Linear Differential Equations in the Complex Domain

From Classical Theory to Forefront
1. Auflage 2020
ISBN: 978-3-030-54662-5
Verlag: Springer International Publishing

Buch, Englisch, Band 2271, 396 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 622 g

Reihe: Lecture Notes in Mathematics

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 usedifferential equations. 

Zielgruppe

Research

Autoren/Hrsg.

Haraoka, Yoshishige

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

- 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.