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Differentialgleichungen im komplexen Gebiet. (Diferenciální rovnice v komplexním oboru.) (Czech) Zbl 0326.34005
Praha: Československá Akademie Věd. 283 S. Kcs 25.00 (1975).
The present book gives a very good explanation of the basic theory of ordinary differential equations and their systems in the complex domain. The results lead to the practical use when studying some special functions. It is assumed that the reader is familiar with the theory of functions in a complex variable and with the basic theory of real analysis. The book is designed to serve as a textbook for an advanced course and as a research monograph. The bibliography contains 24 titles.
The contents are divided into 6 chapters: the first chapter is concerned with the theory of functions of several complex variables. The second chapter deals with existence theorems for solutions of systems of ordinary differential equations in the complex domain. The dependence of solutions on the initial conditions and on parameters is studied too. The third chapter is devoted to the linear equations and their systems.
MSC:
34M99 Ordinary differential equations in the complex domain
34-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations
32-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces
33-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions