Vectors in Three-Dimensional Space 0521292891, 9780521292894

Table of contents :
CONTENTS......Page 5
Preface......Page 7
1.1 Introduction......Page 13
1.2 Scalar multiplication of vectors......Page 15
1.3 Addition and subtraction of vectors......Page 17
1.4 Displacements in Euclidean space......Page 24
1.5 Geometrical applications......Page 29
2.1 Scalar products......Page 36
2.2 Linear dependence and dimension......Page 42
2.3 Components of a vector......Page 47
2.4 Geometrical applications......Page 54
2.5 Coordinate systems......Page 63
3.1 The vector product of two vectors......Page 69
3.2 The distributive law for vector products; components......Page 72
3.3 Products of more than two vectors......Page 77
3.4 Further geometry of planes and lines......Page 84
3.5 Vector equations......Page 92
3.6 Spherical trigonometry......Page 96
4.1 Vectors and matrices......Page 99
4.2 Determinants; inverse of a square matrix......Page 104
4.3 Rotations and reflections in a plane......Page 114
4.4 Rotations and reflections in 3-space......Page 123
4.5 Vector products and axial vectors......Page 134
4.6 Tensors in 3-space......Page 136
4.7 General linear transformations......Page 140
5.1 Definition of curves and surfaces......Page 147
5.2 Differentiation of vectors; moving axes......Page 161
5.3 Differential geometry of curves......Page 170
5.4 Surface integrals......Page 184
5.5 Volume integrals......Page 200
5.6 Properties of Jacobians......Page 212
6.1 Scalar and vector fields......Page 215
6.2 Divergence of a vector field......Page 223
6.3 Gradient of a scalar field; conservative fields......Page 233
6.4 Curl of a vector field; Stokes' theorem......Page 242
6.5 Field operators; the Laplacian......Page 254
Appendix A Some properties of functions of two variables......Page 265
Appendix B Proof of Stokes' theorem......Page 275
Reference list......Page 281
Outline solutions to selected problems......Page 283
Index......Page 297