Introduction to Complex Theory of Differential Equations - Anton Savin, Boris Sternin

Introduction to Complex Theory of Differential Equations

Buch | Softcover
IX, 138 Seiten
2017 | 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-51743-8 (ISBN)
58,84 inkl. MwSt

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.

Boris Sternin is a full professor at the Department of Applied Mathematics at the RUDN University in Moscow. He received his PhD in 1965 from Moscow State University and his Doctor of Physico-Mathematical Sciences in 1984. His main area is partial differential equations, in particular, Global asymptotic methods and Noncommutative theory of elliptic operators. Prof. Sternin has published over 300 scientific articles and 17 books since 1964. Anton Savin is an associate professor at the Department of Applied Mathematics at the RUDN University in Moscow. He received his PhD in 2000 from Moscow State University and his Doctor of physico-mathematical sciences in 2012. Dr. Savin has published over 70 scientific articles and two books since 1997.

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.

Erscheinungsdatum
Reihe/Serie Frontiers in Mathematics
Zusatzinfo IX, 138 p. 43 illus.
Verlagsort Cham
Sprache englisch
Maße 168 x 240 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Naturwissenschaften Geowissenschaften Geophysik
Schlagworte Complex analysis, complex variables • complex-analytic manifolds • complex theory • Differential calculus and equations • Differential Equations • Geophysics • Geophysics/Geodesy • Global Analysis and Analysis on Manifolds • Mathematics • mathematics and statistics • Numerical analysis • Partial differential equations • Poincaré balayage problem • Poincaré balayage problem • Several Complex Variables and Analytic Spaces
ISBN-10 3-319-51743-0 / 3319517430
ISBN-13 978-3-319-51743-8 / 9783319517438
Zustand Neuware
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