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Aristotle D. Michal — Matrix and tensor calculus: with applications to mechanics, elasticity, and aeronautics
Aristotle D. Michal — Matrix and tensor calculus: with applications to mechanics, elasticity, and aeronautics



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Название: Matrix and tensor calculus: with applications to mechanics, elasticity, and aeronautics

Автор: Aristotle D. Michal

Аннотация:

This volume offers a working knowledge of the fundamentals of matrix and tensor calculus that can be applied to a variety of fields, particularly scientific aeronautical engineering. Mathematicians, physicists, and meteorologists as well as engineers will benefit from its skillful combination of mathematical statements and immediate practical applications.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 144

Добавлена в каталог: 18.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Aircraft flutter, calculation of      34 35 36
Aircraft flutter, description of      32
Aircraft flutter, matric differential equation of      33
Aircraft flutter, need for matric theory in calculations for fast aircraft      37
Aitken      124
Appell      125
Bingham      14 124
Biot      34 113 124
Bleakney      124
Bocher      111 124
Born      111 124
Boundary layer, theory of Prandtl      109
Boundary layer, thickness of      109
Boundary-layer equations      104 105 106 107 108
Brillouin      117 125
Carslaw      34 124
Cartan      121
Cayley — Hamilton theorem for matrices      12
Chien      x 105 127
Christopfel symbols, Euclidean      53
Christopfel symbols, multidimensional Euclidean      95
Christopfel symbols, proof of law of transformation of      114 115
Christopfel symbols, Riemannian      96
Codazzi equations for a surface      122
Collar      1 34 35 124
Compressible fluids      103 104
Contraction of a tensor      116
Correlation tensor field in turbulence      73 74
Cosserat, E. and F.      117
Covariant differentiation of Euclidean metric tensor      59
Covariant differentiation of scalar field      60
Covariant differentiation of tensor fields in general      58
Covariant differentiation of vector fields      56 57
Covariant differentiation, its commutativity in Euclidean spaces      58 59
Covariant differentiation, its non-commutativity in general in Riemannian spaces      99 100
Cramer's rule      111
Crystalline media      93
Curvature of a surface, Gaussian      123
Curvature of a surface, mean      123
Darboux      126
Den Hartog      124
Differential equations of small oscillations      24 25
Differential equations with variable coefficients      21 22
Differential equations, example      25 26
Differential equations, frequencies and amplitudes      29 30 31
Differential equations, harmonic solutions      28
Differential equations, solution of linear      20
Differentiation of matrices      16
Dirac      111 124
Duncan      1 34 35 124
Dynamical systems with n degrees of freedom      24 101
Dynamical systems with n degrees of freedom, Lagrange's equations of motion of      24 101
Eisenhart      118 126
Elastic deformation, change in volume under      79 80 81
Elastic deformation, matrix methods in formulation of finite      38 39 40
Elastic deformation, tensor methods in formulation of finite      75 76 77
Elastic potential      91 92
Equation of continuity      69 70 71 103
Ertel      114 116 126
Euclidean Christoffel symbols      53
Euclidean Christoffel symbols for Euclidean plane      54
Euclidean Christoffel symbols, alternative form for      54
Euclidean Christoffel symbols, exercise on      55
Euclidean Christoffel symbols, law of transformation of      53
Euclidean Christoffel symbols, multidimensional      95
Euclidean metric tensor      43
Euclidean metric tensor, exercises on      47
Euclidean metric tensor, its law of transformation      46
Euclidean spaces      42
Euclidean spaces, multidimensional      95
Euler — Lagrange equations for geodesics      100
Eulerian strain tensor      77 78
Fantappie      112 124
Fluids, compressible      103 104
Fluids, incompressible      103 104
Fluids, incompressible, boundary-layer equations for      104 105 106
Fluids, Navier — Stokes equations for incompressible viscous      104
Fluids, Navier — Stokes equations for viscous      69 70
Frazer      1 34 35 124
Functionals      18 112
Fundamental forms of a surface      122
Garrick      36 125
Gauss      43
Gauss, equations for a surface      122
General theory of relativity      42
Geodesic coordinates      97
Geodesics      100
Geodesics, dynamical trajectories as      118 119 120 121
Geodesics, Euler — Lagrange equations for      100
Goursat      118 121
Holzer      124
Homogeneous strains      83
Homogeneous strains, fundamental theorem on      84 85 86
Hooke's law      94
Hotelling      111 124
Howarth      126
Hydrodynamics      42
Hydrodynamics, Eulerian equations      116
Hydrodynamics, Lagrangean equations      116
Integral invariants      121
Isotropic medium      92 93 94
Isotropic medium, condition for      92 93
Isotropic medium, stress-strain, relations for      93 94
Isotropic strain      84
Jaeger      34 124
Jeffreys      126
JORDAN      111 124
Karman      x 34 38 74 113 124 126
Kasner      126
Killing's differential equations      88
Kinetic potential      101
Kirchhoff      117 126
Kussner      124
Lagrange's equations of motion      24 201 102
Lagrangean strain tensor      77 78
Lamb      116 126
Laplace equation      62 63
Laplace equation for vector fields      65
