Items related to Ordinary Differential Equations
Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms.
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Review:
"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"
"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"
From the Back Cover:
"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"
"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
From the reviews: "... This book is an excellent text for a course whose goal is a mathematical treatment of differential equations and the related physical systems." L'Enseignment Mathematique "... Arnold's book is unique as a sophisticated but accessible introduction to the modern theory, and we should be grateful that it exists in a convenient language." Mathematical Association of America Monthly
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- PublisherMit Pr
- Publication date1967
- ISBN 10 0262570149
- ISBN 13 9780262570145
- BindingPaperback
- Rating
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