Advanced complex analysis / Barry Simon.

Format:

Book

Author/Creator:

Simon, Barry, 1946- author.

Series:

Simon, Barry, 1946- Comprehensive course in analysis ; 2B

A comprehensive course in analysis ; Part 2B

Language:

English

Subjects (All):

Mathematical analysis--Textbooks.

Mathematical analysis.

Physical Description:

1 online resource (322 pages)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2015]

Language Note:

English

Summary:

A Comprehensive Course in Analysis by Poincare 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 2B provides a comprehensive look at a number of subjects of complex analysis not included in Part 2A. Presented in this volume are the theory of conformal metrics (including the Poincare metric, the Ahlfors-Robinson proof of Picard's theorem, and Bell's proof of the Painleve smoothness theorem), topics in analytic number theory (including Jacobi's two- and four-square theorems, the Dirichlet prime progression theorem, the prime number theorem, and the Hardy-Littlewood asymptotics for the number of partitions), the theory of Fuschian differential equations, asymptotic methods (including Euler's method, stationary phase, the saddle-point method, and the WKB method), univalent functions (including an introduction to SLE), and Nevanlinna theory. The chapters on Fuschian differential equations and on asymptotic methods can be viewed as a minicourse on the theory of special functions.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and indexes.

Description based on print version record.

ISBN:

9781470427597

1-4704-2759-1