國立高雄大學圖資館 |

Language: English

Back

Principles of complex analysis

Lvovski, Serge.

Principles of complex analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Principles of complex analysisby Serge Lvovski.
Author:	Lvovski, Serge.
Published:	Cham :Springer International Publishing :2020.
Description:	xiii, 257 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Functions of complex variables.
Online resource:	https://doi.org/10.1007/978-3-030-59365-0
ISBN:	9783030593650$q(electronic bk.)

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.1..

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$q(electronic bk.)

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

185972
Functions of complex variables.

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

Dewey Class. No.: 515.9

Principles of complex analysis
LDR:02300nmm a2200349 a 4500 001 586253
003 DE-He213
005 20210128104750.0
006 m d
007 cr nn 008maaau
008 210323s2020 sz s 0 eng d
020 $a 9783030593650$q(electronic bk.)
020 $a 9783030593643$q(paper)
024 7 $a 10.1007/978-3-030-59365-0 $2 doi
035 $a 978-3-030-59365-0
040 $a GP $c GP
041 1 $a eng $h rus
050 4 $a QA331.7 $b .L8613 2020
072 7 $a PBKD $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKD $2 thema
082 0 4 $a 515.9 $2 23
090 $a QA331.7 $b .L979 2020
100 1 $a Lvovski, Serge. $3 877632
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 185972
650 0 $a Geometry, Algebraic. $3 190843
650 1 4 $a Functions of a Complex Variable. $3 275780
650 2 4 $a Algebraic Geometry. $3 274807
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Moscow lectures ; $v v.1. $3 816290
856 4 0 $u https://doi.org/10.1007/978-3-030-59365-0
950 $a Mathematics and Statistics (SpringerNature-11649)