Schouten J.A. — Tensor Analysis for Physicists :: Электронная библиотека попечительского совета мехмата МГУ

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Schouten J.A. — Tensor Analysis for Physicists

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Название: Tensor Analysis for Physicists

Автор: Schouten J.A.

Аннотация:

This rigorous and advanced mathematical explanation of classic tensor analysis was written by one of the founders of tensor calculus. Its concise exposition of the mathematical basis of the discipline is integrated with well-chosen physical examples of the theory, including those involving elasticity, classical dynamics, relativity, and Dirac's matrix calculus.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1951

Количество страниц: 275

Добавлена в каталог: 19.05.2013

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Предметный указатель

$A_{\lambda}^{\kappa^{'}}$ , $A_{\lambda^{'}}^{\kappa}$       1
$A_{\lambda}^{\kappa}$       61 115
$E^{X}_{x}$ (v. Dantzig)      252 257
$E_{(\kappa)}^{\kappa_{1}...\kappa_{n}},e^{(\kappa)}_{\lambda_{1}...\lambda_{1}}$       28
$E_{n}$       2 111
$E_{n}$ , centred      3
$g_{A}$       1 115
$G_{eq}$       3 115
$G_{ho}$       3 115
$G_{or}$       3 116
$G_{ro}$       4 116
$G_{sa}$       3 115
$G_{un}$       42 244
$g_{\lambda\kappa}$ , $g^{\kappa\lambda}$       91 92
$G_{\mu\lambda}$       100 123
$I_{(h)}^{\kappa_{1}...\kappa_{n}},i^{(h)}_{\lambda_{1}...\lambda_{1}}$       38 117
$K_{\mu\lambda}$       100 13
$K_{\nu\dot{\mu}\lambda^{\kappa}}$       99
$R_{n}$       111
$R_{\dot{\nu}\dot{\mu}\dot{\lambda}} ^{\kappa}$       98 122
$R_{\mu\lambda}$       100 123
$S_{\dot{\mu}\dot{\lambda}} ^{\kappa}$       87 121
$S_{\mu\lambda}$       139
$T^{\kappa\lambda}$ , $\mathfrak{T}^{\kappa\lambda}$       142
$U_{n}$       42 240
$V_{n}$       91
$X_{n-1}$ -building covariant vector fields      64
$X_{n}$       59 110
$[\mathfrak{L}]$       79
$\Delta$       84ff 121
$\Delta$ -density      29 113
$\delta$ -function      251
$\delta_{\lambda}^{\kappa}$ , $\delta^{h}_{i}$ , $\delta_{\lambda}^{\kappa^{'}}$       14 19 61
$\Gamma^{\kappa_{\mu\lambda}}$       85 121 123
$\langle|,|\rangle$       251
$\ll$       172
$\mathfrak{g}$       39 92 117
$\mathfrak{G}_{\lambda\kappa}$       101 123 229
$\mathfrak{I}$       39
$\nabla^{2}$       104
$\nabla_{\mu}$       65 66 86ff 121
$\Omega_{ji} ^{h}$       82 121 144
$\widetilde{\mathfrak{E}}^{\kappa_{1}...\kappa_{n}},\widetilde{\mathfrak{e}}_{\lambda_{1}...\lambda_{1}}$       29 115
$\{_{\mu\lambda}^{\kappa}\}$       92 122
$_{=}^{*}$       15
$_{=}^{h}$       103
$_{\lambda}^{e^{\kappa}}$ , $^{\kappa}_{e_{\lambda}}$       12 61
Absolute dimension      127 130ff
Absolute invariant      78 119
Addition      19 113
Affine geometry      2
Affine group      1
Affine space      2
Affinor      17 112
Allowable coordinate systems      2 59
Allowable systems of fundamental units      126
Alternating product      113
Alternation      20 113
angle      39 117
Anholonomic components      81
Anholonomic coordinate systems      81 102 123 194
Anholonomic mechanical systems      194
Antilinear transformation      249
Antisymmetric tensor      23
Axial bivector      52
Axial vector      52f
Basic bra      266
Bianchi, identity of      100 123
Bibliography      268
Birkhoff, G.D.      190
Bivector      54 56
Bivector-tensor      99
Bose statistics      254
Boundary value problems      106 124
Bra      243 250ff
Brandt, L.      9 59
Brillouin, L.      9 59 139 169
Brinkman, H.W.      239
Burkhardt, H.      103
Cady, W.G.      139 147 152 164 169 179 180 187
Cartesian coordinate systems      37
Cayley’s matrix calculus      40
Centre      3
Centred $E_{n}$       3 111
Christoffel symbol      92 102
Christoffel, L.B.      169
Commuting operators      247
Commuting set      259
Complete set of eigenkets (bras)      248 256
Conservation of momentum and energy      227
Contraction      19
Contravariant      9
Coordinate transformations      2
Coordinate- $E_{p}$ ’s      6
Coordinates, allowable      2 59
Coordinates, curvilinear      59 110
Coordinates, rectilinear      1 111
Coupling constants      184
Covariant vector      10
Crystal classes      152ff
Curvature affinor      98f 103 122f
Curvature of $V_{2}$       102
Curvature of $V_{n}$       94ff
Curvilinear coordinates      59 110
D, $\mathfrak{D}^{\alpha}$       131 133 215
Dead indices      13 113
Decomposition of p-vector into blades      27
Definite, positive, negative      35 242
Deformation      139
densities      31 13
Derived units      126
Deviator      156
Diagonal matrix      262f
Dimension of domain      12 112
Dirac, P.A.M.      197 240 243 247 250 252 253 255 256 259 263 265 266 267
Direction      5
Displacement      84
div      67 118
Div, divergence      66 118
Divergence, principal theorem of      73
Domain with respect to an index      21
Domain, contravariant, covariant      12 112
Dorgelo, H.      29 45 127 131
Duration      37 91
Duschek, A.      40
Ecart geodesique      193
Eddington, A.S.      214
Effect, linear      160
Eiconal functions      202 203
Eigenket (bra)      246 254
Eigenstate      256
Eigenvalue      42 115 254 256
Eigenvector      43 115
Einstein convention      1
Einstein space      229 239
Einstein, A.      214
Eisenhart, L.P.      9 19 59 84 91
Elastic coefficients, adiabatic      144
Elastic coefficients, element of world lino      201
Elastic coefficients, elementary divisors      34
Elastic coefficients, isothermal      145
Emde, F.      105
Enantiomorphous      155
Energy function      174 178
Equiscalar $X_{n-1}$ 's      65
Equivoluminar      3
Euler      210
Eulerian angles      211
F, $F_{\beta}$       131 133 135
Fair, J.E.      164 185 187

