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Introduction to Complex Theory of Differential Equations : Frontiers in Mathematics - Anton Savin

Introduction to Complex Theory of Differential Equations

Frontiers in Mathematics

Paperback

Published: 5th April 2017
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This book deals with complex theory of differential equations or more precisely, with the theory of differential equations on complex-analytic manifolds.

The theory of differential equations on real manifolds is very well known. It is described in thousands of papers and its usefulness does not require comments or explanations. However, complex theory of partial differential equations is so far not in the focus of specialists on differential equations. Indeed, besides its remarkable beauty, this theory can be used to solve a number of problems in real theory, for instance, Poincare balayage problem, mother body problem in geophysics, etc.

The monograph does not require the reader to be familiar with advanced notions in complex analysis, differential equations, or topology. With its numerous examples and exercises, it will appeal to advanced undergraduate and graduate students, bus also to researchers who intend to familiarize themselves with the subject.

Leray residues.- Ramied integrals.- Asymptotics of ramied integrals.- Ramied Fourier transform.- Properties of ramied Fourier transform.- The Cauchy problem for equations with constant coefficients.- Singularities of the solution of Cauchy problem.- The Cauchy problem for equations with variable coefficients. Leray's uniformization.- Balayage inwards problem.- Mother body problem.- Hints for exercises.

ISBN: 9783319517438
ISBN-10: 3319517430
Series: Frontiers in Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 138
Published: 5th April 2017
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 21.0 x 15.0  x 2.2
Weight (kg): 0.38