| 書目名稱 | Complex Analysis, Riemann Surfaces and Integrable Systems | | 編輯 | Sergey M. Natanzon | | 視頻video | http://file.papertrans.cn/232/231391/231391.mp4 | | 概述 | Using basic tools from the first year of university studies, the book leads a reader to the impressive achievements of mathematics of the 21st century.Studying the book, the reader will get acquainted | | 叢書名稱 | Moscow Lectures | | 圖書封面 |  | | 描述 | .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, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contracted space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We also construct theta functions that are very important for a range of applications. ..After that, we turn to modern applications of this theory. First, we build the (important for mathematics and mathematical physics) Kadomtsev-Petviashvili?hierarchy?and use validated results to arrive at important solutions to these differential equations.?We subsequently use the theory of harmonic functions and the theory of differential hierarchies to explicitly construct a conformal?mapping that translates an arbitrary contractible domain into a standard disk | | 出版日期 | Textbook 2019 | | 關(guān)鍵詞 | meromorphic functions; Riemann theorem; harmonic functions; Fuchsian groups; Riemann surfaces; moduli of | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-34640-9 | | isbn_softcover | 978-3-030-34642-3 | | isbn_ebook | 978-3-030-34640-9Series ISSN 2522-0314 Series E-ISSN 2522-0322 | | issn_series | 2522-0314 | | copyright | Springer Nature Switzerland AG 2019 |
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