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Principles of complex analysis

Lvovski, Serge.

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Principles of complex analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Principles of complex analysis/ by Serge Lvovski.
Author:	Lvovski, Serge.
Published:	Cham :Springer International Publishing : : 2020.,
Description:	xiii, 257 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Functions of complex variables. -
Online resource:	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. - Cham :Springer International Publishing :2020. - xiii, 257 p. :ill., digital ;24 cm. - Moscow lectures,v.62522-0314 ;. - Moscow lectures ;v.6..

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:

523875
Functions of complex variables.

LC Class. No.: QA331.7 / .L8613 2020

Dewey Class. No.: 515.9

Principles of complex analysis
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100 1 $a Lvovski, Serge. $3 3504331
240 1 0 $a Print︠s︡ipy kompleksnogo analiza. $l English
245 1 0 $a Principles of complex analysis $h [electronic resource] / $c by Serge Lvovski.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xiii, 257 p. : $b ill., digital ; $c 24 cm.
490 1 $a Moscow lectures, $x 2522-0314 ; $v v.6
505 0 $a 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.
520 $a 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.
650 0 $a Functions of complex variables. $3 523875
650 0 $a Geometry, Algebraic. $3 532048
650 1 4 $a Functions of a Complex Variable. $3 897310
650 2 4 $a Algebraic Geometry. $3 893861
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Moscow lectures ; $v v.6. $3 3504332
856 4 0 $u https://doi.org/10.1007/978-3-030-59365-0
950 $a Mathematics and Statistics (SpringerNature-11649)