Review

Apr 19, 2018  Geometric methods in the theory of ordinary differential equation by Vladimir. Arnold For undergraduate level please see the following MO post: Good differential equations text for undergraduates who want to become pure mathematicians.

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

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Summary

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.

Not for sale on the Indian subcontinent.

Reviews

• 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

Authors: Arnold, Vladimir I.

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• ISBN 978-3-540-34563-3
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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

From the reviews:

'Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation … . The new edition is highly recommended as a general reference for the essential theory of ordinary differential equations and as a textbook for an introductory course for serious undergraduate or graduate students. … In the US system, it is an excellent text for an introductory graduate course.' (Carmen Chicone, SIAM Review, Vol. 49 (2), 2007)

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'Vladimir Arnold’s is a master, not just of the technical realm of differential equations but of pedagogy and exposition as well. … The writing throughout is crisp and clear. … Arnold’s says that the book is based on a year-long sequence of lectures for second-year mathematics majors in Moscow. In the U.S., this material is probably most appropriate for advanced undergraduates or first-year graduate students.' (William J. Satzer, MathDL, August, 2007)

Buy this book

• ISBN 978-3-540-34563-3
• Free shipping for individuals worldwide
• Usually dispatched within 3 to 5 business days.
• The final prices may differ from the prices shown due to specifics of VAT rules

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Bibliographic Information

• Vladimir I. Arnold

Softcover ISBN

978-3-540-34563-3

Series ISSN

0172-5939

Edition Number

1

Number of Pages

IV, 338

Number of Illustrations

272 b/w illustrations

Additional Information

Original Russion edition published by Nauka, Moscow, 1984

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