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| McQuistan R.B. — Scalar and Vector Fields: a Physical Interpretation |
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| Предметный указатель |
Acceleration, centripetal 53
Acceleration, tangential 53
Acceleration, vector 50 125
Acylic regions 62
Addition, vector 24
Algebra, vector 24—44
Ampere's law 307
Angle, of contingence 51
Angle, plane 75
Angle, solid 75
Angular, displacement 5 119
Angular, momentum 55
Angular, velocity 6 37
arc, regular 61
Area element 7 61
Associative law, of addition 27
Axial vector 6
B-field 252
Barrier 63
Binormal plane 53
Biot — Savart law 252
boundary conditions 275ff
Boundedness 20 274
Calculus, vector 45—77
Cartesian coordinates 78ff
centripetal acceleration 53
Chord 48
Circulation 173ff
Closed surface 8
Commutative law, of addition 27
Complete set 131
Component 28 33
Composition, law of 3
Concentration 193
Conservative field 257
Continuity 20ff
Contour lines 13 144
Convective derivative 288
Coordinate systems 78ff 232
Coordinate systems, three-dimensional 82ff
Coordinate systems, two-dimensional 79ff
Coriolis, theorem of 126
Coulomb gauge 296
Cross product 34
Curl, operator 173ff 191
Curl, operator in orthogonal systems 234ff
Curvilinear coordinate, systems 221
d'Alembert’s equations 296
Derivative of a vector 46
Derivative, convective 288
Derivative, directional 139
Derivative, operator 191
Derivative, partial 58 139
Differentiable 20
Differential 58
Differential field operators 189ff
Differentiation, of a vector 45
Differentiation, partial 58 139
Dipoles 278
Dirac delta function 282
Direction 2
Directional derivative 139 191
Dirichlet condition 281 284
Discontinuity 275
Distributive law 30 35
Divergence, operator 161 190 232
Divergence, Theorem 216
Dot product 30
Double layer 278
Eigenfunction 127ff
Eigenvalue 127ff
electric field 102 222 239
Electrodynamic potential 307
Electromagnetism 1
Electrostatic potential 194 248
Element of area 7
Element of length 6
Element of volume 85
Equality of vectors 24
Euler’s hydrodynamic equation 288
Faraday’s law 307
Field, conservative 257
Field, discontinuities 20 275ff
Field, electromagnetic 305
Field, gravitational 241
Field, harmonic 225
Field, integral properties of 199ff
Field, inverse square 241
Field, irrotational 154ff 245ff
Field, lines 18 94
Field, operators 189 196 227
Field, potentials 239ff 264ff
Field, representation 78
Field, scalar 1 10
Field, solenoidal 255
Field, time-dependent 286ff
Field, vector 15ff
Fixed vectors 8
Flow lines 18
Flux 161
Flux lines 18
Frame of reference 24 123
Free vector 8 9
Function space 127ff
Gauge invariance 260
Gauge transformation 260 308
Gauss’s divergence theorem 213 265
Gauss’s law 216
Generation 167
Gradient of a Scalar Field 135ff
Gradient, operator 190 231
Gravitational, fields 241
Gravitational, potentials 248
Green’s functions 281
Green’s Theorem 223 265
Harmonic fields 225
Helmholtz’s theorem 261
Improper integrals 274
Infinitesimal displacements 78 227
Inhomogeneous wave equation 296 309
Integral transformations 299
Integral transformations, surface-to-line 199
Integral transformations, volume-to-surface 213
Integration, vector 56
Intensity 18
Invariant form 1
Irrotational fields 154 245 256
Isothermal surfaces 14 147
KirchhofTs solution 302
Kronecker delta 128
Laplace equation 249 264
Laplacian 192 195 235
Line integration 59 65
Line scalar source density 223
Line vector source density 278
Linear independence 132
Linearity 20 22
Lorentz condition 308
Maclaurin series 192
Magnetic field 306
Magnetic induction 252
| Magnetic vector potential 255
Magnitude 2 18
Mass flow rate 167
Matrix formulation of field transforms 111
Moment of force 38
Moment of momentum 55
Momentum, angular 55
Momentum, linear 55
Multiplication 28—42
Multiplication of a vector by a scalar 29
Multiplication, cross or vector 34
Multiplication, dot or scalar 30
Multiplication, scalar triple product 39
Multiplication, vector triple product 41
Multiply connected regions 62
Multivalued functions 21
Neumann conditions 281 284
Newton’s Second Law 56 288
Ohmic medium 310
Open surface 8
Operators, differential 189 227
Orthogonal coordinate systems 33 116 227
Orthogonal sets of functions 127
Osculating plane 51
Partial differentiation 58 139
Permittivity 248
Piecewise smooth 61
Plane angle 75
Point functions 10
Polar coordinates 80ff
Position vector 7 123 194
Potentials 239 248
Potentials, electrodynamic 307
Potentials, electromagnetic 305
Potentials, harmonic 225
Potentials, retarded 292
Potentials, scalar 256
Potentials, vector 257
Pseudoscalars 2
Pseudovectors 6
Quadratic integrability 131
Radial direction 81ff
Radial vector field 95
Radius of curvature 51
Rectangular coordinates 79ff
Rectifiable curve 60
Reference line 79
Reference plane 82 85
Regular arc 61
Regular surface element 62
Resolution 27
Resultant 25
Retarded potentials 292
Right-hand rule 35
Right-hand screw 5 6 8
Right-handed coordinate system 82ff 116
Rotating observer 125
Scalar, fields 10
Scalar, function 63
Scalar, multiplication 30
Scalar, potentials 256
Scalar, quantities 2
Scalar, source density 247
Scalar, surface souce density 296
Scalar, Triple product 39
Scalar, variable 45
Sense 2
Simply or singly connected region 62
Single valued 20 21
sinks 161 173
Sliding vectors 8 9
Smoothness 60
Solenoidal fields 257
Solid angles 75
sources 161 173
Space curve 6
Spherical coordinates 89
Stokes’s theorem 199
Stream lines 18
Substraction, vector 24
Surface, closed 8
Surface, element 7
Surface, integration 59 71
Surface, open 8
Tangent 49
Tangential, acceleration 53
Tangential, normal system 53
Tangential, vectors 51
Tangential, velocity 49
Taylor expansion 168 182
Temperature field 10 194
Three-dimensional coordinate systems 82
Time-dependent fields and potentials 286
torque 38 55
Transformation of coordinates 78ff
Transformation of integrals 199ff
Transformation, gauge 266
Transformation, parameter 229
Two-dimensional coordinate systems 79
Uniform continuity 21
Unit vector 33
Vector field of transformations 111
Vector field, general 261
Vector field, irrotational 154
Vector field, representation 93ff
Vector field, solenoidal 257
Vector field, time-dependent 286
Vector field, transformation 103ff
Vector, addition 24
Vector, algebra 24—44
Vector, axial 6
Vector, determinant form 39
Vector, division 42
Vector, fixed 8 10
Vector, free 8 9
Vector, multiplication 34
Vector, point 8 10
Vector, polar 6
Vector, position 7
Vector, potential 251ff
Vector, quantities 3
Vector, sliding 8 9
Vector, source density 252
Vector, sources 251
Vector, space 127ff
Vector, tangential 51
Vector, triple product 41
Vector, unit 33
Vector, zero 29
Velocity, angular 6 124
Velocity, linear 49 124
Velocity, space 287
Volume, charge density 248 306
Volume, integration 59 76
Volume, mass density 245
Volume, vector source density 252 264
Volumetric flow rate 74
Vortex Motion 183
Wave equation 296 310
Work 32 68 247
Zero vector 29
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