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Heinbockel J.H. — Introduction to tensor calculus and continuum mechanics
Heinbockel J.H. — Introduction to tensor calculus and continuum mechanics

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Название: Introduction to tensor calculus and continuum mechanics

Автор: Heinbockel J.H.

Аннотация:

Introduction to Tensor Calculus and Continuum Mechanics is an advanced College level mathematics text. The first part of the text introduces basic concepts, notations and operations associated with the subject area of tensor calculus. The material presented is developed at a slow pace with a detailed explanation of the many tensor operations. The first half of the text concludes with an introduction to the application of tensor concepts to differential geometry and relativity. The second half of the text presents applications of tensors to areas from continuum mechanics. Tensor calculus is applied to the areas of dynamics, elasticity, fluids, electricity and magnetism. Many of the basic equations from physics, engineering and science are developed which makes the text an excellent reference work. The second half of the text concludes with an introduction to quaternions, multivectors and Clifford algebra.


Язык: en

Рубрика: Математика/Анализ/Тензорный анализ, формы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 367

Добавлена в каталог: 21.10.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$e-\delta$ identity      12
Absolute differentiation      120
Absolute scalar field      43
Absolute tensor      45 46 47 48
Acceleration      121 190 192
Action integral      198
Addition of systems      6 51
Addition of tensors      6 51
Adherence boundary condition      294
Aelotropic material      245
Affine transformation      86 107
Airy stress function      264
Almansi strain tensor      229
Alternating tensor      6 7
Ampere's law      176 301 337 341
Angle between vectors      80 82
angular momentum      218 287
Angular velocity      86 87 201 203
Arc length      60 67 133
Associated tensors      79
Auxiliary magnetic field      338
Axis of symmetry      247
Basic equations elasticity      236 253 270
Basic equations for a continuum      236
Basic equations of fluids      281 287
Basis vectors      1 2 37 48
Beltrami      262
Bernoulli's theorem      292
Biharmonic equation      186 265
Bilinear form      97
Binormal vector      130
Biot — Savart law      336
Bipolar coordinates      73
Boltzmann equation      302 306
boundary conditions      257 294
Bulk coefficient of viscosity      285
bulk modulus      251
Cartesian coordinates      19 20 42 67 83
Cartesian tensors      84 87 226
Cauchy stress law      216
Cauchy — Riemann equations      293 321
Charge density      323
Christoffel symbols      108 110 111
Circulation      293
Codazzi equations      139
Coefficient of viscosity      285
Cofactors      25 26 32
Compatibility equations      259 260 262
Completely skew symmetric system      31
Compound pendulum      195 209
Compressible material      231
Conic sections      151
Conical coordinates      74
Conjugate dyad      49
Conjugate metric tensor      36 77
Conservation of angular momentum      218 295
Conservation of energy      295
Conservation of linear momentum      217 295
Conservation of mass      233 295
Conservative electric field      323
Conservative system      191 298
Constitutive equations      242 251 281 287
Continuity equation      106 234 287 335
Contraction      6 52
Contravariant components      36 44
Contravariant tensor      45
Coordinate curves      37 67
Coordinate surfaces      37 67
Coordinate transformations      37
Coulomb law      322
Covariant components      36 47
Covariant differentiation      113 114 117
Covariant tensor      46
Cross product      11
Curl      21 173
Curvature      130 131 134 149
Curvature tensor      134 145
Curvilinear coordinates      66 81
Cylindrical coordinates      18 42 69
Deformation      222
Derivative of tensor      108
Derivatives and indicial notation      18 31
Determinant      10 25 32 33
Dielectric tensor      333
Differential geometry      129
Diffusion equation      303
Dilatation      232
Direction cosines      85
Displacement vector      333
Dissipation function      297
Distribution function      302
Divergence      21 172
Divergence theorem      24
Dot product      5
Double dot product      50 62
Dual tensor      100
Dummy index      4 5
Dyads      48 62 63
Dynamics      187
e Permutation symbol      6 7 12
Eigenvalues      179 189
Eigenvectors      179 186
Einstein tensor      156
Elastic constants      243 248
Elastic stiffness      242
Elasticity      211 213
Electric flux      327
Electric units      322
Electrodynamics      339
Electromagnetic energy      341
Electromagnetic stress      341 342
Electrostatic field      322 333
Elliptic coordinates      72
Elliptical cylindrical coordinates      71
Enthalpy      298
entropy      300
Epsilon permutation symbol      83
Equation of state      300
Equilibrium equations      273 300
Equipotential curves      325
