Complex Analysis, Riemann Surfaces and Integrable Systems

Name: Complex Analysis, Riemann Surfaces and Integrable Systems
Brand: Springer Nature Switzerland AG
SKU: 9783030346393
Price: 24478 HUF
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Szerző: Sergey M. Natanzon, Natalia Tsilevich

Nyelv:

Kötés: Kemény kötésű

Kiadó: Springer Nature Switzerland AG

Elérhetőség: Beszállítói készleten

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This book is devoted to classical and modern achievements in complex analysis. In order to benefit m...

Információk a könyvről

Szerző

Sergey M. Natanzon, Natalia Tsilevich

Nyelv

Angol

Kötés

Könyv - Kemény kötésű

Kiadva

2020

oldal

139

EAN

9783030346393

Enbook ID

24865132

Kiadó

Springer Nature Switzerland AG

Súly

454

Méretek

155 x 235 x 15

Teljes leírás

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 - a classical problem that has important applications in hydrodynamics, gas dynamics, etc. The book is based on numerous lecture courses given by the author at the Independent University of Moscow and at the Mathematics Department of the Higher School of Economics.

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Complex Analysis, Riemann Surfaces and Integrable Systems

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