Linear Differential Equations in the Complex Domain

- 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.

"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)