Authors:
- 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
Part of the book series: Moscow Lectures (ML, volume 6)
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Table of contents (13 chapters)
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Front Matter
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Back Matter
About this book
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.
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Authors and Affiliations
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National Research University Higher School of Economics, Moscow, Russia, Federal Science Center System, Research Institute of Russian Academy of Sciences (FGU FNC NIISI RAN), Moscow, Russia
Serge Lvovski
About the author
Bibliographic Information
Book Title: Principles of Complex Analysis
Authors: Serge Lvovski
Series Title: Moscow Lectures
DOI: https://doi.org/10.1007/978-3-030-59365-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-59364-3Published: 27 September 2020
Softcover ISBN: 978-3-030-59367-4Published: 28 September 2021
eBook ISBN: 978-3-030-59365-0Published: 26 September 2020
Series ISSN: 2522-0314
Series E-ISSN: 2522-0322
Edition Number: 1
Number of Pages: XIII, 257