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Weinreich G. — Geometrical vectors
Weinreich G. — Geometrical vectors



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Название: Geometrical vectors

Автор: Weinreich G.

Аннотация:

Every advanced undergraduate and graduate student of physics must master the concepts of vectors and vector analysis. Yet most books cover this topic by merely repeating the introductory-level treatment based on a limited algebraic or analytic view of the subject. Geometrical Vectors introduces a more sophisticated approach, which not only brings together many loose ends of the traditional treatment, but also leads directly into the practical use of vectors in general curvilinear coordinates by carefully separating those relationships which are topologically invariant from those which are not. Based on the essentially geometric nature of the subject, this approach builds consistently on students' prior knowledge and geometrical intuition. Written in an informal and personal style, Geometrical Vectors provides a handy guide for any student of vector analysis. Clear, carefully constructed line drawings illustrate key points in the text, and problem sets as well as physical examples are provided.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 127

Добавлена в каталог: 24.11.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
"co-" vs "contra-"      48—50
"Del" operator      99
"Hanging laundry" construction      63
Acceleration      14
Addition of arrows      20
Addition of sheaves      37—38
Addition of stacks      20—22 25
Addition of thumbtacks      36—37
Addition of vectors      2
arrow      14 20
Associative law      20 28
Axial scalar      32—34 39
Axial sense      see "Sense genders"
Basis      67 79
Basis, arrow      68 71—72 82
Basis, conversion of      96—99
Basis, scalar capacity      69—70
Basis, scalar density      69—70
Basis, sheaf      68 81
Basis, stack      68 72 82
Basis, thumbtack      68 80—81
Cartesian coordinates      2 17 74—75 see
Commutative law      20 28
components      4—6 69 79—80
Components of basis vectors      74
Conservative field      65
Constitutive relations      93—94
Contravariant vector      see "Arrow"
Contravariant vector density      see "Sheaf"
Coordinate system      5 66—69
Coordinate transformation vs space distortion      9—10 70
Covariant vector      see "Stack"
Covariant vector capacity      see "Thumbtack"
Cross product      1 3 26—31 49 83—84 109
Cross product, arrow-arrow      27—28
Cross product, arrow-sheaf      43—44
Cross product, stack-stack      34—36
Cross product, thumbtack-stack      44—45
Curl      3 57—60
Curl of gradient      58
Curl, computation of      86—88
Curl, divergence of      61
Curl, inverse of      63
Curved space      1 109—110
Cylindrical coordinates      17 75—77 100—101 105 106
Determinants      84 104
Direction type      see "Orientation of lines and planes"
Displacement      13—14 17
Distance      103 109—110
Distributive law      20 24 28
Divergence      3 60—62
Divergence of curl      61
Divergence, computation of      88—90
Divergence, inverse of      63
Dot product      3 82
Dot product, stack-arrow      22—24 73
Dot product, stack-sheaf      46—47
Dot product, thumbtack-arrow      47—48
Dot product, thumbtack-sheaf      46
Electric charge      11 65
electric field      6—9 11 16 24 65
electromagnetic field      93—94
Energy      34
entropy      34
Equation of continuity      105
Euclidean space      1—2
Field      9 53—55
Gauss's theorem      61—62
Gradient      3 55—57
Gradient, computation of      85—86
Gradient, curl of      58
Gradient, inverse of      62—63
Hydrodynamics      105
interval      see "Distance"
Kronecker delta      73
Laplacian      98—99 101 105 109
Left-handed system      85 90 91
Maxwell equations      93—94 111
Menagerie (table)      48
Metric      102—104 106 110
Multiplication of vector by density or capacity      51—52
Multiplication of vector by scalar      2—3 19 36
Notation for vectors      22 27 36
Orientation of lines and planes      15 27—28 48 95
Orientation of lines and planes, conversion between      16 40—42 95
Orthogonal systems      77 80 99—102 105
Orthonormality      73 82 90
Parallel vectors      18—19
Parallelogram rule      2 20—21
Perpendicular vectors      16 18—19 27
Polar sense      see "Sense genders"
Potential difference      6—7 11
Pressure      105
Propagation vector      24
Pseudoscalar      see "Axial scalar"
Radius vector      9 72
Reference frame      see "Coordinate system"
Reflection      29—30 39
Relativity      1 110—111
Right-hand rule      3 28—29 32 35 39 45
Right-handed system      85 90 91
Rotation of coordinate system      6—7
Scalar capacity      47—48
Scalar density      47—48
Scalar product      see "Dot product" "Triple
Scale factors      101—102
Scale, change of      6—8
Sense genders      28—34 39
Sense genders of bases      84—85
Sheaf      34—38 49—50
Size of symbols      16—17 53—55
Spherical coordinates      74—75 80 105 106
STACK      15—16 49
Stokes's theorem      59—60
Tensor analysis      111—112
Thumbtack      27—28 36—37 49—50
Time      6 14 110
Topological invariance      4 10—11 17—19 22 40—42 74 93—94 111
Traditional approach      2—4 6—8 27 64
Triple cross product      91
Triple scalar product      52 84 90
Underlying Cartesian system      94—96 109
Unit cell      66—69
Unit vectors      77 80 101—102 105
Vector product      see "Cross product" "Triple
Velocity      6 14 105
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