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Borisenko A.I., Tarapov I.E. — Vector and Tensor Analysis with Applications
Borisenko A.I., Tarapov I.E. — Vector and Tensor Analysis with Applications

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Название: Vector and Tensor Analysis with Applications

Авторы: Borisenko A.I., Tarapov I.E.

Аннотация:

The present book is a freely revised and restyled version of the third edition of the Russian original (Moscow, 1966). As in other volumes of this series, I have not hesitated to introduce a number of pedagogical and mathematical improvements that occurred to me in the course of doing the translation. I have also added a brief Bibliography, confined to books in English dealing with approximately the same topics, at about the same level.


Язык: en

Рубрика: Математика/Алгебра/Линейная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: revised English edition

Год издания: 1968

Количество страниц: 257

Добавлена в каталог: 02.12.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Acceleration field of a moving fluid      165—166
Angular velocity      45
Antisymmetrization      107
Arc length      32 86
Archimedes’ law      208
Aris, R.      72 96 97 204 206
Axial vector      18 109
Barotropic flow      233
Basis      9
Basis vectors      9 85
Basis vectors, direct transformation of      13
Basis vectors, direct transformation of, coefficients of      13
Basis vectors, inverse transformation of      13
Basis vectors, inverse transformation of, coefficients of      13
Basis, left-handed      21
Basis, local      85
Basis, orthogonal      34
Basis, reciprocal      24
Basis, right-handed      21
Bernoulli’s law      234
Biharmonic equation      232
Biot — Savart law      214
Bipolar coordinates      101
Bound vector      3
Boyanovitch, D.      240
Buck, R. C      140
Cartesian tensors      61
Center of charge      48
Center of mass      54
Characteristic directions      109
Characteristic equation      114
Characteristic plane      119
Characteristic values      109
Characteristic vectors      109
Christoffel symbols      187—190
Christoffel symbols of the first kind      187
Christoffel symbols of the second kind      188
Circulation      136 235 236
Collinearity condition      43
Collision of particles      49—51
components      15
Components, contravariant      28
Components, covariant      28
Components, physical      30
Constitutive relations      228
Contravariant components      28
Contravariant components, relation of, to covariant components      31
Control surface      210
Coordinate curve      11 84
Coordinate curve, positive direction along      85
Coordinate surface      84
Coordinate system(s), nonorthogonal      13
Coordinate system(s), oblique      10
Coordinate system(s), orthogonal      11 86
Coordinate system(s), rectangular      10ff
Coordinate system(s), rectangular, transformation of      38—39
coordinates      11
Coordinates, curvilinear      11 82—88
Coordinates, cylindrical      82
Coordinates, generalized      82
Coordinates, generalized, basis of      85
Coordinates, orthogonal      11 86
Coordinates, polar      11 12
Coordinates, polar, generalized      12
Coordinates, spherical      83
Covariant components      28
Covariant components, relation of, to contravariant components      31
Covariant derivative      186
Covariant differentiation      185—196
Covariant differentiation of tensors      190—191
Covariant differentiation of vectors      185—187
Cross product      see “Vector product”
Curl      161—164
Current density      226
Curvature      175
Curvilinear coordinates      11 86
Cylindrical coordinates      82
Deformation tensor      2 70—72
Del operator      see “Operator $\nabla$
Deviators      122
Dielectric tensor      100
Differential operators      168ff
Differential operators in generalized coordinates      192—196
Differential operators in orthogonal curvilinear coordinates      171—174
Dipole moment      47
Directional derivative of a scalar field      147—148
Directional derivative of a vector field      164—165
Dirichlet problem      222
Dissipation function      127
Divergence      155—161 193—194
Divergence of the velocity field of a fluid      157—158
Divergence theorem      157
Dot product      see “Scalar product”
Dummy indices      34 91
Dyad      93
d’Alembertian operator      230
Efflux      154
Eigenvalues      109
Eigenvectors      109
Electric displacement      110 228
electric field      19 110 226
Electromagnetic waves      244
Electromagnetic waves, plane monochromatic      245
Electromotive force      226
Equation of continuity      159
Eulerian angles      46
Faraday’s law of induction      226
Finite rotations      4—5
Fluid contour      240
Fluid dynamics      203—211
Fluid motion, equations of      203—208
Flux density      209
Free energy      133
Free vector      2
Frenet — Serret formulas      176
Fundamental theorem of vector analysis      223
Gauss’ Theorem      137—139
Gradient      92 147 150—151 192—193
Green’s formulas      201
Green’s Theorem      139—140
Harmonic functions      219
Harmonic functions, properties of      220—222
Helmholtz’s theorem      249
Higher-order tensors      76—77
Higher-order tensors in generalized coordinates      90
Hodograph      35
Homogeneous form of degree      3 76
Homogeneous linear form      76
Homogeneous quadratic form      76
Ideal fluid      207
Infinitesimal rotations      5 44—45
Influx      154
Inhomogeneous wave equation      230
Integral theorems      196—203
Integral theorems, related to Gauss’ theorem      197—198
