Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Davis H. F., Snider A. D. — Introduction to Vector Analysis
Davis H. F., Snider A. D. — Introduction to Vector Analysis

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Introduction to Vector Analysis

Авторы: Davis H. F., Snider A. D.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: third edition

Год издания: 1975

Количество страниц: 336

Добавлена в каталог: 05.07.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$\nabla$      102
$\partial_{i j}$      46
$\partial_{i}$      111
$\sum$      45
$\varepsilon_{ijk}$      45
Acceleration      2 63—73
Acceleration, angular      63
Acceleration, centripetal      63
Acceleration, Coriolis      75
Acceleration, normal to a curve      63
Acceleration, tangential to a curve      63
Acceleration, tensor form      257
Addition      see Sum
Affinor      229
Angle between planes      27
Angle between vectors      16—17
Angle, direction      10
Angle, positive sense      29
ARC      59 (see also Curve)
Arc length      59 60
Arc length, in orthogonal curvilinear coordinates      191
Area cosine principle      145
Basis      219 (see also Components Coordinates)
Basis, dual      221
Basis, normal      241
Basis, reciprocal      221
Basis, tangent      241
Binormal      68
Boundary, oriented      139 206
Bounded domain      158
Cartesian coordinates      7 187 256
Center of mass      14
Chain rule      80 287
Christoffel symbols      250
circular motion      63
Circulation      117
Cofactor      215
components      7 8
Components, contravariant      222
Components, covariant      222
Components, mixed      264
Components, physical      242
Components, stress      226
Components, tensor      227 262
Continuity equation      86
Contraction of a tensor      253
coordinates      see also Components
Coordinates, affine      259
Coordinates, Cartesian      7 187 256
Coordinates, Cartesian, non-uniqueness      256
Coordinates, change of      13 260—276
Coordinates, orthogonal      189—193
Coordinates, polar      188
Coordinates, right-handed      32 207
Coordinates, spherical      188
Cosine law      24
Cosine principle      145
Cosines, direction      10
Cross product      32 (see also Vector product)
Curl      97—99
Curl, and swirl      97
Curl, as differential of a one-form      202
Curl, formula      97
Curl, formula, in cylindrical coordinates      195
Curl, formula, in general coordinates      255
Curl, formula, in orthogonal coordinates      194
Curl, formula, in spherical coordinates      195
Curl, invariance      255
Curl, physical significance      97
Curl, tensor      255
Curvature      63 67—68
Curve, arc length      59—60 191
Curve, characteristic      86
Curve, closed      54
Curve, curvature      63 67—68
Curve, oriented      55
Curve, parametric equations      53
Curve, regular      55
Curve, smooth      54
Curve, space      52
Curve, tangent to      57 61
Degenerate line segment      1 2
Del notation      102
Delta, Kronecker      46
Density, as a differential form      199
Density, flux      89 149
Density, mass      3
Density, scalar      242 267
Derivative, as an operator      104
Derivative, chain rule      80 287
Derivative, directional      79
Derivative, intrinsic      258
Derivative, of a determinant      253
Derivative, of a vector field      251 257 264
Derivative, of a vector function      50 258 260
Derivative, partial      79
Determinant      see also Jacobian
Determinant, and matrices      214
Determinant, cofactor      215
Determinant, differentiation rule      253
Determinant, formula      215
Determinant, symbolic      97
Differential      see also Derivative
Differential form      114 198
Differential, of a differential form      201
Differential, total      201
Displacement      11 54
Distance      3
Distance, between a point and a plane      27
Distance, between planes      27—28
Divergence      88—94
Divergence theorem      165 171
Divergence theorem, and differential forms      209
Divergence theorem, and Gauss’s law      165
Divergence theorem, heuristic proof      165
Divergence theorem, proof      171
Divergence, as differential of a two-form      203
Divergence, dependence on coordinates      254
Divergence, in cylindrical coordinates      195
Divergence, in general coordinates      254
Divergence, in orthogonal coordinates      193 243
Divergence, in spherical coordinates      195
Divergence, invariance      256
Division, points of      22
Domain      see also Region
Domain, bounded      158
Domain, simply-connected      121
Domain, star-shaped      122
Dot product      22 (see also Scalar product)
Duality      221 240
Dummy      231
Dyadic      280
Einstein convention      253
electric field      86
Equipotential      79
Equivalence of line segments      1 14
Factor, scale      190
Field, as a differential form      198
