Vector Field
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Scalar and Vector Algebra -Prerequisites
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The purpose of this chapter is to provide a transition from the elementary study of vectors to their study at degree or diploma level. To a large extent, therefore, this chapter should act as a summary of results previously mastered by the student, and it is assumed that the student is already familiar with such things as the triangle law of addition of vectors, the scalar and cross products of vectors and the triple scalar product of vectors. These results will only be summarised here. In addition to this summary the study of vectors will be introduced with more formalism, and it is assumed that the student is already familiar with the vector space axioms and, in addition, the rotation of axes and the transformation matrix used to represent this. Finally, certain important results that may not have been introduced at a more elementary level will be given. These results are given, firstly, for the sake of completeness, and secondly, because they are referred to in subsequent proofs and it is therefore important that the student should have seen them.
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Contents of
Vector Field
1 Scalar and Vector Algebra -Prerequisites
2 Formal definition of a vector
3 The position vector
4 About vectors
5 Orthonormal basis
6 Scalar product
7 Scalar invariant
8 Resolute of a vector
9 The cross (vector) product
10 Distributive law
11 Basis vectors
12 Area of the parallelogram
13 Parallel, anti-parallel
14 The triple scalar product
15 The triple vector product
16 Quadruple vector products
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