Overview
- Provides a lucid exposition of modern complex theory of differential equations, which has its origins in the works of Jean Leray
- Includes more than 40 figures and numerous examples and exercises
- Defines all the required terms along the way, making the book self-contained
Part of the book series: Frontiers in Mathematics (FM)
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Table of contents (10 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds.
Although the theory of differential equations on real manifolds is well known – it is described in thousands of papers and its usefulness requires no comments or explanations – to date specialists on differential equations have not focused on the complex theory of partial differential equations. However, as well as being remarkably beautiful, this theory can be used to solve a number of problems in real theory, for instance, the Poincaré balayage problem and the mother body problem in geophysics.
The monograph does not require readers to be familiar with advanced notions in complex analysis, differential equations, or topology. With its numerous examples and exercises, it appeals to advanced undergraduate and graduate students, and also to researchers wanting to familiarize themselves with the subject.
Authors and Affiliations
About the authors
Anton Savin is an associate professor at the Department of Applied Mathematics at the RUDN University in Moscow. He received his PhD in 2000 from Moscow State University and his Doctor of physico-mathematical sciences in 2012. Dr. Savin has published over 70 scientific articles and two books since 1997.
Bibliographic Information
Book Title: Introduction to Complex Theory of Differential Equations
Authors: Anton Savin, Boris Sternin
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/978-3-319-51744-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-51743-8Published: 05 April 2017
eBook ISBN: 978-3-319-51744-5Published: 28 March 2017
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: IX, 138
Number of Illustrations: 43 b/w illustrations
Topics: Global Analysis and Analysis on Manifolds, Partial Differential Equations, Several Complex Variables and Analytic Spaces, Geophysics/Geodesy