عنوان

Complex analysis, Riemann surfaces and integrable systems /

شابک

3030346404

شابک

9783030346409

شابک اشتباه

9783030346393

عنوان اصلي

Complex analysis, Riemann surfaces and integrable systems /

نام عام مواد

[Book]

نام نخستين پديدآور

Sergey M. Natanzon.

محل نشرو پخش و غیره

Cham :

نام ناشر، پخش کننده و غيره

Springer,

تاریخ نشرو بخش و غیره

©2019.

نام خاص و کميت اثر

1 online resource (148 pages)

عنوان فروست

Moscow Lectures ;

مشخصه جلد

v. 3

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

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.

بدون عنوان

0

متن يادداشت

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.

منبع سفارش / آدرس اشتراک

Springer Nature

شماره انبار

com.springer.onix.9783030346409

عنوان

Complex Analysis, Riemann Surfaces and Integrable Systems.

شماره استاندارد بين المللي کتاب و موسيقي

9783030346393

موضوع مستند نشده

Functions of complex variables.

موضوع مستند نشده

Integral equations.

موضوع مستند نشده

Riemann surfaces.

موضوع مستند نشده

Functions of complex variables.

موضوع مستند نشده

Integral equations.

موضوع مستند نشده

Riemann surfaces.

شماره

ويراست

شماره رده

مستند نام اشخاص تاييد نشده

Natanzon, S. M.,1948-

تاريخ عمليات

20200823094540.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y