Concise Vector Analysis (eBook)

Front Cover 1
Concise Vector Analysys 4
Copyright Page 5
Table of Contents 6
PREFACE 8
Chapter 1. Vectors and Vector Addition 10
1.1. Vectors 10
1.2. Representation of vectors 11
1.3 Vector addition 12
1.4 - a , O, .a 14
1.5 Resolution of a vector 16
1.6 Point dividing AB in the ratio m:n 
19 
1.7 Centroid or mean centre of n points 21
Exercises I 23
Chapter 2. Products of Vectors 25
2.1 Scalar product 25
2.2 Vector product 31
2.3 Triple products 37
2.4 Mutual moment of two lines 39
2.5 Positive and negative triads 40
Exercise IIc 
41 
Chapter 3. Vector Calculus 47
3.1 Vector function of a scalar 47
3.2 Unit tangent vector . 51
3.3 Functions of a vector 53
3.4 Map of a field 54
3.5 Directional derivative 57
3.6 Gradient vector 59
Exercises III 
64 
Chapter 4. Vector Calculus 
67 
4.1 Line integrals 67
4.2 Line integral of grad ø 
74 
4.3 Surface integrals 80
4.4 Volume integrals 87
4.5 Divergence 90
4.6 Gauss's transformatio 94
4.7 Curl A 97
4.8 Stokes' theorem 101
4.9 The operator . 103
4.10 The Laplacian operator 105
4.11 Orthogonal curvilinear coordinates 105
Exercises 4 107
Chapter 5. Some Applications 112
5.1 Equivalence of force systems 112
5.2 Poinsot's Central Axis 116
5.3 Space-curve 122
5.4 Infinitesimal rotations. Angular velocity 126
5.5 Angular velocity of a rigid body 128
5.6 Gauss's theorem 133
5.7 Gravitational potential 139
5.8 Equipotential surfaces 149
5.9 Green's theorems 151
Exercises 5 
154 
Index 160