Field, conservative      123—135
Field, differentiable      123
Field, irrotational      131
Field, matrix      261
Field, scalar      78 (see also Potential)
Field, solenoidal      137
Field, tensor      240 263
Field, vector      85
Field, velocity      86
Flow line      86
Flow, fluid      86 92
Flow, heat      148
Fluids      86 92
Flux      89 149
force      2 3 12
Force, central      75
Force, centrifugal      63
Force, centripetal      63
Force, lines of      86
FORM      114 198
Frenet formulas      70
Functions      see also Field
Functions, and operators      100—104
Functions, harmonic      104
Functions, linear      233
Functions, scalar-valued      78
Functions, vector-valued      50
Gauss’s law      149 153
Geodesic equations      257
Gradient      80
Gradient, as an operator      100—104
Gradient, as differential of a zero-form      202
Gradient, in cylindrical coordinates      195
Gradient, in general coordinates      254 261
Gradient, in orthogonal coordinates      193 254
Gradient, in spherical coordinates      195
Green’s Theorem      180—185
Harmonic      104
Heat      148
Identities, algebraic      42
Identities, analytic (in del notation)      107—108
Identity matrix      212
Independence, linear      42 237
Index, dummy      231
Index, free      231
Inner product      22 (see also Scalar product)
Integrals      see Line integrals Surface etc.
Invariance      249 255
Inverse of a matrix      216
Isobar      79
Isotherm      79
Jacobian      241 266
Jacobian, volume integrals      270
Kepler’s second law      75
Kernel letter      265
Kramer’s rule      42
Kronecker delta      46
Laplace’s equation      104
Laplacian      103—105
Laplacian, and differential forms      203
Laplacian, formula      104
Laplacian, formula, dependence on coordinates      256
Laplacian, formula, in cylindrical coordinates      195
Laplacian, formula, in general coordinates      255
Laplacian, formula, in orthogonal coordinates      193 243
Laplacian, formula, in spherical coordinates      195
Laplacian, physical interpretation      104
Line integrals      114
Line integrals, dependence on path      115 124
Line, equations      19—21
Line, flow      86
Line, stream      86
Line, vector parallel      21
Lines of force      86
Magnitude of a vector      2 5 10
Mass      3
Matrix      209 (see also Determinant)
Matrix, column      210
Matrix, identity      212
Matrix, inverse      216
Matrix, row      210
Matrix, trace of      253
Matrix, transpose of      214
Matrix, zero      212
Maximum principle      22
Mechanics      see Force Velocity etc.
Metric      see Tensor metric
Metric concepts      223 245
Mobius strip      140
Momentum, angular      279
Multiple, scalar      6
Multiplication      see Product Scalar Vector
nabla      102
Neighborhood      119
Newton’s Second Law      75 249 257
Nonorientable surface      140
Normal, to a curve      67
Normal, to a plane      27
Normal, to a surface      81 139 142
One-form      198
Operators      100—104
Orientation      29 206
Orientation, of arcs      55
Orientation, of boundaries      139 206
Orientation, of planes      29—30
Orientation, of points      207
Orientation, of regions      207
Orientation, of surfaces      139
Orthogonal curvilinear coordinates      187—195 (see also Coordinates)
Osculating circle      64
Parallelepiped, volume      38
Parallelogram law      4
Parallelogram, area      32
Parallelogram, geometry of      15—16 18
Parametrization      19 53
Permutation symbol      215
Physical components      242
Planes      see also Distance
Planes, angle between      27
Planes, equations      25—28
Planes, vectors perpendicular to      27
Point of division      22
Point, boundary      120
Point, interior      120
Polar coordinates      73 188
Position vector      11 19 65
Potential      123
Potential, vector      137
Pressure      79
Pressure and stress      226
Principal normal      67
PRODUCT      see also Scalar Product Vector
Product, cross      31—37
Product, dot      22
Product, inner      22
Product, of a vector by a scalar      6 9
Product, of differential forms      199
Product, of matrices      215
Product, wedge      199
Pseudoscalar      268
Pseudovector      245 268
Pythagorean Theorem      8
Quaternions      276—279
Radius of curvature      64
Rank of a tensor      232
Reciprocal basis      221
Reflection      245 281
Region, boundary point      120
Region, bounded      158
Region, connected      120
Region, interior point      120
Region, open      120
Region, oriented      207
Region, simply-connected      121
Resultant      12
Right-hand rule      31 32
Rotation      12
scalar      3
Scalar density      266
Scalar field      78—86
Scalar field, as a differential form      198
Scalar multiple      6
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте