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A fresh modern approach to the geometric qualitative theory of ordinary differential equations ... suitable for advanced undergraduates and some graduate students. The notions of vector field, phase space, phase flow, and one parameter groups of transformations dominate the entire presentation. The author is acutely aware of the pitfalls of this abstract approach (e.g., putting the reader to sleep) and does a brilliant job of presenting only the most essential ideas with an easily grasped notation, a minimum formalism, and very careful motivation. -- Technometrics This college-level textbook treats the subject of ordinary differential equations in an entirely new way. A wealth of topics is presented masterfully, accompanied by many thought-provoking examples, problems, and 259 figures. The author emphasizes the geometrical and intuitive aspects and at the same time familiarizes the student with concepts, such as flows and manifolds and tangent bundles, traditionally not found in textbooks of this level. The exposition is guided by applications taken mainly from mechanics. One can expect this book to bring new life into this old subject. -- American Scientist
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