Advanced Complex Analysis: A Comprehensive Course in Analysis, Part 2B
About this Title
Publication Year: 2015; Volume 2.2
ISBNs: 978-1-4704-1101-5 (print); 978-1-4704-2759-7 (online)
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 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 Poincaré metric, the Ahlfors-Robinson proof of Picard's theorem, and Bell's proof of the Painlevé 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 Fuchsian 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 Fuchsian differential equations and on asymptotic methods can be viewed as a minicourse on the theory of special functions.
Researchers (mathematicians and some applied mathematicians and physicists) using analysis, professors teaching analysis at the graduate level, graduate students who need any kind of analysis in their work.
Table of Contents
- Chapter 12. Riemannian metrics and complex analysis
- Chapter 13. Some topics in analytic number theory
- Chapter 14. Ordinary differential equations in the complex domain
- Chapter 15. Asymptotic methods
- Chapter 16. Univalent functions and Loewner evolution
- Chapter 17. Nevanlinna theory