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haraoka yoshishige - linear differential equations in the complex domain

Linear Differential Equations in the Complex Domain From Classical Theory to Forefront




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 11/2020
Edizione: 1st ed. 2020





Trama

This book provides a detailed introduction to recent developments in the theory of linear differential systems and integrable total differential systems. Starting from the basic theory of linear ordinary differential equations and integrable systems, it proceeds to describe Katz theory and its applications, extending it to the case of several variables. In addition, connection problems, deformation theory, and the theory of integral representations are comprehensively covered. Complete proofs are given, offering the reader a precise account of the classical and modern theory of linear differential equations in the complex domain, including an exposition of Pfaffian systems and their monodromy problems.
 
The prerequisites are a course in complex analysis and the basics of differential equations, topology and differential geometry. This book will be useful for graduate students, specialists in differential equations, and for non-specialists who want to use differential equations.
 





Sommario

- Introduction. - Part I Ordinary Differential Equations. - Scalar Differential Equations and Systems of Differential Equations. - Analysis at a Regular Point. - Regular Singular Points. - Monodromy. - Connection Problem. - Fuchsian Differential Equations. - Deformation Theory. - Integral Representations of Solutions of Euler Type. - Irregular Singular Points. - Part II Completely Integrable Systems. - Linear Pfaffian Systems and Integrability Condition. - Regular Singularity. - Monodromy Representations. - Middle Convolution.










Altre Informazioni

ISBN:

9783030546625

Condizione: Nuovo
Collana: Lecture Notes in Mathematics
Dimensioni: 235 x 155 mm Ø 629 gr
Formato: Brossura
Illustration Notes:XIII, 396 p. 47 illus.
Pagine Arabe: 396
Pagine Romane: xiii


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