Description 
1 online resource 
Series 
Moscow lectures ; volume 6 

Moscow lectures ; v. 6.

Contents 
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 
Summary 
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 
Bibliography 
Includes bibliographical references and index 
Notes 
Translated from Russian 

Online resource; title from digital title page (viewed on November 12, 2020) 
Subject 
Functions of complex variables.


Geometry, Algebraic.


Functions of complex variables.


Geometry, Algebraic.

Form 
Electronic book

ISBN 
9783030593650 

3030593657 
