Ordinary Differential Equations with Applications

Couverture
Springer Science & Business Media, 1999 - 561 pages
This book developed over 20 years of the author teaching the course at his own university. It serves as a text for a graduate level course in the theory of ordinary differential equations, written from a dynamical systems point of view. It contains both theory and applications, with the applications interwoven with the theory throughout the text. The author also links ordinary differential equations with advanced mathematical topics such as differential geometry, Lie group theory, analysis in infinite-dimensional spaces and even abstract algebra. The second edition incorporates corrections and improvements of the original text. New material includes a proof of the Grobman-Hartman theorem for flows based on the Lie derivative, more extensive treatment of the Euler-Lagrange equation and its applications, a proof of Noether's theorem on the existence of first integrals in the presence of symmetries and a new section on dynamic bifurcation with a proof of Pontryagin's formula. The impressive array of existing exercises has been more than doubled in size and further enhanced in scope, providing mathematics, physical science and engineering graduate students with a thorough introduction to the theory and application of ordinary differential equations. Reviews of the first edition: ``As an applied mathematics text on linear and nonlinear equations, the book by Chicone is written with stimulating enthusiasm. It will certainly appeal to many students and researchers.'' -- F. Verhulst, SIAM Review ``The author writes lucidly and in an engaging conversational style. His book is wide-ranging in its subject matter, thorough in its presentation, and written at a generally high level of generality, detail, and rigor.'' -- D. S. Shafer, Mathematical Reviews.
 

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Table des matières

II
1
III
4
IV
6
V
12
VI
14
VII
17
VIII
23
IX
28
XLVI
247
XLVII
249
XLVIII
261
XLIX
274
L
278
LI
283
LII
302
LIII
305

X
36
XI
44
XII
52
XIII
56
XIV
71
XVI
79
XVII
93
XVIII
98
XIX
100
XX
106
XXI
116
XXII
117
XXIII
127
XXIV
128
XXVI
130
XXVII
131
XXVIII
135
XXIX
151
XXX
155
XXXI
162
XXXII
176
XXXIII
179
XXXIV
183
XXXV
185
XXXVI
199
XXXVII
203
XXXVIII
205
XXXIX
206
XL
215
XLI
222
XLII
228
XLIII
233
XLIV
236
XLV
241
LV
311
LVI
316
LVII
324
LVIII
326
LIX
340
LX
343
LXII
347
LXIII
356
LXIV
367
LXV
374
LXVI
382
LXVII
384
LXVIII
391
LXIX
396
LXX
406
LXXI
421
LXXII
422
LXXIII
431
LXXIV
434
LXXV
451
LXXVI
460
LXXVII
477
LXXVIII
483
LXXIX
484
LXXXI
486
LXXXII
487
LXXXIII
489
LXXXIV
496
LXXXV
502
LXXXVI
513
LXXXVII
530
LXXXVIII
545
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