Introduction to Complex Theory of Differential Equations / Anton Savin, Bosris Sternin.

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Introduction to Complex Theory of Differential Equations / Anton Savin, Bosris Sternin.

9783319517445 (electronic book)
3319517449 (electronic book)
3319517430
9783319517438

Cham, Switzerland : Springer International Publishing AG, [2017]

English

1 online resource.

10.1007/978-3-319-51744-5 doi

QA371 .S38 2017

515/.35

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.

Includes bibliographical references and index.

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Frontiers in mathematics.

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