Integral theorems, related to Stokes’ theorem      198—200
Invariance of tensor equations      81—82
Invariants of a tensor      121
Isotropic tensor      96
Kibel, I. A.      240
Kochin, N. E.      240
Kronecker delta      39
Kutta — Joukowski theorem      235—236
Laplace’s equation      219
Laplacian (operator)      169 194—196
Laplacian field      219
Left-handed basis      21
Level surface      146
Line integral      136
Lorentz condition      230
Magnetic field      19 226
Magnetic induction      228
magnetization      228
Magnetomotive force      227
Marion, J. B.      231
Matrix      64
Maxwell’s equations      226
Metric coefficients      34 87
Metric tensor      32 86
Metric tensor, verification of tensor character of      90
Moment of a force      19 56
Moment of inertia tensor      68—70 110—113
Momentum flux density      209
Momentum theorem      209
Motion under gravitational attraction      53—54
Moving trihedral      175
Multiple-valued potential      213
Multiply connected region      145
Nabla operator      see “Operator $\nabla$
Navier — Stokes equation      207
Neumann problem      222
Neutral charge system      48
Newton’s Second Law      82
Newton’s second law, invariance of      82
Nutation      46
Ohm’s Law      228
Operator $\nabla$      149 168ff
Orthogonal bases      34
Orthogonal coordinates      11 86
Orthogonal transformation      122
Orthogonal transformation, improper      123
Orthogonal transformation, proper      123
Orthogonality conditions      39
Orthonormality conditions      15
Osculating plane      175
Parallel displacement condition      187
Physical components      30
Poisson’s equation      224
Polar axis      11
Polar vector      18
Polarization      228
Pole      11
Potential      211
Potential field      211
Potential, multiple-valued      213
Poynting’s vector      232
Precession      46
Principal directions      109
Pseudotensor(s)      109 122—126
Pseudotensor(s), components of      124
Pseudotensor(s), unit      126
Quadric surface      64
Radius of curvature      175
Radius of torsion      176
Radok, J. R. M.      240
Rate of deformation tensor      72—75
Reciprocal bases      24
Retarded potentials      244
Ricci’s theorem      191
Right-handed basis      21
Roze, N. V.      240
Scalar fields      145 ff.
Scalar potential      211 228
Scalar product      14
Scalar product in variance of      79
Scalar product, commutativity of      14
Scalar product, distributivity of      15
Scalar triple product      20
Second-order tensors      63—75
Second-order tensors, components of      64
Second-order tensors, transformation law of      64
Shilov, G. E.      123 133
Silverman, R. A.      123
Simply connected region      144
Singular point      152
Sink      154 155 160
Sink, strength of      155 160
Sliding vector      3
Solenoidal field      216
Source      154 155 160
Source, strength of      155 160
Spherical coordinates      83
Spherical trigonometry      41—42
Stokes’ Theorem      137 141—144
Strain tensor      see “Deformation tensor”
Stream function      217
streamline      151 217
Stress tensor      1 66—68 110 167
Stress tensor in generalized coordinates      92
Stress tensor, viscous      96
Summation convention      26—27
Symmetrization      107
Tensor analysis      134ff
Tensor ellipsoid      118—120
Tensor field      135 166
Tensor field, continuous      135
Tensor field, flux of      166
Tensor field, homogeneous      135
Tensor field, nonstationary      135
Tensor function of a scalar function      134
Tensor function of a scalar function, derivative of      134
Tensor(s) in generalized coordinate systems      88
Tensor(s), addition of      103
Tensor(s), antisymmetric      106
Tensor(s), antisymmetric part of      107
Tensor(s), antisymmetric, equivalence of, to axial vector      107—109
Tensor(s), Cartesian      61
Tensor(s), characteristic directions of      109
Tensor(s), characteristic equation of      114
Tensor(s), characteristic values of      109
Tensor(s), characteristic vectors of      109
Tensor(s), contraction of      104
Tensor(s), contravariant      91
Tensor(s), contravariant components of      89
Tensor(s), covariant      91
Tensor(s), covariant components of      89
Tensor(s), covariant differentiation of      190—191
Tensor(s), deformation      70—72
Tensor(s), eigenvalues of      109
Tensor(s), eigenvectors of      109
Tensor(s), equations      81
Tensor(s), equations, invariance of      81—82
Tensor(s), first-order      61—63
Tensor(s), invariants of      121
Tensor(s), isotropic      96
Tensor(s), mixed      91
Tensor(s), mixed components of      89
Tensor(s), moment of inertia      68—70
Tensor(s), moment of inertia in two dimensions      110—113
Tensor(s), multiplication of      104
Tensor(s), of order n      59 76
Tensor(s), of order n, components of      59 76
Tensor(s), of order n, components of, transformation law of      76
Tensor(s), physical components of      91
Tensor(s), principal directions of      109
Tensor(s), product of      104
Tensor(s), product of, inner      105
Tensor(s), product of, outer      104
Tensor(s), rate of deformation      72—75
Tensor(s), reduction of, to principal axes      109—120
Tensor(s), second-order      63—75
Tensor(s), stress      66—68 110
Tensor(s), symmetric      105
Tensor(s), symmetric part of      107
Tensor(s), transformation of, under rotation about a coordinate axis      77—81
Tensor(s), two-dimensional      79
Tensor(s), unit      70
Tensor(s), zeroth-order      60—61
Thomson’s theorem      241
Torsion      176
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