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| Cohen A. — An Introduction to the Lie Theory of One-parameter Groups. With Applications to the Solution of Differential Equations |
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Название: An Introduction to the Lie Theory of One-parameter Groups. With Applications to the Solution of Differential Equations
Автор: Cohen A.
Язык: 
Рубрика: Математика/
Статус предметного указателя: Готов указатель с номерами страниц
ed2k:
Год издания: 1911
Количество страниц: 270
Добавлена в каталог: 14.04.2013
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| Предметный указатель |
Affine transformation 3 54
Alternant 44
Alternant of symbols of extended transformations 209
Asymptotic lines 80
Bernoulli equation 58
Canonical form 26 34 64 155
Canonical variables 26 34 64 156
Change of variables 23 33 188
Characteristic function of infinitesimal contact transformation 186
Classification of two-parameter groups 152
Commutator 45
Complete system 104 106 110
Complete system, equivalent 106
Complete system, Jacobian 107 110
Contact infinitesimal 185
Contact transformation 178 181
Curvature, lines of 81
Curve of union of elements 175 189
Differential equation of 1. order 189
Differential equation of 1. order invariant under group 40 44 45 46 48 50 52 194 231
Differential equation of 2. order invariant under group 86 90 134 137 148 165 236
Differential equation of n. order invariant under group 99 101 236
Differential equation of n. order not invariant under any group 206
Differential invariant 51 88 194
Dilatations 185 186
Displacements 212
Distinct groups 122 123 125
Distinct infinitesimal transformations 7
Elements, lineal 175
Elements, union of 175 194
Equivalent complete systems 106
Essential parameters 214
Essential parameters, condition for 226
Extended group 42 84
Extended point transformation 41 83 180
First differential invariant 51 194
First integral 191
General expression for group leaving differential equation of 1. order unaltered 49
Group 1 28 211
Group of contact transformations 185
Group of infinitesimal transformations 146
Group, distinct 122 123 125
Group, extended 42 84
Group, involving one parameter 1 28
Group, involving r parameters 211
Group, property 2
Group, trivial 39 119 196
Group. generated by infinitesimal transformation 10 12 14 30 220
Homogeneous differential equation (Boole) 93
Identical transformation 4
Independent linear partial differential equations 104
Infinitesimal contact transformation 185
Infinitesimal contact transformation, characteristic function of 186
Infinitesimal contact transformation, symbol of 186
Infinitesimal transformation 6 29 197 215 218
Infinitesimal transformation, distinct 7
Infinitesimal transformation, group generated by 10 12 14 30 220
Infinitesimal transformation, linearly independent 143 217
Infinitesimal transformation, r-parameter group of 146
Infinitesimal transformation, symbol of 8 42 84 85 218
Integrating factor 37 47 69 76
Integrating factor, common to two differential equations 72
Integrating factor, two, for the same differential equation 48
Intermediary integral 191
Invariant 16 31
Invariant, curve 17 18 31 32
Invariant, differential 51 88 194
Invariant, differential equation see "Differential equation"
Invariant, equation 18 32
Invariant, family of curves 20 22
Invariant, linear partial differential equation 115 118 119 122 124
Invariant, point 17 19 31
Invariant, surface 31 32
Inverse transformation 3 29 211
Involute 70
Involute of a circle 70
| Involution, functions in 179
Isothermal curves 72 79 203
Jacobi's identity 121
Jacobian complete system 107 110
Lie group 3
Lie's principal theorem 225
Lineal element 175
Linear ordinary differential equation of 1. order 56 57
Linear ordinary differential equation of 2. order 92 94 139 140 173 174
Linear ordinary differential equation of n. order 102
Linear partial differential equation invariant under a group 115 118 119
Linear partial differential equation invariant under two groups 122 124
Linearly independent infinitesimal transformations 143 217
Linearly independent infinitesimal transformations, number of, leaving differential equation of order n 72
Linearly independent infinitesimal transformations, number of, leaving differential equation of order n, unaltered limited 143 146
Lines of curvature 81
Method of solution of complete system 111 113
Method of solution of differential equation of 1. order 38 49 63 66 193
Method of solution of differential equation of 2. order 88 134 137 165 169 193
Method of solution of differential equation of n. order 101
Method of solution of linear partial differential equation 119 124
Minimal lines 78
n-times-extended group 84
n-times-extended transformation 83
Once-extended group 42
Once-extended transformation 41
Parallel curves 70
Path-curve 4 10 11 17 18 19 31 67
Perspective transformation 3
Point transformation 40
Point transformation, extended 41 83 180
Poissonian symbol 179
Product of transformations 2
Projective transformation, general 213
r-parameter group of infinitesimal transformations 146
r-parameter group of transformations 211 214
Reciprocal polars, transformation by 180 184
Riccati equation 52 59 201
Rotations 2
Second differential invariant 88
Separation of variables 63
Similitudinous transformation 3
Singular solution 66
Subgroup 149
Symbol of extended infinitesimal transformation 42 84 85
Symbol of infinitesimal contact transformation 186
Symbol of infinitesimal transformation 8 218
Transform of a transformation 24
Transformation by reciprocal polars 180 184
Transformation, affine 3 54
Transformation, contact 178 181
Transformation, extended 41 83
Transformation, general projective 213
Transformation, group of 1 28 211
Transformation, identical 4
Transformation, infinitesimal 6 29 185 197 215 218
Transformation, inverse 3 29 211
Transformation, perspective 3
Transformation, point 40
Transformation, product of 2
Transformation, similitudinous 3
Translation 2 53 212
Trivial group 39 119 196
Twice-extended group 84
Twice-extended transformation 83
Two-parameter groups, classification of 152
Two-parameter subgroups always exist 150
Types of differential equations of 1. order invariant under given groups 52 231
Types of differential equations of 2. order invariant under given groups 90 236
Types of differential equations of n. order invariant under given groups 101 236
Union of elements 175 176 194
Union of elements, curve of 175 189
United elements 175
Variables, canonical 26 34 64 156
Variables, change of 23 33 188
Variables, separation of 63
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