Tensor Calculus a Concise Course

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Courier Corporation
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Contents

CHAPTER
1
NDimensional space
2
Indicia and summation conventions
3
Contra variant vectors
4
Co variant vectors
6
Invariants
7
Second order tensors
8
Higher order tensors
9
Surface First fundamental form
63
Surface vectors
66
Permutation surface tensor
68
Surface covariant differentiation
70
Geodesic curvature
71
Normal vector
73
Tensor derivatives of tensors
74
Second fundamental form
76

Addition subtraction and multiplication of tensors
11
Contraction
12
Quotient law
13
Conjugate symmetric tensors of the second order
15
CHAPTER II
17
Length of a Curve
18
Magnitude of a vector
19
Associate tensors
20
Angle between two vectors orthogonality
21
Principal directions
22
CHAPTER III
26
Transformation law of Christoffel symbols
28
Covariant differentiation of vectors 80
33
Laws of covariant differentiation 85
35
CHAPTER IV
38
Nullgeodesies
41
Parallelism
44
Covariant derivative
46
CHAPTER V
49
Curvature tensor
50
Ricci tensor Curvature invariant
52
Bianchis identity
53
Riemannian curvature
54
Flat space
55
Space of constant curvature
56
CHAPTER VI
58
Vector product
60
Frenet formulae
61
Third fundamental form
77
GaussCodazzi equations
78
Normal curvature asymptotic lines
79
Principal curvatures lines of curvature
81
CARTESIAN TENSORS ELASTICITY PAGE 53 Orthogonal transformations
83
Rotations
85
Intrinsic derivatives
86
Cartesian tensors
88
Infinitesimal strain
89
Stress
92
Equations of equilibrium
94
Generalised Hookes law
95
Isotropic tensors
96
Homogeneous and isotropic body
98
Curvilinear coordinates
100
Mechanics of continuous matter
103
CHAPTER vm
106
Maxwells Equations
109
General theory
111
Spherically symmetrical metric
113
Schwarzschild metric
115
Planetary motion
116
Einsteins universe
118
De Sitters universe
120
Bibliography
122
Index Ml
123
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