Page 370 - Intro to Tensor Calculus
P. 370
364 INDEX
D
Deformation 222
Equilibrium equations 273,300
Derivative of tensor 108
Elastic constants 243,248
Derivatives and indicial notation 18, 31
Equipotential curves 325
Determinant 10, 25, 32, 33
Euler number 294
Dielectric tensor 333
Euler-Lagrange equations 192
Differential geometry 129
Eulerian angles 201, 209
Diffusion equation 303
Eulerian form 287
Dilatation 232
Eulerian system 227
Direction cosines 85
Eulers equations of motion 204
Displacement vector 333
F
Dissipation function 297
Distribution function 302 Faraday’s law 176,301, 340
Divergence 21, 172 Field lines 324, 327
Divergence theorem 24 Field electric 322
Dot product 5 First fundamental form 133,143
Double dot product 50, 62 Fourier law 297, 299
Dual tensor 100 Free indices 3
Dummy index 4, 5 Frenet-Serret formulas 131, 188
Dyads 48,62,63 Froude number 294
Dynamics 187 Fluids 281
E G
e Permutation symbol 6, 7, 12 Gas law 300
e-δ identity 12 Gauss divergence theorem 24, 330
Eigenvalues 179,189 Gauss equations 138
Eigenvectors 179,186 Gauss’s law for electricity 176,301,328
Einstein tensor 156 Gauss’s law for magnetism 176,301,341
Elastic constants 248 Gaussian curvature 137,139, 149
Elastic stiffness 242 Geodesics 140, 146
Elasticity 211,213 Geodesic curvature 135, 140
Electrostatic field 322,333 General tensor 48
Electric flux 327 Generalized e − δ identity 84, 104
Electric units 322 Generalized Hooke’s law 242
Electrodynamics 339 Generalized Kronecker delta 13, 31
Electromagnetic energy 341 Generalized stress strain 242
Electromagnetic stress 341,342 Geometry in Riemannian Space 80
Elliptic coordinates 72 Gradient 20, 171
Elliptical cylindrical coordinates 71 Gradient basis 37
Enthalpy 298 Green’s theorem 24
Entropy 300 Group properties 41, 54
Epsilon permutation symbol 83 Generalized velocity 121
Equation of state 300 Generalized acceleration 121
