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Cover: 9783030593674 | Principles of Complex Analysis | Serge Lvovski | Taschenbuch | xiii
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Principles of Complex Analysis
Taschenbuch von Serge Lvovski
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
Serge Lvovski is associate professor at the Faculty of Mathematics of Higher School of Economics, Moscow, and research fellow in the Laboratory of Algebraic Geometry and its Applications.
Zusammenfassung

Conformal mappings are introduced on an early stage, so the reader can learn to manipulate with subsets of the complex plane before passing to more sophisticated subjects

A special long section is devoted to evaluation of residues and evaluation of integrals using residues

The final chapter, which is devoted to Riemann surfaces, provides an elementary introduction into this subject which motivates the reader to study more technical parts of the theory

Inhaltsverzeichnis

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.

Details
Erscheinungsjahr: 2021
Fachbereich: Analysis
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Moscow Lectures
Inhalt: xiii
257 S.
ISBN-13: 9783030593674
ISBN-10: 3030593673
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Lvovski, Serge
Hersteller: Springer
Palgrave Macmillan
Springer International Publishing AG
Moscow Lectures
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 15 mm
Von/Mit: Serge Lvovski
Erscheinungsdatum: 28.09.2021
Gewicht: 0,417 kg
Artikel-ID: 120515991
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