Advanced complex analysis
Author(s)
Bibliographic Information
Advanced complex analysis
(A comprehensive course in analysis, pt. 2B)
American Mathematical Society, c2015
Available at 30 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
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  Aichi
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  Kyoto
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  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
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  Tokushima
  Kagawa
  Ehime
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  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
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  United States of America
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
SIM||14||11200035501775
Note
Includes bibliographical references and indexes
Description and Table of Contents
Description
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.
Table of Contents
Riemannian metrics and complex analysis
Some topics in analytic number theory
Ordinary differential equations in the complex domain
Asymptotic methods
Univalent functions and Loewner evolution
Nevanlinna theory
Bibliography
Symbol index
Subject index
Author index
Index of capsule biographies
by "Nielsen BookData"