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Principles of Complex Analysis

Principles of Complex Analysis

Wydawnictwo Springer Nature Customer Service Center GmbH
Data wydania 01/09/2020
Wydanie Pierwsze
Liczba stron 257
Forma publikacji książka w twardej oprawie
Poziom zaawansowania Dla profesjonalistów, specjalistów i badaczy naukowych
Język angielski
ISBN 9783030593643
Kategorie Analizy i zmienne kompleksowe, Geometria algebraiczna
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Opis książki

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.

Principles of Complex Analysis

Spis treści

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.

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