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Tables of Contents for Vectors and Tensors in Engineering and Physics
Chapter/Section Title
Page #
Page Count
Preface
v
Vector Algebra
1
16
Introduction
1
1
Historical Notes
1
1
Vector Basics
2
3
Dot and Cross Product
5
4
Physical Scalars and Vectors
9
7
Notation of Others
16
1
Tensor Algebra
17
12
Tensors Defined
17
3
Basic Properties of Tensors
20
2
More Properties of Second-Order Tensors
22
2
Physical Tensors
24
4
Notation of Others
28
1
Cartesian Components
29
22
Components of a Vector and Coordinates of a Point
29
5
Tensor Components
34
2
Eigenvector Representations
36
6
Geometric Distortions and the Polar Decomposition Theorem
42
3
Physical Applications
45
5
Notation of Others
50
1
General Components
51
22
Change of Cartesian Base Vectors and Coordinate Systems
51
4
Rotations in Two Dimensions
55
5
Rotations in Three Dimensions
60
2
Invariance of Tensor Components
62
5
General Bases
67
4
Notation of Others
71
2
Tensor Fields of One Variable
73
26
Basic Calculus of Vector Fields
73
2
Moving Base Vectors
75
3
Newtonian Mechanics of a Particle
78
6
Differential Geometry of a Space Curve
84
4
Motion of a Rigid Body
88
9
Notation of Others
97
2
Tensor Fields of Many Variables
99
32
Differentiation of Scalar Fields
99
5
Differentiation of Vector Fields
104
4
Line, Surface, and Volume Integrals
108
5
Green's Theorem and Potential Fields of Two Variables
113
9
Stokes' and Divergence Theorems and Potential Fields of Three Variables
122
7
Notation of Others
129
2
Applications
131
46
Heat Conduction
131
7
Solid Mechanics
138
10
Fluid Mechanics
148
9
Newtonian Orbital Mechanics
157
7
Electromagnetic Theory
164
12
Notation of Others
176
1
General Coordinates
177
30
General Curvilinear Coordinates
177
7
Orthogonal Curvilinear Coordinates
184
7
Surface Coordinates
191
9
Mechanics of Curved Membranes
200
5
Notation of Others
205
2
Four-Dimensional Spacetime
207
18
Special Relativity
207
9
General Relativity
216
6
Notation of Others
222
3
REFERENCES
225
6
Historical
225
1
Mathematical
225
2
Physical
227
4
Answers to Problems
231
44
Index
275