Ordinary Differential Equations

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Springer Science & Business Media, May 8, 1992 - Mathematics - 334 pages
6 Reviews
The first two chapters of this book have been thoroughly revised and sig nificantly expanded. Sections have been added on elementary methods of in tegration (on homogeneous and inhomogeneous first-order linear equations and on homogeneous and quasi-homogeneous equations), on first-order linear and quasi-linear partial differential equations, on equations not solved for the derivative, and on Sturm's theorems on the zeros of second-order linear equa tions. Thus the new edition contains all the questions of the current syllabus in the theory of ordinary differential equations. In discussing special devices for integration the author has tried through out to lay bare the geometric essence of the methods being studied and to show how these methods work in applications, especially in mechanics. Thus to solve an inhomogeneous linear equation we introduce the delta-function and calculate the retarded Green's function; quasi-homogeneous equations lead to the theory of similarity and the law of universal gravitation, while the theorem on differentiability of the solution with respect to the initial conditions leads to the study of the relative motion of celestial bodies in neighboring orbits. The author has permitted himself to include some historical digressions in this preface. Differential equations were invented by Newton (1642-1727).
  

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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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