Euler number      294
Euler — Lagrange equations      192
Euler's equations of motion      204
Eulerian angles      201 209
Eulerian form      287
Eulerian system      227
Faraday's law      176 301 340
Field electric      322
Field lines      324 327
First fundamental form      133 143
Fluids      281
Fourier law      297 299
Free indices      3
Frenet — Serret formulas      131 188
Froude number      294
Gas law      300
Gauss divergence theorem      24 330
Gauss equations      138
Gauss's law for electricity      176 301 328
Gauss's law for magnetism      176 301 341
Gaussian curvature      137 139 149
General tensor      48
Generalized $e-\delta$ identity      84 104
Generalized acceleration      121
Generalized Hooke's law      242
Generalized Kronecker delta      13 31
Generalized stress strain      242
Generalized velocity      121
Geodesic curvature      35 140
Geodesies      140 146
Geometry in Riemannian Space      80
Gradient      20 171
Gradient basis      37
Green's theorem      24
Group properties      41 54
Hamiltonian      208
Heat equation      316
Hexagonal material      247
Higher order tensors      47 93
Hooke's law      212 242 252
Hydrodynamic equations      283
Ideal fluid      283
Idemfactor      50
Incompressible material      231
Index notation      1 2 14
Indicial notation      1 2 14 24
Inertia      30
Inner product      52
Integral theorems      24
Intrinsic derivative      120
Invariant      43
Inviscid fluid      283
Isotropic material      248
Isotropic tensor      104
Jacobian      17 30 40 101 127
Jump discontinuity      330
Kinematic viscosity      302
kinetic energy      201
Kronecker delta      3 8 13 31 76
Lagrange's equation of motion      191 196
Lagrangian      209
Lame's constants      251
Laplacian      174
Linear form      96
Linear momentum      209 287
Linear transformation      86
Linear viscous fluids      284
Lorentz transformation      57
Magnetic field      334
Magnetic permeability      337
Magnetization vector      337
Magnetostatics      334 338
Magnitude of vector      80
Material derivative      234 288
Material symmetry      244 246
Maximum, minimum curvature      130 140
Maxwell equations      176 339
Maxwell transfer equation      308
Mean curvature      137 148
Metric tensor      36 65
Meusnier's theorem      150
Mixed tensor      49
Mohr's circle      185
Moment of inertia      30 184 200
Momentum      217 218
Multilinear forms      96 98
Multiplication of tensors      6 51
Navier — Stokes equations      288 290
Navier's equations      254 257
Newtonian fluids      286
Nonviscous fluid      283
Normal curvature      135 136
Normal plane      188
Normal stress      214
Normal vector      130 132
Notation for physical components      92
Oblate spheroidal coordinates      75
Oblique coordinates      60
Oblique cylindrical coordinates      102
Order      2
Orthogonal coordinates      78 86
Orthotropic material      246
Osculating plane      188
Outer product      6 51
Papkovich — Neuber solution      258
Parabolic coordinates      70
Parabolic cylindrical coordinates      69
Parallel vector field      122
Particle motion      190
Pendulum system      197 210
Perfect gas      283 299
permutations      6
Phase space      302
Physical components      88 91 93
Piezoelectric      300
Pitch, roll, Yaw      209
Plane Couette flow      315
Plane Poiseuille flow      316
Plane strain      263
Plane stress      264
Poisson's equation      329
Poisson's ratio      212
Polar element      273
Polarization vector      333
Polyads      48
potential energy      191
Potential function      323
Poynting's vector      341
Pressure      283
Principal axes      183
Projection      35
Prolated spheroidal coordinates      74
Pully system      194 207
Quotient law      53
Radius of curvature      130 136
Range convention      2 3
Rate of deformation      281 286
Rate of strain      281
Rayleigh implusive flow      317
Reciprocal basis      35 38
Rectifying plane      188
Relative motion      155 202
Relative scalar      127
Relative tensor      50 121
Relativity      151
Reynolds number      294
Ricci's theorem      119
Riemann Christoffel tensor      116 129 139 147
Riemann space      80
Rigid body rotation      199
Rotation of axes      85 87 107
Rules for indices      2
scalar      40 43
Scalar invariant      43 62 105
Scalar potential      191
Scaled variables      293
Second fundamental form      135 145
Second order tensor      47
Shearing stresses      214
simple pendulum      194
Simple pulley system      193
Skew symmetric system      3 31
Skewed coordinates      60 102
Solid angle      328
Space curves      130
Special tensors      65
Spherical coordinates      18 43 56 69 103 194
St. Venant      258
Stokes flow      318
Stokes hypothesis      285
Stokes theorem      24
Straight line      60
strain      218 225 228
Strain deviator      279
Stress      214
Stress deviator      279
Strong conservative form      298
Strouhal number      294
Subscripts      2
Subtraction of tensors      51 62
1 2
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