Vectors in 2 or 3 Dimensions provides an introduction to vectors from their very basics. The author has approached the subject from a geometrical standpoint and although applications to mechanics will be pointed out and techniques from linear algebra employed, it is the geometric view which is emphasised throughout.
Properties of vectors are initially introduced before moving on to vector algebra and transformation geometry. Vector calculus as a means of studying curves and surfaces in 3 dimensions and the concept of isometry are introduced later, providing a stepping stone to more advanced theories.
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Vector equation of a straight line
Scalar products and equations of planes
Vector products and intersection of planes
Linear combinations and bases
Linear transformations of R3 matrices and change of basis
Vector valued functions of a single variable
Cylindrical and spherical polars