LEADER 02778nam 2200541 450 001 9910483266603321 005 20220321143204.0 010 $a3-030-59365-7 024 7 $a10.1007/978-3-030-59365-0 035 $a(CKB)4100000011476653 035 $a(MiAaPQ)EBC6357791 035 $a(DE-He213)978-3-030-59365-0 035 $a(MiAaPQ)EBC6647510 035 $a(Au-PeEL)EBL6357791 035 $a(OCoLC)1198557825 035 $a(Au-PeEL)EBL6647510 035 $a(PPN)25022237X 035 $a(EXLCZ)994100000011476653 100 $a20220321d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPrinciples of complex analysis /$fSerge Lvovski 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$dİ2020 215 $a1 online resource (XIII, 257 p.) 225 1 $aMoscow Lectures,$x2522-0314 ;$v6 311 $a3-030-59364-9 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Preliminaries -- Derivatives of functions of complex variable -- Practicing conformal mappings -- Integrals of functions of complex variable -- Cauchy theorem and its consequences -- Homotopy and analytic continuation -- Laurent series and singular points -- Residues -- Local properties of holomorphic functions -- Conformal mappings I -- Infinite sums and products -- Conformal mappings II -- Introduction to Riemann surfaces. 330 $aThis is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level. The author stresses the aspects of complex analysis that are most important for the student planning to study algebraic geometry and related topics. The exposition is rigorous but elementary: abstract notions are introduced only if they are really indispensable. This approach provides a motivation for the reader to digest more abstract definitions (e.g., those of sheaves or line bundles, which are not mentioned in the book) when he/she is ready for that level of abstraction indeed. In the chapter on Riemann surfaces, several key results on compact Riemann surfaces are stated and proved in the first nontrivial case, i.e. that of elliptic curves. 410 0$aMoscow Lectures,$x2522-0314 ;$v6 606 $aFunctions of complex variables 606 $aGeometry, Algebraic 615 0$aFunctions of complex variables. 615 0$aGeometry, Algebraic. 676 $a515.9 700 $aLvovski$b Serge$0849327 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483266603321 996 $aPrinciples of Complex Analysis$91896821 997 $aUNINA