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Bliss G.A. — Lectures on the Calculus of Variations
Bliss G.A. — Lectures on the Calculus of Variations



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Название: Lectures on the Calculus of Variations

Автор: Bliss G.A.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1946

Количество страниц: 292

Добавлена в каталог: 03.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Accessory minimum problems and differential equations      27 55 84 89 118 228 229
Accessory minimum problems and differential equations, canonical accessory equations      135 229
Accessory minimum problems and differential equations, conjugate systems of solutions      233
Admissible sets of variables and arcs      7 66 133 194
Admissible variations      195
Auxiliary theorems for the problem in 3-space      18 38
Auxiliary theorems for the problem of Bolza      237
bernoulli      4 147
BLISS      13 16 54 60 147 187 219 260 264 269
Bolza      v 43 147 157 187 188 219 269
Boundary value problems      260
Canonical variables and equations      65 92 132 207 209
Canonical variables and equations for second variation      134 229
Caratheodory      77 188
Characteristic numbers and sets      261
Clebsch      187 219 220
Clebsch, his necessary condition III for the problem of Bolza      224
Conjugate points      28 84 253
Conjugate points, determination of      32 88 119 259
Conjugate points, geometric interpretation      34
Conjugate points, two definitions      26 28
Conjugate systems of solutions of the accessory equations      233
Cope      187
Curves of quickest descent      78
Darboux      24
Elementary family of arcs      194
Envelope theorems      24 25 88
Envelope theorems for parametric problems      116
Equivalence of problems      189
Erdman, corner condition      12 203
Euler      37
Euler, differential equations      12 82 87 111 203
examples      v
Examples, brachistochrone problem      4
Examples, shortest distance problem      3
Examples, the integral of the special relativity theory      8
Existence theorems for differential equations      274 276
Existence theorems for differential equations, derivatives of solutions with respect to constants of integration      278 281 282
Existence theorems for differential equations, the imbedding theorem      277
Extremals      15 111 207
Extremals as characteristics of the Hamilton — Jacobi equation      73
Extremals of a field      45 51 125 238
Extremals, non-singular      15 207
Fields of extremals      44 124 237
Fields of extremals, method of constructing      46 237
Focal points for general problems with one end-point variable      170
Focal points of a surface in 3-space      150
Focal points, dependence of focal points upon curvature      175
Fundamental formula related to second variation      59 99
Fundamental lemma      10
Galileo      3
Goldstine      vi 7 148 170 257
Graves      vi 43 147 188 219
Hahn      7 219
Hahn, theorem of Hahn      159
Hamilton      65 67 81 92
Hamilton, construction of a complete integral      141
Hamilton, the Hamilton — Jacobi partial differential equation      71 94 138
Hestenes      vi 41 147 148 187 188 264
Hilbert, differentiability condition      13 204
hu      187
Imbedding lemma      196 198
Imbedding theorems for an admissible arc in a family of such arcs      196 198
Imbedding theorems for differential equations in general      277
Imbedding theorems for parametric problems      112
Imbedding theorems for problem of Bolza      208
Imbedding theorems for problems in 3-space      16 68
Implicit function theorems      270 272
Integrals independent of the path of integration      49
jacobi      37 65 67 81 92 147
Jacobi, condition IV for other problems      83 88 116
Jacobi, differential equations      27
Jacobi, his necessary condition IV for the problem in 3-space      26 27
Kneser      147
Lagrange      187 188
legendre      23 37
Levi      54
Malnate      54
Mayer      37 187 188 219
McShane      vi 187 188 219
Morse      vi 157 187 188 219
Multiplier rule      202
Myers, F.G.      188
Myers, S.B.      187 219
Non-tangency condition      192
Normality for minima of functions of a finite number of variables      210
Normality for the problem of Bolza      213
Normality on an interval      218
Notations for conditions, $II^{'}_{N}$      41 127 235
Notations for conditions, $IV^{'}_{1}$, $IV^{'}_{2}$, $IV_{3}$      257 263
Notations for conditions, I, II, III      11 22 87 108 235
Notations for conditions, IV      26 83 88 117 165 235
Notations for conditions, primed conditions      40 127 166 235
Parametric problems      102
Parametric problems, fundamental properties of their integrands      106
Parametric problems, their integrals      104
Reid      vi 41 43 54 188 219
Schoenberg      187
Separated end-conditions      191
Slope functions of a family of extremals      38
Slope functions of a field      44 51 89 124 237
Sufficiency theorems for abnormal cases of Hestenes      264
Sufficiency theorems for strong relative minima      42 235
Sufficiency theorems for weak relative minima      40 252
Sufficiency theorems without the use of fields      59 62
Sufficiency theorems, fundamental sufficiency theorems      46 125 241 247
Sufficiency theorems, table of necessary and of sufficient conditions for a minimum      43 132
Transversality      25 149 162 202
Transversality, transversal surface      49
Variations      6
Variations, equations of variation      194
Variations, first and second variations      10 84 97 199 226 243
Variations, positive definite second variation      227
Variations` of an admissible family of arcs      195
Von Escherich      219
Weierstrass      37 41 43 54 220
Weierstrass, corner condition      12 82
Weierstrass, his integral formula      45 56 125 241
Weierstrass, his necessary condition II      22 83 109 223
Zermelo      24
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