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Cohen A. — An Introduction to the Lie Theory of One-parameter Groups. With Applications to the Solution of Differential Equations
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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1911

Количество страниц: 270

Добавлена в каталог: 14.04.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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