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000924858 019__ $$a1137838326
000924858 020__ $$a9783030346409$$q(electronic book)
000924858 020__ $$a3030346404$$q(electronic book)
000924858 020__ $$z9783030346393
000924858 0247_ $$a10.1007/978-3-030-34
000924858 035__ $$aSP(OCoLC)on1135668784
000924858 035__ $$aSP(OCoLC)1135668784$$z(OCoLC)1137838326
000924858 040__ $$aEBLCP$$beng$$cEBLCP$$dOCLCO$$dGW5XE$$dLQU$$dOCLCF
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000924858 049__ $$aISEA
000924858 050_4 $$aQA331
000924858 08204 $$a515/.9$$223
000924858 1001_ $$aNatanzon, S. M.,$$d1948-
000924858 24510 $$aComplex analysis, Riemann surfaces and integrable systems /$$cSergey M. Natanzon.
000924858 260__ $$aCham :$$bSpringer,$$cc2019.
000924858 300__ $$a1 online resource (148 pages).
000924858 336__ $$atext$$btxt$$2rdacontent
000924858 337__ $$acomputer$$bc$$2rdamedia
000924858 338__ $$aonline resource$$bcr$$2rdacarrier
000924858 4901_ $$aMoscow Lectures ;$$vv.3
000924858 504__ $$aIncludes bibliographical references and index.
000924858 5050_ $$aHolomorphic 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.
000924858 506__ $$aAccess limited to authorized users.
000924858 520__ $$aThis 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.
000924858 588__ $$aDescription based on print version record.
000924858 650_0 $$aFunctions of complex variables.
000924858 650_0 $$aRiemann surfaces.
000924858 650_0 $$aIntegral equations.
000924858 77608 $$iPrint version:$$aNatanzon, Sergey M.$$tComplex Analysis, Riemann Surfaces and Integrable Systems$$dCham : Springer International Publishing AG,c2020$$z9783030346393
000924858 830_0 $$aMoscow lectures ;$$vv. 3.
000924858 852__ $$bebk
000924858 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-34640-9$$zOnline Access$$91397441.1
000924858 909CO $$ooai:library.usi.edu:924858$$pGLOBAL_SET
000924858 980__ $$aEBOOK
000924858 980__ $$aBIB
000924858 982__ $$aEbook
000924858 983__ $$aOnline
000924858 994__ $$a92$$bISE