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Principles of Complex Analysis

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Principles of Complex Analysis/ by Serge Lvovski.
作者:	Lvovski, Serge.
面頁冊數:	XIII, 257 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Algebraic Geometry. -
電子資源:	https://doi.org/10.1007/978-3-030-59365-0
ISBN:	9783030593650

Principles of Complex Analysis
Lvovski, Serge.

Principles of Complex Analysis[electronic resource] /by Serge Lvovski. - 1st ed. 2020. - XIII, 257 p.online resource. - Moscow Lectures,62522-0314 ;. - Moscow Lectures,2.

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.

ISBN: 9783030593650

Standard No.: 10.1007/978-3-030-59365-0doiSubjects--Topical Terms:

670184
Algebraic Geometry.

LC Class. No.: QA331-355

Dewey Class. No.: 515.9

Principles of Complex Analysis
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