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Introduction to Complex Theory of Differential Equations
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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, Poincaré 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.
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