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Tables of Contents for Tensor Calculus
Chapter/Section Title
Page #
Page Count
Tensor Algebra
Introduction
1
1
N-Dimensional space
2
1
Transformation of co-ordinates
2
1
Indicial and summation conventions
3
1
Contravariant vectors
4
2
Covariant vectors
6
1
Invariants
7
1
Second order tensors
8
1
Higher order tensors
9
2
Addition, subtraction and multiplication of tensors
11
1
Contraction
12
1
Quotient law
13
2
Conjugate symmetric tensors of the second order
15
2
The Line Element
Fundamental tensor
17
1
Length of a Curve
18
1
Magnitude of a vector
19
1
Associate tensors
20
1
Angle between two vectors --- orthogonality
21
1
Principal directions
22
4
Covariant Differentiation
Christoffel symbols
26
2
Transformation law of Christoffel symbols
28
2
Covariant differentiation of vectors
30
3
Covariant differentiation of tensors
33
2
Laws of covariant differentiation
35
1
Intrinsic derivatives
36
2
Geodesics - Parallelism
Geodesics
38
3
Null-geodesics
41
1
Geodesic coordinates
41
3
Parallelism
44
2
Covariant derivative
46
3
Curvature Tensor
Riemann-Christoffel tensor
49
1
Curvature tensor
50
2
Ricci tensor --- Curvature invariant
52
1
Bianchi's identity
53
1
Riemannian curvature
54
1
Flat space
55
1
Space of constant curvature
56
2
Euclidean Three-Dimensional Differential Geometry
Permutation tensors
58
2
Vector product
60
1
Frenet formulae
61
2
Surface --- First fundamental form
63
3
Surface vectors
66
2
Permutation surface tensor
68
2
Surface covariant differentiation
70
1
Geodesic curvature
71
2
Normal vector
73
1
Tensor derivatives of tensors
74
2
Second fundamental form
76
1
Third fundamental form
77
1
Gauss-Codazzi equations
78
1
Normal curvature --- asymptotic lines
79
2
Principal curvatures --- lines of curvature
81
2
Cartesian Tensors - Elasticity
Orthogonal transformations
83
2
Rotations
85
3
Cartesian tensors
88
1
Infinitesimal strain
89
3
Stress
92
2
Equations of equilibrium
94
1
Generalised Hooke's law
95
1
Isotropic tensors
96
2
Homogeneous and isotropic body
98
2
Curvilinear coordinates
100
3
Mechanics of continuous matter
103
3
Theory of Relativity
Special theory
106
3
Maxwell's Equations
109
2
General theory
111
2
Spherically symmetrical metric
113
2
Schwarzschild metric
115
1
Planetary motion
116
2
Einstein's universe
118
2
De Sitter's universe
120
2
Bibliography
122
1
Index
123