Ordinary Differential Equations

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Springer Science & Business Media, 1992 - Differential equations - 334 pages
6 Reviews

There are dozens of books on ODEs, but none with the elegant geometric insight of Arnol'd's book. Arnol'd puts a clear emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on theroutine presentation of algorithms for solving special classes of equations.Of course, the reader learns how to solve equations, but with much more understanding of the systems, the solutions and the techniques. Vector fields and one-parameter groups of transformations come right from the startand Arnol'd uses this "language" throughout the book. This fundamental difference from the standard presentation allows him to explain some of the real mathematics of ODEs in a very understandable way and without hidingthe substance. The text is also rich with examples and connections with mechanics. Where possible, Arnol'd proceeds by physical reasoning, using it as a convenient shorthand for much longer formal mathematical reasoning. This technique helps the student get a feel for the subject. Following Arnol'd's guiding geometric and qualitative principles, there are 272 figures in the book, but not a single complicated formula. Also, the text is peppered with historicalremarks, which put the material in context, showing how the ideas have developped since Newton and Leibniz. This book is an excellent text for a course whose goal is a mathematical treatment of differential equations and the related physical systems.

  

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Contents

I
13
II
36
III
48
IV
57
V
66
VI
76
VII
89
IX
104
XXIII
195
XXIV
199
XXV
210
XXVI
215
XXVII
221
XXVIII
229
XXIX
241
XXX
256

X
116
XI
121
XII
129
XIII
138
XIV
152
XVI
155
XVII
162
XVIII
169
XIX
173
XX
177
XXI
181
XXII
185
XXXI
264
XXXII
267
XXXIV
269
XXXV
279
XXXVI
288
XXXVIII
298
XXXIX
304
XL
309
XLI
323
XLII
324
XLIII
331
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About the author (1992)

Arnol'd, Steklov Mathematical Institute

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