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| Schey H.M. — DIV, Grad, Curl, and All That: An Informal Text on Vector Calculus |
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| Предметный указатель |
Ampere’s circuital law 98
Ampere’s circuital law, differential form of 100
Arfken, G. 146
Arnold, Matthew 1
Capping surface 92—93
Central forces 71
Central forces, irrotational nature of 105
Chalmers, P.R. 114
Charge density 8
Circulation law 73
Circulation law, differential form of 90—91
Conservation 49—50 52
Continuity equation 52 109
Coulomb’s law 6
Coulomb’s law, and path independence 71—73
Curl 75—90
Curl, alternative definition of 111—112
Curl, and path independence 101—104
Curl, definition of 80—81
Curl, determinant form of 81
Curl, in Cartesian coordinates 80—81
Curl, in cylindrical coordinates 84—85
Curl, in spherical coordinates 85
Current density 51 99
DEL 43—44 118
Del, and curl 82
Del, and divergence 43—44
Del, and gradient 118
Del, and Laplacian 122—123
Denham, Sir John 11
Diffusion equation 146
Directional denvative 130—136
Divergence 36—43
Divergence theorem 44—52 109 155
Divergence theorem, applications of 49—52
Divergence theorem, derivation of 44—48
Divergence theorem, illustration of 47—48
Divergence theorem, in two dimensions 109
Divergence theorem, statement of 47
Divergence theorem, Stokes’ theorem, relation to 107—110
Divergence theorem, validity of 47—48
Divergence, definition of 36
Divergence, in Cartesian coordinates 41—42 57
Divergence, in cylindrical coordinates 41—42 58
Divergence, in spherical coordinates 41—42 58
Electric charge 5—6 8—10
electric field 7 8
Electromotive force 108
Electrostatic potential 121
Electrostatics 5—8
Fick’s law 146
Field line 9—10
Flux 29—32
Gauge transformation 154
Gauss’ law 11—12
Gauss’ law, differential form of 40 49
Gauss’ law, use in finding field 32—36 55—56
Gauss’ Theorem see “Divergence theorem”
Gradient 114—155
Gradient, alternative definition of 151
| Gradient, and path independence 118
Gradient, example of 118
Gradient, in Cartesian coordinates 120
Gradient, in cylindrical coordinates 120 142—143
Gradient, in spherical coordinates 120 150
Green’s Theorem 148
Heat flow equation 147
Irrotational 88n 105 147
Laplace’s equation 123—124
Laplace’s equation, in Cartesian coordinates 122
Laplace’s equation, in cylindrical coordinates 128
Laplace’s equation, in spherical coordinates 125
Laplace’s equation, solutions of 123—130
Laplace’s equation, uniqueness of solutions of 130 150—151
Laplacian 122
Line integral 63—72
Line integral, and path independence 72—73
Line integral, definition of 64—65
Line integral, evaluation of 66—67 69—70
Magnetic field 98
Maxwell’s equations 8 40 100 108
mks units ix 6
Normal vector 12—17
Normal vector, alternative form of 150
Normal vector, uniqueness of 16n 153
Path independence 70—71
Path independence, and central forces 103
Path independence, and curl 101—102
Planck’s constant 148
Poisson’s equation 122
Right-hand rule 79 87
Rot (rotation) 80n
Scalar function 37 120
Scalar potential 154
Schrodinger equation 147—148
Smooth 114 118—119
Smooth, defined 100n
Solenoidal 58
Sophocles 63 156
Stokes’ Theorem 92—102
Stokes’ theorem, and simply connected regions 100—101 102 107—108
Stokes’ theorem, applications of 98—100
Stokes’ theorem, derivation of 93—96
Stokes’ theorem, divergence theorem, relation to 110
Stokes’ theorem, illustration of 96—97
Stokes’ theorem, in two dimensions 109—110
Stokes’ theorem, statement of 96
Stokes’ theorem, validity of 96
Superposition 6—7
Surface integral 17—29
Surface integral, definition of 17—21
Surface integral, evaluation of 21—29 54—55
Tangent vector 67—68
Taylor series 131
Unit normal see “Normal vector”
Unit tangent 67—68
Vector functions 2—5
Vector potential 153
Velocity potential 147
Wave equation 147—148
Work 64 67
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