Introduction to Complex Theory of Differential Equations
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Beschreibung
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.
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.
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
Autor*in
Anton Savin
Themen in »Introduction to Complex Theory of Differential Equations«
differential equations complex theory complex-analytic manifolds partial differential equations geophysics Poincaré balayage problem