Author(s): Murray Spiegel, Seymour Lipschutz, Dennis Spellman
Series: Schaum’s outline series
Edition: 2nd
Publisher: McGraw-Hill Education
Year: 2009
Language: English
Pages: 249
Contents......Page 8
1.1 Introduction......Page 12
1.2 Vector Algebra......Page 13
1.4 Rectangular Unit Vectors i, j, k......Page 14
1.7 Vector Field......Page 16
1.8 Vector Space R[Sup(n)]......Page 17
2.2 Dot or Scalar Product......Page 32
2.4 Triple Products......Page 33
2.5 Reciprocal Sets of Vectors......Page 34
3.2 Ordinary Derivatives of Vector-Valued Functions......Page 55
3.3 Continuity and Differentiability......Page 57
3.4 Partial Derivative of Vectors......Page 58
3.5 Differential Geometry......Page 59
4.2 Gradient......Page 80
4.3 Divergence......Page 81
4.5 Formulas Involving ▽......Page 82
4.6 Invariance......Page 83
5.2 Ordinary Integrals of Vector Valued Functions......Page 108
5.3 Line Integrals......Page 109
5.4 Surface Integrals......Page 110
5.5 Volume Integrals......Page 111
6.2 Main Theorems......Page 137
6.3 Related Integral Theorems......Page 138
7.3 Orthogonal Curvilinear Coordinates......Page 168
7.4 Unit Vectors in Curvilinear Systems......Page 169
7.6 Gradient, Divergence, Curl......Page 170
7.7 Special Orthogonal Coordinate Systems......Page 171
8.3 Coordinate Transformations......Page 200
8.5 Contravariant, Covariant, and Mixed Tensors......Page 201
8.6 Tensors of Rank Greater Than Two, Tensor Fields......Page 202
8.8 Matrices......Page 203
8.10 Associated Tensors......Page 205
8.12 Length of a Vector, Angle between Vectors, Geodesics......Page 206
8.13 Covariant Derivative......Page 207
8.16 Intrinsic or Absolute Derivative......Page 208
8.17 Relative and Absolute Tensors......Page 209
D......Page 246
M......Page 247
S......Page 248
Z......Page 249
