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Author Lvovski, Serge, author

Title Principles of complex analysis / Serge Lvovski
Published Cham, Switzerland : Springer, [2020]


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.
Geometría algebraica
Funciones de variables complejas
Functions of complex variables
Geometry, Algebraic
Form Electronic book
ISBN 9783030593650
Other Titles Print︠s︡ipy kompleksnogo analiza. English