Fermi statistics      254
Field in $X_{n}$       60
Field invariant for point transformations      75
Field of physical objects      127
Film-space      193
First integral      205 207
Fixed indices      2 110
Fokker, A.      171 214
Four-dimensional velocity vector      218 222
Free indices      19
Fresnel equations      177
Functions in involution      206
Functions of observables      257ff
Fundamental tensor      36 42 91 92 117 242
Fundamental units      126
Galilei group      220
Gauss, equation of      193
Gauss, theorem of      70
Generating set of transformations      153
Geodesic      88 122
Geometric image      127 130ff
Geometric object, quantity      9 60 112
Giorgi, system of      131
Givens, J.W.      24 40 45 58
Grad, gradient      64 118
Gravitation      229ff
Green’s function      107 125
Green’s identities      104 123f
Green’s medium      176
Green’s Theorem      105 124
Group      1
H, $\mathfrak{H}^{\alpha\beta}$       131 133 215
Hamel, G.      195 197
Hamilton — Jacobi equations      203
Hamiltonian equation      198 201
Hamiltonian function      198
Hamiltonian relation      200
Hermitian bivector      241
Hermitian tensor      241
Horak, Z.      194
Hybrid quantities      241
Hyperplane, coordinates      6
Identifications after introduction of screw sense      46
Identifications for $G_{eq}$       45 116
Identifications for $G_{or}$       46 116 117
Identifications for $G_{ro}$       47ff 116 117
Identities of the curvature affinor      99 123
Identity of Bianchi      100 123
Improper $E_{p-1}$       5
Incompressible fluid in $X_{3}$       72
indefinite      35 242
INDEX      35 114
indices      1
Indices, dead, living      13
Indices, running, fixed      2 110
Indices, saturated, free      19
Intermediate components      17 110
Intersection      5
Interval functions      251
Inverse      1 18
Isomer      20 113
Jahnke, E.      105
Jordan, P.      240
Junction      6
K      100 123
Kasner, E.      239
Kernel letter      2 110
Kernel-index method      2
Ket      243 250ff
Klein, principle of      4
Koga, I.      177
Kramers, H.      240
Kronecker, L.      103 105
Kronocker symbols      14 19 61
Lack, F.K.      164 185 187
Lagrange      210
Lagrange derivative      78ff 120 123
Lagrange equation      80 198 200
Leibniz, rule of      77
Length      37 91 117 252
Levi Civita, T.      5 59 84
Lichnerowicz, A.      1 9
Lie derivative      76ff 114
Lie differential      74ff 119
Linear displacement      85 121
Lowering of indices      38
Mason, W.P.      142 147 164 179 180
Matrices and quantities of valence two      33 114
Matrix calculus in $E_{n}$ and $R_{n}$       39 117
Matter density      225
Maupertuis equation      210
Mean energy density $\mathfrak{E}$       230
Mean energy-current density $\mathfrak{E}^{\alpha}$       231
Mean momentum-current density $\mathfrak{F}^{\alpha\beta}$       231
Mean particle current density $\mathfrak{R} \dot{u}^{\alpha}$       230
Measuring vectors      12 61
Meet      5
Meyer, W.F.      103
Michal, A.D.      9
Michelson — Morley experiment      218
Minkowski geometry      216
Minor      1
Mitschleppen      75
Mixed affinor      17 112
Mixed product      113
Mixing      20 113
Momentum-energy tensor density      225f
Momentum-energy vector      223
Multiplication      19 113
Multiplication of matrices      39
Multivector      23ff 113
n-vectors      28
nabla      86
Natural derivative      64 66 118
Natural parameter      89 122
Neumann, principle of      156
Newton’s gravitational constant      288
Nonor      157
Norm      243
Normal coordinates      89ff 122
Normal forms of bivector      35
Normal forms of tensor of valence two      34
Normalizing eigenkets (bras) to r, to $\delta$       255 257
Null cone      37 117
Null curve      91 94
Null direction      91
Null form      4
Null manifold      4
Null vector      3 24 37 91 117
Object of anholonomity      82 120
Object transformations      9
Observable      256
Orientation      3 7 112
Oriented $R_{n}$       4
Oriented centred $E_{n}$       3
Origin      3
Orthogonal normal forms      42
Orthogonal transformation      3
Orthogonality (kots and bras)      252
Ostrogradski, theorem of      70
parallel      5
Parallelepiped      25
Parallelogram of forces      10
Parallelotope      25
Parametric form      5
Particle density $\mathfrak{R}$       91 230
Pauli, W.      214 239
Perfect fluid      237
Perfectly perfect fluid      239
Phase factor      243 255

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