Laplace equation in curvilinear coordinates      63 64
Levi-Civita      117 127
LIB      121
Libber      ix 124 125
Lie      x 104 105
Line element      42
Line element in curvilinear coordinates      45 46 47
Line element, exercises on      45 46 47
Line element, geodesic form of      105
Line element, Riemannian      96
Linear algebraic equations, solutions      9
Linear algebraic equations, solutions, numerical      14
Linear algebraic equations, solutions, punched-card methods      14
Linear differential equations in matrices      21 22
Linear differential equations with constant coefficients      20
Linear differential equations with variable coefficients      21 22
Linear differential equations, application of matric exponential to      20
Linear differential equations, method of successive substitutions in solution of      22
Lipp      ix
Love      126
MacDuffee      125
Martin      112 125
Matric exponential, application to systems of linear differential equations with constant coefficients      20
Matric exponential, convergence of      112
Matric exponential, definition of      15
Matric exponential, properties of      16
Matric power series, definition of      15
Matric power series, theorem on computation of      18
Matrix of same type      2
Matrix, addition      2
Matrix, adjoint of      39
Matrix, application of inverse, to solution of linear algebraic equations      9
Matrix, Cayley — Hamilton theorem      12
Matrix, characteristic equation of      12
Matrix, characteristic function of      12
Matrix, characteristic roots of      12
Matrix, column      2
Matrix, definition of      1
Matrix, differentiation of, with respect to numerical variable      16
Matrix, dynamical      29
Matrix, example of non-commutativity of matrix multiplication      5
Matrix, index and power laws      11
Matrix, integration of, with respect to numerical variable      17
Matrix, inverse      8
Matrix, multiplication      5
Matrix, multiplication by number      11
Matrix, norm of      112
Matrix, order      2
Matrix, polynomials in a      11
Matrix, row      2
Matrix, rule for computation of inverse      13
Matrix, square      2
Matrix, strain      39 40 41
Matrix, symmetric      40
Matrix, trace of      13 111
Matrix, unit      4
Matrix, zero      3
McConnell      122 126
Michal      ix x 112 114 116 118 121 125 126
Millikan      x
Multiple-point tensor fields      71 72 73 74
Multiple-point tensor fields in elasticity theory      76
Multiple-point tensor fields in Euclidean geometry      71 72 73 74
Multiple-point tensor fields in turbulence      73 74
Murnaghan      117 126
Navier — Stokes differential equations for a viscous fluid      69
Navier — Stokes differential equations in curvilinear coordinates      70
Navier — Stokes differential equations subject to condition of incompressibility      104
Norm of a matrix      112
Normal coordinates      116
Normed linear ring      112
Oldenburger      125
Pipes      125
Plastic deformation      114
Poincare      121
Poisson equation      66 67 68
Principal radii of curvature of boundary-layer surface      108
Putt      ix
Quadratic differential form      45 46
Reutter      127
Ricci      117 127
Riemann      127
Riemann — Christoffel curvature tensor      99 100
Riemannian geometry      96 97 98 99 100
Riemannian geometry, applications to boundary-layer theory      103 104 105 106 107 108 109 110 121 123
Riemannian geometry, applications to classical dynamics      101 102
Riemannian geometry, example      98
Riemannian geometry, infinite dimensional, x      118
Rigid displacement      40 77
Scalar density      60 61 67
Scalar field      49
Scalar field, relative      60 61 62
Schwarz      124
Strain invariant      82 117 118
Strain matrix      39 40 41
Strain matrix in infinitesimal theory      41
Strain tensor      48 49
Strain tensor, Eulerian      77
Strain tensor, Lagrangean      77
Strain tensor, variation of      86 87 88
Stress tensor      89 90
Stress tensor, symmetry of      91
Stress vector      89 90
Stress-strain relations for isotropic medium      93 94
Summation convention      4 43
Sylvester's theorem      112 113
Synge      127
Tensor analysis      56
Tensor analysis in multidimensional Euclidean spaces      95
Tensor analysis in Riemannian spaces      97 99 100
Tensor analysis, applications to boundary-layer theory      103 104 105 106 107 108 109 110 121 122 123
Tensor analysis, applications to classical dynamics      101 102 118 119 120 121
Tensor field of rank two, contravariant      50
Tensor field of rank two, covariant      50
Tensor field of rank two, mixed      50
Tensor field, contraction of a      116
Tensor field, covariant differentiation of      57 58
Tensor field, exercises on      59
Tensor field, general definition of      57 58
Tensor field, property of a      59
Tensor field, relative      60 117
Tensor field, Riemann — Christoffel curvature      99 100
Tensor field, weight of      60
Theodorsen      33 36 125
Thomas      114 116 118 126 127
Timoshenko      125
Turbulence      73 74
Turbulence, correlation tensor field in      73 74
Veblen      114 127
Vector field in rectangular cartesian coordinates      50
Vector field, contravariant      49
Vector field, covariant      49
Velocity field      51
Velocity field, divergence of      103 117
Volterra      112 125
Wave equation      65 66
Webster      116 127
Wedderburn      125
Whitehead      114 127
Whittaker      28 125 127
Wright      127
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