Ordinary Differential Equations (Springer Textbook S.) - Softcover

Arnold, Vladimir I.

Softcover

ISBN 10: 3540548130 ISBN 13: 9783540548133

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1992

Synopsis

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. 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." --SIAM REVIEW

About this title

Review

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)

"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)

Synopsis

There are dozens of books on ODEs, but none with the elegantgeometric insight of Arnol'd's book.Arnol'd puts a clear emphasis on the qualitative andgeometric properties of ODEs and their solutions, ratherthan on theroutine presentation of algorithms for solvingspecial classes of equations.Of course, the reader learnshow to solve equations, but with much more understandingof the systems, the solutions and the techniques.Vector fields and one-parameter groups of transformationscome right from the startand Arnol'd uses this "language"throughout the book. This fundamental difference from thestandard presentation allows him to explain some of the realmathematics of ODEs in a very understandable way and withouthidingthe substance.The text is also rich with examples and connections withmechanics. Where possible, Arnol'd proceeds by physicalreasoning, using it as a convenient shorthand for muchlonger formal mathematical reasoning. This technique helpsthe student get a feel for the subject.Following Arnol'd's guiding geometric and qualitativeprinciples, there are 272 figures in the book, but not asingle complicated formula.

Also, the text is peppered withhistoricalremarks, which put the material in context,showing how the ideas have developped since Newton andLeibniz.This book is an excellent text for a course whose goal is amathematical treatment of differential equations and therelated physical systems.

Edition details

• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Publication date: 1992
• ISBN 10: 3540548130
• ISBN 13: 9783540548133
• Binding: Paperback
• Language: English
• Edition number: 2
• Number of pages: 342