Ordinary Differential Equations

by Arnold, Vladimir I.

• ISBN13: 9783540345633
• ISBN10: 3540345639
• Format: Paperback
• Copyright: 2006-08-15
• Publisher: SPRINGER - VERLAG

Summary

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.