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Introduction to Complex Theory of Differential Equations

  • Anton Savin
  • Boris Sternin

Part of the Frontiers in Mathematics book series (FM)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Anton Savin, Boris Sternin
    Pages 1-10
  3. Anton Savin, Boris Sternin
    Pages 11-29
  4. Anton Savin, Boris Sternin
    Pages 31-42
  5. Anton Savin, Boris Sternin
    Pages 43-52
  6. Anton Savin, Boris Sternin
    Pages 53-59
  7. Anton Savin, Boris Sternin
    Pages 61-68
  8. Anton Savin, Boris Sternin
    Pages 69-79
  9. Anton Savin, Boris Sternin
    Pages 95-107
  10. Anton Savin, Boris Sternin
    Pages 109-128
  11. Back Matter
    Pages 129-138

About this book

Introduction

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.

Keywords

differential equations complex theory complex-analytic manifolds partial differential equations geophysics Poincaré balayage problem

Authors and affiliations

  • Anton Savin
    • 1
  • Boris Sternin
    • 2
  1. 1.Department of Applied MathematicsRUDN UniversityMoscowRussia
  2. 2.Department of Applied MathematicsRUDN UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-51744-5
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-51743-8
  • Online ISBN 978-3-319-51744-5
  • Series Print ISSN 1660-8046
  • Series Online ISSN 1660-8054
  • Buy this book on publisher's site