عنوان

Complex analysis, Riemann surfaces and integrable systems

(Number (ISBN

9783030346409

Number

E3606

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

Complex analysis, Riemann surfaces and integrable systems

First Statement of Responsibility

Sergey M. Natanzon

Place of Publication, Distribution, etc.

Cham, Switzerland

Name of Publisher, Distributor, etc.

Springer

Date of Publication, Distribution, etc.

2019

Specific Material Designation and Extent of Item

xiii, 139 p.

Other Physical Details

ill

Series Title

(Moscow lectures

Volume Designation

v. 3)

Text of Note

Includes bibliographical references and index

Text of Note

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

0

Text of Note

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

Entry Element

Functions of complex variables

Entry Element

Integral equations

a03

a06

Riemann surfaces

Class number

Book number

Natanzon, S. M., 1948-

Country

Iran

Agency

University of Tehran. Library of College of Science

Date of Transaction

20221211

Date and Hour of Consultation and Access

UT_SCI_BL_DB_1003867_0001.pdf

e

BL

278840

a

Y