Williamson R.E., Crowell R.H., Trotter H.F. — Calculus of vector functions :: Электронная библиотека попечительского совета мехмата МГУ

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Williamson R.E., Crowell R.H., Trotter H.F. — Calculus of vector functions

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Название: Calculus of vector functions

Авторы: Williamson R.E., Crowell R.H., Trotter H.F.

Аннотация:

This book presents the contents of a standard course on functions of
several variables, following the unifying idea that calculus deals with linear
aipproximations to functions.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 1968

Количество страниц: 434

Добавлена в каталог: 20.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

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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