Price: $95.00
MAA Member Price: $85.50
AMS Member Price: $76.00
Hardcover ISBN:  978-1-4704-1100-8
eBook ISBN:  978-1-4704-2757-3
Product Code:  SIMON/2.1.B
List Price: $194.00 $146.50
MAA Member Price: $174.60 $131.85
AMS Member Price: $155.20 $117.20
  • Book Details
     
     
    2015; 641 pp
    MSC: Primary 30; 33; 40; Secondary 34; 41; 44

    A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis.

    Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.

    Readership

    Researchers (mathematicians and some applied mathematicians and physicists) using analysis, professors teaching analysis at the graduate level, and graduate students who need any kind of analysis in their work.

    This item is also available as part of a set:
  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Preliminaries
    • Chapter 2. The Cauchy integral theorem: Basics
    • Chapter 3. Consequences of the Cauchy integral formula
    • Chapter 4. Chains and the ultimate Cauchy integral theorem
    • Chapter 5. More consequences of the CIT
    • Chapter 6. Spaces of analytic functions
    • Chapter 7. Fractional linear transformations
    • Chapter 8. Conformal maps
    • Chapter 9. Zeros of analytic functions and product formulae
    • Chapter 10. Elliptic functions
    • Chapter 11. Selected additional topics
  • Additional Material
     
     
  • Reviews
     
     
    • There is no need to belabor the point that this is a fabulous set of texts and will be a smash hit in graduate programs with good taste and good students willing to work hard and ready for exposure to mathematical culture of a wonderful sort. In addition to being a fine mathematician and teacher of mathematics, Simon is something of a raconteur (in the best sense of the word) with a strong interest in history. The books are peppered with historical asides and human interest material, and this feature adds to their readability. Indeed, they are beautifully and clearly written and certainly make for a major contribution to the literature at the intended level and beyond. When I learned that the AMS (which is to be congratulated with this publication) was launching this series by Barry Simon, I, of course, expected a great deal. I was by no means disappointed; these books are terrific.

      MAA Online
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
2015; 641 pp
MSC: Primary 30; 33; 40; Secondary 34; 41; 44

A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis.

Part 2A is devoted to basic complex analysis. It interweaves three analytic threads associated with Cauchy, Riemann, and Weierstrass, respectively. Cauchy's view focuses on the differential and integral calculus of functions of a complex variable, with the key topics being the Cauchy integral formula and contour integration. For Riemann, the geometry of the complex plane is central, with key topics being fractional linear transformations and conformal mapping. For Weierstrass, the power series is king, with key topics being spaces of analytic functions, the product formulas of Weierstrass and Hadamard, and the Weierstrass theory of elliptic functions. Subjects in this volume that are often missing in other texts include the Cauchy integral theorem when the contour is the boundary of a Jordan region, continued fractions, two proofs of the big Picard theorem, the uniformization theorem, Ahlfors's function, the sheaf of analytic germs, and Jacobi, as well as Weierstrass, elliptic functions.

Readership

Researchers (mathematicians and some applied mathematicians and physicists) using analysis, professors teaching analysis at the graduate level, and graduate students who need any kind of analysis in their work.

This item is also available as part of a set:
  • Chapters
  • Chapter 1. Preliminaries
  • Chapter 2. The Cauchy integral theorem: Basics
  • Chapter 3. Consequences of the Cauchy integral formula
  • Chapter 4. Chains and the ultimate Cauchy integral theorem
  • Chapter 5. More consequences of the CIT
  • Chapter 6. Spaces of analytic functions
  • Chapter 7. Fractional linear transformations
  • Chapter 8. Conformal maps
  • Chapter 9. Zeros of analytic functions and product formulae
  • Chapter 10. Elliptic functions
  • Chapter 11. Selected additional topics
  • There is no need to belabor the point that this is a fabulous set of texts and will be a smash hit in graduate programs with good taste and good students willing to work hard and ready for exposure to mathematical culture of a wonderful sort. In addition to being a fine mathematician and teacher of mathematics, Simon is something of a raconteur (in the best sense of the word) with a strong interest in history. The books are peppered with historical asides and human interest material, and this feature adds to their readability. Indeed, they are beautifully and clearly written and certainly make for a major contribution to the literature at the intended level and beyond. When I learned that the AMS (which is to be congratulated with this publication) was launching this series by Barry Simon, I, of course, expected a great deal. I was by no means disappointed; these books are terrific.

    MAA Online
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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