عنوان

Complex analysis, Riemann surfaces and integrable systems

شابک

9783030346409

شماره

E3606

زبان متن نوشتاري يا گفتاري و مانند آن

انگلیسی

عنوان اصلي

Complex analysis, Riemann surfaces and integrable systems

نام نخستين پديدآور

Sergey M. Natanzon

محل نشرو پخش و غیره

Cham, Switzerland

نام ناشر، پخش کننده و غيره

Springer

تاریخ نشرو بخش و غیره

2019

نام خاص و کميت اثر

xiii, 139 p.

ساير جزييات

ill

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

عنصر شناسه ای

Functions of complex variables

عنصر شناسه ای

Integral equations

داده رابط بین فیلدها

a03

داده رابط بین فیلدها

a06

موضوع مستند نشده

Riemann surfaces

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Natanzon, S. M., 1948-

کشور

Iran

سازمان

University of Tehran. Library of College of Science

تاريخ عمليات

20221211

تاريخ و ساعت مذاکره و دسترسي

UT_SCI_BL_DB_1003867_0001.pdf

فرمت انتشار

e

نوع ماده

BL

کد کاربرگه

278840

سطح دسترسي

a

تكميل شده

Y