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Hestenes D., Sobczyk G. — Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics (Fundamental Theories of Physics)
Hestenes D., Sobczyk G. — Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics (Fundamental Theories of Physics)

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Название: Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics (Fundamental Theories of Physics)

Авторы: Hestenes D., Sobczyk G.

Аннотация:

i have been working a few years in geometric calculus and i believe this book should be in every house of every geometrist and every person that is intersted in geometric concepts with physics applications


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd

Год издания: 1987

Количество страниц: 165

Добавлена в каталог: 20.07.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
*-operator      241
Active transformation      135
Adjoint, exterior derivative      242
Adjoint, function      50 55
Adjoint, matrix      33
Adjoint, orthogonal transformation      86
Adjoint, outermorphism      68 116
Adjoint, transformation      50 166
Adjugate vectors      37
Adjugate vectors, matrix      33
Affine connexion      221
Affine curvature tensor      223
Affine differential      223
Affine extensor      221
Affine geometry      221
Affine tensor      222
Algebraic extension      xiii
Alternating r-form      33 132
Analytic function      183
Analytic function on a manifold      261
Angle between multivectors      14
Angular velocity      163
Anticonformal tensor      211
Antiderivative operator      259
Argument principle      274
Axioms of geometric algebra      3
Basis      17
Bazin's identity      38
Bianchi identity      191 196
Biform      117
Biform, selfdual      124
Bilinear forms      96
Bilinear forms, inner product      96
Bilinear forms, non-singular      97
Bilinear forms, positive definite      101
Bilinear forms, skew      97
Bilinear forms, symmetric      101
Bivector      4 80 83
Bivector, Darboux      240
Bivector, null      300
Blade      4
Blade, null      42
Blade, preserving      114
Blade, singular      42
Boundary      250
Boundary, point      140
Bracket      159
Bracket, dual      161 173
Canonical forms      64 94
Canonical normal transformation      88
Canonical orthogonal transformation      90
Canonical rotation      91
Canonical rotor      107
Canonical skewsymmetric transformation      80
Canonical symmetric transformation      79
Cartan      225 299
Cartan, first structural equation      245
Cartan, mobile      230
Cartan, second structural equation      245
Cauchy's integral formula      263 265
Cauchy's integral formula, several complex variables      265
Cayley form for simple rotor      108
Cayley — Hamilton theorem      73
Central projection      174
Chain rule      56
Change of variables      266
Characteristic equation      73
Characteristic equation, multivectors      71 85
Characteristic equation, polynomial      73 74 77
Chern      279
Chord algebra      139 140
Christoffel symbols      236
Classical group      105
Classical mechanics      viii
Clifford algebra      vii 42
Clifford group      104
Clifford numbers      42
Closed form      146 156
Closed manifold      251 269
Cocurl      156
Codazzi — Mainardi      195 198
Coderivative      155 204
Codifferential      155 202
Codifferential, exterior      156
Codifferential, related manifolds      202
Codivergence      156
Coefficients of connection      235
Cohomology theory      252 276
Combinatorial identity      59
Commutator product      14
Comoving frame      237
Compact group      301
Complex plane      181
Complex r-vector      113
Complex scalars      122
Compound determinant      38
Conformal tensor      210
Conformal transformation      210 286
Conformal Weyl tensor      219
Conformally related manifolds      210
Conjugation      80
Connection      221
Connection, 1-forms      244
Connection, coefficients of      235
Constant of a manifold      251
Continuity of rotation      108
Contraction      114 132
Contraction, r-form      34
Contravariant components      133
Coordinate frame      228
Coordinate functions      228
coordinates      228
Coordinates, Plucker      30
Covariant components      133
Covariant derivative      155 236
Cramer's rule      32
Curl      49
Curl tensor      150 163 189
Curvature      191 232
Curvature, classical covariant form      246
Curvature, extrinsic      195
Curvature, first      254
Curvature, Gaussian      198
Curvature, geodesic      279
Curvature, intrinsic      195
Curvature, mean      197
Curvature, Riemann      190 191
Curvature, scalar      193
Curvature, total      195
Darboux bivector      240
Degree formula      268
Degree of a mapping      268
Delta-function      260
Derivative      45 55 141 155
Derivative from an integral      252
Derivative of a skew transformation      80
Derivative, directional      45 54 141
Derivative, factorization      60 61
Derivative, intrinsic      155
