Overview
- Presents the first systematic account of the classical and modern theory of complex linear differential equations, covering results previously scattered throughout the literature
- Gives a clear introduction to advanced (non-standard) topics and recent developments in the theory
- Offers a detailed presentation with many examples and full proofs, making it accessible to graduate students and non-specialists
- Provides motivation and historical background for each topic covered
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2271)
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About this book
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.
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.
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Keywords
Table of contents (14 chapters)
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Front Matter
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Ordinary Differential Equations
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Front Matter
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Completely Integrable Systems
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Front Matter
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Back Matter
Reviews
“The author has made many contributions to the related global theory of Fuchsian equations, including hypergeometric-type equations and Okubo systems. In this monograph, the author leads the reader to the forefront of this field.” (Shun Shimomura, Mathematical Reviews, March, 2022)
“The main purpose of this interesting book is an introduction to recent developments in the theory of linear ordinary differential systems and linear completely integrable total differential systems. … The book is designed to be suitable for use as a primary textbook in an advanced graduate course or as a supplementary source for beginning graduate courses. … The book contains numerous examples, which can be useful as a reference for researchers.” (Valentine Tyshchenko, zbMATH 1460.34002, 2021)
Authors and Affiliations
Bibliographic Information
Book Title: Linear Differential Equations in the Complex Domain
Book Subtitle: From Classical Theory to Forefront
Authors: Yoshishige Haraoka
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-54663-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-54662-5Published: 17 November 2020
eBook ISBN: 978-3-030-54663-2Published: 16 November 2020
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIII, 396
Number of Illustrations: 47 b/w illustrations
Topics: Analysis, Functions of a Complex Variable, Special Functions, Global Analysis and Analysis on Manifolds