Principles of Complex Analysis - Serge Lvovski

Principles of Complex Analysis

(Autor)

Buch | Softcover
XIII, 257 Seiten
2021 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-59367-4 (ISBN)
64,19 inkl. MwSt

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.


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.



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.

"The book is well written, and the precision of the arguments given is carried out on a high level. This is undoubtedly a valuable book for students and can be recommended." (Adam Lecko, Mathematical Reviews, April, 2022)

“The book is well written, and the precision of the arguments given is carried out on a high level. This is undoubtedly a valuable book for students and can be recommended.” (Adam Lecko, Mathematical Reviews, April, 2022)

Erscheinungsdatum
Reihe/Serie Moscow Lectures
Zusatzinfo XIII, 257 p.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 421 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
Schlagworte Cauchy formula • complex analysis. • conformal mapping • holomorhic function • residue • Riemann surface
ISBN-10 3-030-59367-3 / 3030593673
ISBN-13 978-3-030-59367-4 / 9783030593674
Zustand Neuware
Haben Sie eine Frage zum Produkt?
Mehr entdecken
aus dem Bereich

von Tilo Arens; Frank Hettlich; Christian Karpfinger …

Buch | Hardcover (2022)
Springer Spektrum (Verlag)
79,99