Derivative, manifold      140 252 254
Derivative, multivector      54
Derivative, point      142 252
Derivative, simplicial      61
Derivative, vector      45 49 252
Determinant      35
Determinant of a matrix      36 72
Determinant, transformation      33 36 70
Differentiable vector manifold      140
Differential      45 54 142 165
Differential form      146 241
Differential form, double dual      241
Differential form, dual      241
Differential form, exterior derivative      242
Differential of an extensor      142
Differential of the identity      48
Differential, exterior      145
Differential, first      45
Differential, interior      146
Differential, left      286
Differential, mobile      231
Differential, product rule      47 49
Differential, right      286
Differential, scalar      46
Differential, second      48 54 143
Differentiation formulas      51 52
Differentiation formulas of pesudoscalar      154
Differentiation formulas, identities      57 58
Direct sum      24
Directed integral      250 251
Directed volume element      250
Directional derivative      141
Directional derivative, coderivative      155 204
Divergence      49 147 172 255
Divergence from an integral      255
Dual form      241
Dual frame      28
Dual frame of 1-forms      244
Dual frame of 1-forms, bracket      161 173
Dual frame of 1-forms, space      22
Duality      22 28
Duality of inner and outer products      23
Eigen-blade      76
Eigen-value      75 88
Eigen-vector      75
Einstein tensor      194
Elliptic rotor      107
Embedding algebra      140
Embedding problem      140
Embedding space      140
Euclidean axiom      41 101
Euclidean metric      102
Euclidean space      102
Euler characteristic      276
Extensor      131 142
Extensor, coderivative      155
Extensor, field      142
Exterior coedifferential      156
Exterior derivative      242
Exterior differential      145 255
Exterior product      34
Factor space      26
Factor space, factoring      24 61
Fermi — Walker transport      238
Fiducial frame      230
Fiducial system      230
Fiducial tensor      230
Field      141
Field, closed      156
Field, exact      156
Field, index      272
Field, tensor      142
Flanders      279
Frame      27 226
Frame, metric of      226
Frame, pseudoscalar of      29 226
Frame, reciprocal      28 226
Franke's identity      40
Frenet equations      239
Fundamental theorem of calculus      256
Fundamental theorem of Lie group theory      288
Gauss map      198
Gauss Theorem (generalized)      258
Gauss — Bonnet theorem      279
Gauss — Bonnet theorem, generalized      276
Gaussian curvature      198 276
Gaussian curvature of m-sphere      199
Geodesic      205 238
Geodesic curvature      279
Geodesic curvature, equation      206
Geometric algebra      xiii 3 19
Geometric algebra of an n-vector      19
Geometric algebra, dimension      19
Geometric algebra, extension of number      xiii
Geometric algebra, signature of      42
Grade      1 4
Grade of a tensor      131
Grade, operator      4
Grade, preserving      114
Gradient      49
Gram — Schmidt orthogonalization      28
Green's function      261
Group generator      288
Group germ      285
Group manifold      284
Haar measure      289
Helmholtz theorem      260
Homogeneous      4
Homogeneous, coordinates      302
Homogeneous, function      136
Homogeneous, multivector      4
Homogeneous, polynomial      136
Homology theory      252
Hyperbolic rotor      107
Hypersurface      196
Hypersurface, mean curvature of      197
imaginary numbers      xii 113 180
Implicit function theorem      271
Induced transformation      165
Induced transformation of a form      242
Induced transformation of a manifold      173
Inner product      6
Inner product, bilinear form      96
Integrability      48 51 143 146 151 170 229
Integrability, differential      48
Integrability, mobiles      233
Integrability, projections      149
Integrability, vector derivative      51
integral      250
Integral, change of variables      267
Integral, Kronecker      273
Integral, oriented      250
Integral, Riemann      250
Interior differential      146
Interior product of r-forms      34
Interior product of r-forms of differential forms      243
Intersection of vector spaces      24
Intrinsic curvature      195
Inverse function theorem      269 270
Inverse of an r-blade      17
Inversions of Euclidean space      175
Isometric transformation      210 214
Jacobi identity      14 228
Jacobi identity for determinants      39
Jacobian      166 171 267
Killing form      299
Klein, Felix      xi
Kronecker delta      28
Kronecker integral      273
Lagrange identity      37
Laplace expansion      35
Laplacian      51 158 186
Law of Cosines      14
Left differential      286
Left translation      286
Lie algebra      283 288
Lie bracket      53 159 289
Lie group      284
Lie's theorems      288
Linear space      20
Linear transformation      64 66
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