Complex Analysis, Riemann Surfaces and Integrable Systems

• Main Author: Natanzon, Sergey M. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Moscow Lectures, 3
• Subjects: Mathematical analysis.; Analysis (Mathematics).; Analysis.

This book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided. We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic,...

Table of Contents:

• Holomorphic functions
• Meromorphic functions
• Riemann's theorem
• Harmonic functions
• Riemann surfaces and their modules
• Compact Riemann surfaces and algebraic curves
• Riemann-Roch theorem and theta functions
• Integrable Systems
• The formula for the conformal mapping of an arbitrary domain into the unit disk.