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Spivak M. — Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus
Spivak M. — Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus



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Название: Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus

Автор: Spivak M.

Язык: en

Рубрика: Математика/Геометрия и топология/Дифференциальная геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1965

Количество страниц: 146

Добавлена в каталог: 23.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{\infty}$      26
Absolute differential form      126
Absolute tensor      126
Absolute value      1
Algebra, fundamental theorem of      105
Alternating tensor      78
Analytic function      105
angle      4
Angle, preserving      4
Angle, solid      131
Approximation      15
Archimedes      137
Area      56
Area, element of      126
Area, surface      126 127
Basis, usual for $R^n$      3
Bilinear function      3 23
Boundary of a chain      97 98
Boundary of a manifold-with-boundary      113
Boundary, of a set      7
Buoyant force      137
Cauchy integral formula      106
Cauchy integral theorem      106
Cauchy — Riemann equations      105
Cavalieri’s principle      62
Chain      97 100
Chain rule      19 32
Change of variable      67—72
Characteristic function      55
Closed curve      106
Closed differential form      92
Closed rectangle      5
Closed set      5
Compact      7
complex numbers      104
Complex variables      105
Component function      11 87
composition      11
Cone, generalized      131
Consistent choices of orientation      117
Constant function      20
Constraints      122
Content      56
Content zero      51
Continuous differential form      88
Continuous function      12
Continuous vector field      87
Continuously differentiable      31
Convergence      137
Coordinate condition      111
Coordinate system      111
Coordinate system, polar      73
Counterclockwise orientation      134
Cover      7
Cross product      84
Cube, singular      97
Cube, standard n-cube      97
Curl      88 137
Curve      97
Curve, closed      106
Curve, differentiable      96
Degenerate singular cube      105
Derivative      16
Derivative, directional      33
Derivative, partial      25
Derivative, partial, higher-order (mixed)      26
Derivative, partial, second-order (mixed)      26
Diffeomorphism      109
Differentiable = $C^{\infty}$      88
Differentiable curve      96
Differentiable differential form      88
Differentiable differential form on a manifold      117
Differentiable function      15 16 105
Differentiable function, continuously      31
Differentiable vector field      87
Differentiable vector field on a manifold      115
Differential      91
Differential form      88
Differential form, absolute      126
Differential form, closed      92
Differential form, continuous      88
Differential form, differentiable      88
Differential form, exact      92
Differential form, on a manifold      117
Differential form, on a manifold, differentiable      117
Dimension of a manifold      109
Dimension of a manifold-with-boundary      113
Directional derivative      33
Distance      4
Divergence of a field      88 137
Divergence theorem      135
Domain      11
Dual space      5
Element of area      126
Element of length      126
Element of volume      see "Volume element"
End point      87
Equal up to nth order      18
Euclidean space      1
Exact differential form      92
Exterior of a set      7
Faces of a singular cube      98
Field      see "Vector field"
FORM      see "Differential form"
Fubini’s Theorem      58
Function      11
Function, $C^{\infty}$      26
Function, analytic      105
Function, characteristic      55
Function, component      11 87
Function, composition of      11
Function, constant      20
Function, continuous      12
Function, continuously differentiable      31
Function, differentiable      15 16 105
Function, homogeneous      34
Function, identity      11
Function, implicitly defined      41 see
Function, integrable      48
Function, inverse      11 34—39 see
Function, projection      11
Fundamental theorem of algebra      105
Fundamental theorem of calculus      100—104
Gauss      134
Generalized cone      131
grad f      96
Graph      11 115
Green’s Theorem      134
Half-space      113
Heine — Borel theorem      7
Homogeneous function      34
Homotopy      108
Identity function      11
Implicit function theorem      41
Implicitly defined function      41
Incompressible fluid      137
Independence of parameterization      104
Induced orientation      119
Inequality      see "Triangle inequality"
Inner product      2 77
Inner product, preserving      4
Inner product, usual      77 87
Integrable function      48
integral      48
Integral Formula, Cauchy      106
Integral of a form on a manifold      123—124
Integral of a form over a chain      101
Integral over a set      55
Integral over an open set      65
Integral theorem, Cauchy      106
Integral, iterated      59 60
Integral, line      101
Integral, lower      58
Integral, surface      102
Integral, upper      58
Interior of a set      7
Inverse function      11 34—39
Inverse function theorem      35
Irrotational fluid      137
Iterated integral      59 60
Jacobian matrix      17
Jordan-measurable      56
Kelvin      74
Lac locus      106
Lagrange’s method      122
Lagrangian multiplier      122
Leibnitz’s rule      62
Length      56 126
Length = norm      1
Length, element of      126
LIMIT      11
Line      1
Line integral      101
Linking number      132
Liouville      74
Lower integral      58
Lower sum      47
Manifold      109
Manifold-with-boundary      113
Manifold-with-corners      131 137
Mathematician (old style)      74
Matrix      1
Matrix, Jacobian      17
Matrix, transpose of      23 83
Maxima      26—27
Measure zero      50
Minima      26—27
Moebius strip      119 120 130
Multilinear function      23 75
Multiplier      see "Lagrangian multiplier"
Norm      1
Norm preserving      4
normal      see "Outward unit normal"
Notation      3 44 89
One-one (1-1) function      11
One-sided surface      121
Open cover      7
Open rectangle      5
Open set      5
Orientable manifold      119
Orientation      82 119
Orientation, consistent choices of      117
Orientation, counterclockwise      134
Orientation, induced      119
Orientation, usual      83 87 121
Orientation-preserving      118 123
Oriented manifold      119
Orthogonal vectors      5
Orthonormal basis      77
Oscillation      13
Outward unit normal      119 120
Parameterization, independence of      104
Partial derivative      25
Partial derivative, higher-order (mixed)      26
Partial derivative, second-order (mixed)      26
Partition of a closed interval      46
Partition of a closed rectangle      46
Partition of unity      63
Perpendicular      5
Plane      1
Poincare lemma      94
Point      1
Polar coordinate system      73
Polarization identity      5
Positive definiteness      3 77
PRODUCT      see "Cross product" "Inner "Tensor "Wedge
Projection function      11
Rectangle (closed or open)      5
Refine a partition      47
Rotation of F      137
Sard’s theorem      72
Self-adjoint      85
Sign of a permutation      78
Singular n-cube      97
Solid angle      131
Space      1 see "Euclidean "Half-space" "Tangent
Sphere      111
Standard n-cube      97
Star-shaped      93
Stokes’ Theorem      102 124 135
Subordinate      63
Subrectangles of a partition      46
surface      127
Surface area      126 127
Surface integral      102
symmetric      2 77
Tangent space      86 115
Tangent vector      96
Tensor      75
Tensor product      75
Tensor, absolute      126
Tensor, alternating      78
Torus      115
Transpose of a matrix      23 83
Triangle inequality      4
Unit outward normal      119 120
Upper integral      58
Upper sum      47
Usual      see "Basis" "Inner "Orientation"
Variable, change of      67—72
Variable, complex      see "Complex variables"
Variable, function of n      11
Variable, independent of the first      18
Variable, independent of the second      17
Vector      1
Vector field      87
Vector field on a manifold      115
Vector field on a manifold, continuous      87
Vector field on a manifold, differentiable      115
Vector field, continuous      87
Vector field, differentiable      87
Vector, tangent      96
Vector-valued function      11
Volume      47 56 126
Volume element      83 126
Wedge product      79
Winding number      104
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