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Williamson R.E., Crowell R.H., Trotter H.F. — Calculus of vector functions |
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Предметный указатель |
Absolute maximum, minimum 223
Acceleration vector 119 126
Acceleration: normal 127
Acceleration: tangential 127
Affine function 23 142
Affine subspace 79
angle 33
Approximation: Fourier 268
Approximation: Legendre 291
Approximation: mean-square 288
Approximation: Taylor 253
Arc-length 122 410
Arc-length parametrization 125
Area 310
Area element 327
Area surface 363
Associated column 73
Associated row 73
Basis 61
Bessel's inequality 287
Bilinear function 235
Binormal vector 120
Border of surface 367
Boundary of a set 113
Bounded function, set 305
Box norm 406
Cantor function 410
Cauchy — Schwarz inequality 28 32
Center of mass 129
Centripetal component 127
Centroid 318
Chain rule 119 160 169
Change of variable 319 425
Characteristic equation, roots, vectors 243
Circuit 350
Circulation 351 375
Closed set 113
Closed surface 376
Closure of a set 113
Coefficient matrix 66
Coefficients: Fourier 268 286
Coefficients: Legendre 291
Coefficients: multinomial 255
Cofactor 45
Column of a matrix 11
Column vector 11
Component of a vector 29
Component, tangential, normal 127
Composition of functions 21 111 167
Conditionally convergent integral 339
Connected, polygonally 157
Conservative field 356
Content 304 310
Continuous differentiability 150
Continuous function 109 110
Convergence: conditional 339
Convergence: pointwise 278
Convergence: uniform 279
Convergent family of subsets 335
Convex 10
Coordinate 29
Coordinate functions 95
Coordinate map 86
Coordinate of a vector relative to another vector 29
Coordinate rectangle 304
Coordinate vector 84
Coordinates, of a vector 84
Cramer's rule 47
Critical point 226
Curl 351 372
Curvature 127
Curvilinear coordinates 190
Cylindrical coordinates 192
DEL 385
Dependent vectors 60
Derivative 115 144 146
Derivative with respect to a vector 153
Derivative, directional 155
Determinant 36 37
Diagonal form 237
Diagonal matrix 15
Differentiable function 143
Differential 143
Differential form 392 395 399
Differential, kth-order 255
DIMENSION 62
Directional derivative 155
Discontinuity point, infinite 333
Discontinuity, removable 115
Divergence of a field 352 380
Divergence theorem 381
Domain, space 2
Dot product 26
Echelon form 83
Eigenfunction 288
Eigenvalues 243 288
Eigenvectors 243 288
Element: arc-length 126
Element: surface area 365
Element: volume 327
Elementary matrix 68
Elementary operations 68
Elementary operations, modification 68
Elementary operations, multiplication 68
Elementary operations, transposition 68
Entry, matrix 11
Equipotential surface 167
Equivalent norms 408
Equivalent parametrizations 128 369
Equivalent systems of linear equations 66
Expansion, determinant 44
Expansion: Fourier 268 286
Expansion: Legendre 291
Expansion: multinomial 255
Expansion: Taylor 251 253
Explicit definition 99 101
Exterior derivative 400
Exterior product 395 399(12)
Extreme point, value 223
Field: force 131
Field: gradient 159
Field: vector 102
Flux 352 366 395
Force vector 119
Fourier approximation, coefficients 268
Fourier series 273
Function: composite 21 167
Function: continuous 109
Function: continuously differentiable 150
Function: differentiable 143
Function: limit of 106
Function: linear 19
Function: one-to-one 20
Function: orthogonal 285
Fundamental theorem of calculus 122 163
Gauss's theorem 352 381
Generalized inverse function theorem 210
Gradient 159 232 356
Gradient, local 390
Gradient, temperature 167 369
Gram — Schmidt orthogonalization 294
Graph 95
Greatest lower bound 405
Green's identities 387
Green's theorem 346
grid 305
Harmonic function 384
Homogeneous equation 75
Homogeneous polynomial 236
Hyperbolic paraboloid 237
| Identity function 178
Identity matrix 14
Image 2
Implicit definition 99 101 180 181
Implicit function theorem 205
Implicitly defined surfaces 217
Improper Riemann integral 335
Incompressible field 385 391
Incompressible flow 352
Independent vectors 60
Infimum 405
Infinite discontinuity point 333
Inner product 26
Inner product space 31
Integrable function 306
Integral of function 121 306 317 335
Integral, surface 364
Interior point 112
Inverse function 199
Inverse function theorem 201 210 417
Inverse matrix 15
Invertible matrix 15
Irrotational field 351 385
Isolated point 109
Isomorphism 86
Iterated integral 296
Jacobian determinant 175
Jacobian matrix 146
kinetic energy 356
kth-order differential 255
Lagrange formula 289
Lagrange multipliers 228
Laplace equation 388
Leading entry 72
Least upper bound 405
Lebesque integral 315
Legendre approximation 291
Legendre equation, polynomial 290
Leibnitz rule 316
Length of a curve 122
Length of a vector 27
Level set 101
Limit of function 106
Limit point 105
Line 8
Line integral 130
Line segment 10
linear combination 4 57
Linear function 19
Linear functional 36
Linear momentum 121
Linear operator 288
Linear subspace 58
Linearly dependent, independent 60
Local maximum value, minimum value 223
Logarithmic potential 167
Magnitude of acceleration 119
Magnitude of force 119
Matrix 11
Matrix, diagonal 15
Matrix, elementary 68
Matrix, identity 14
Matrix, inverse 15
Matrix, invertible 15
Matrix, Jacobian 146
Matrix, orthogonal 33
Matrix, product 13
Matrix, symmetric 236 359
Matrix, transformation 20 88
Matrix, transpose 34
Maximum: absolute 223
Maximum: local 223
Mean, of density 341
Mean-square approximation 288
Mean-value theorem 156
mesh 305
Minimum: absolute 223
Minimum: local 223
Minor 36
Mobius strip 103 368
Modification, elementary 68
Moment of inertia 318
Multinomial coefficients 255
Multinomial expansion 255
Multiple integral 306
Multiplication, elementary 68
Multipliers, Lagrange 228
Natural basis 4
Negative definite 249 264
Neighborhood 112
Newtonian potential 167 391
Norm 32 406
Normal component 127
Normal vector 162 219
Null space 58
Numerical multiple 3 11
One-to-one function 20 200
Open coordinate rectangle 304
Open set 112
Operator, linear 288
Orientable surface 367
Orientation: boundary surface 380
Orientation: negative 53
Orientation: positive 53
Orientation: surface 367
Oriented volume 56
Origin 5
Orthogonal functions 285
Orthogonal matrix 33
Orthonormal sequence 286
Orthonormal set 33 286
Paraboloid, hyperbolic 237
Parallelepiped 52
Parametric definition 99 101
Parametrization, arc-length 125
Partial derivative 136 139
Piecewise smooth curve 123 274
Piecewise smooth surface 367
Pivotal column 73
Plane 9 30 211
Pointwise convergence 278
Poisson equation 388
Polar coordinates 187
Polygonally connected 157
Polynomial: Legendre 290
Polynomial: quadratic 235
Polynomial: Taylor 251
Polynomial: trigonometric 268
Positive definite 237 264
potential energy 357
Potential function 167
Potential of a field 356
Potential: logarithmic 167
Potential: Newtonian 167 391
Principal normal 120
Principal value 337
probability density 318
Product rule for determinants 50
Projection 6
Quadratic form 236
Quadratic polynomial 235
Quadratic surface 245
RANGE 2
Range space 2
Real-valued function 95
Rectifiable curve 122
Reduced matrix 72
Remainder, Taylor 252
Removable discontinuity 115
Riemann integral 315 420
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