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＜E-Book＞
Principles of Complex Analysis / by Serge Lvovski
(Moscow Lectures. ISSN:25220322 ; 6)

Edition	1st ed. 2020.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2020
Language	English
Size	XIII, 257 p : online resource
Authors	*Lvovski, Serge author SpringerLink (Online service)
Subjects	LCSH:Functions of complex variables LCSH:Algebraic geometry FREE:Functions of a Complex Variable FREE:Algebraic Geometry
Notes	Introduction -- 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 This 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 HTTP:URL=https://doi.org/10.1007/978-3-030-59365-0

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