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Record Nr. |
UNINA9910254309403321 |
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Autore |
Savin Anton |
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Titolo |
Introduction to Complex Theory of Differential Equations / / by Anton Savin, Boris Sternin |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2017 |
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ISBN |
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Edizione |
[1st ed. 2017.] |
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Descrizione fisica |
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1 online resource (IX, 138 p. 43 illus.) |
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Collana |
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Frontiers in Mathematics, , 1660-8046 |
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Disciplina |
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Soggetti |
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Global analysis (Mathematics) |
Manifolds (Mathematics) |
Differential equations, Partial |
Functions of complex variables |
Geophysics |
Global Analysis and Analysis on Manifolds |
Partial Differential Equations |
Several Complex Variables and Analytic Spaces |
Geophysics/Geodesy |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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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. |
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