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Titlebook: Introduction to Complex Theory of Differential Equations; Anton Savin,Boris Sternin Textbook 2017 Springer International Publishing AG 201

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发表于 2025-3-21 16:12:52 | 显示全部楼层 |阅读模式
书目名称Introduction to Complex Theory of Differential Equations
编辑Anton Savin,Boris Sternin
视频video
概述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.Defin
丛书名称Frontiers in Mathematics
图书封面Titlebook: Introduction to Complex Theory of Differential Equations;  Anton Savin,Boris Sternin Textbook 2017 Springer International Publishing AG 201
描述.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..
出版日期Textbook 2017
关键词differential equations; complex theory; complex-analytic manifolds; partial differential equations; geop
版次1
doihttps://doi.org/10.1007/978-3-319-51744-5
isbn_softcover978-3-319-51743-8
isbn_ebook978-3-319-51744-5Series ISSN 1660-8046 Series E-ISSN 1660-8054
issn_series 1660-8046
copyrightSpringer International Publishing AG 2017
The information of publication is updating

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发表于 2025-3-21 20:23:52 | 显示全部楼层
Mother body problem, and wants to determine the source of this gravitational field located inside the earth. Clearly, the solution of this problem is not unique. For example, it has been well known since the time of Newton that a ball with constant mass density produces the same gravitational field as the same mass concentrated at the center of the ball.
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Textbook 2017s.. . 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 equation
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Ramified integrals,the situation, when the integrand is a single-valued form, the integral is a ramified function as a rule. For this reason, parametric integrals in complex analysis are also called ramified integrals. The aim of this chapter is to describe this phenomenon in examples and then present the general theory of such integrals.
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Leray residues,Residues of differential forms depending on several variables were first considered by Poincaré (1887). Later, such residues appeared in the works of Picard (1901), de Rham (1932—1936), and others. In this chapter we explain the theory of residues constructed by Leray (1959).
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