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An introduction to ordinary differential equations. (English) Zbl 1158.34001
Universitext. New York, NY: Springer (ISBN 978-0-387-71275-8/pbk). xii, 322 p. (2008).
The textbook is devoted to a systematic and rigorous introduction to the theory of ordinary differential equations. It is organized into 42 class-tested lectures, Preface, References and Index. The book covers topics such as: historical notes, exact equations, existence, uniqueness, Picard approximation and continuous dependence of initial conditions, linear systems, periodic solutions and asymptotic behavior, stability theory, oscillatory equations, linear boundary value problems and Green’s functions, maximum principles, Sturm-Liouville problems and eigenfunction expansions, nonlinear boundary value problems and topics for further studies. The theoretical treatment is organized around theorems and complete proofs, while the practical part include numerous exercises with answers or hints. Written by two prolific leaders in the field of ordinary differential equations and nonlinear analysis, the textbook provides a very clear, well-organized and lucid introduction to ordinary differential equations, with an implicit orientation towards the most recent research topics and methods in the field and related areas.

MSC:
34-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations
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