ABSTRACT
In this chapter, we begin with a review the basic concept of a vector, vector addition and how to represent and plot vectors in Python. We will then introduce scalar and vector fields, and show how to use the dot product and cross product–operations on vectors. Triple vector and scalar products are introduced and we demonstrate how SymPy can be used to demonstrate vector identities. After establishing the basic rules for Cartesian vectors, we present non-Cartesian coordinate systems (polar, cylindrical and spherical) and their unit vectors. We discuss the derivatives of time-dependent vectors, and return to Cartesian coordinates to discuss how to use vectors to develop parametric equations for lines and planes, and how to represent them graphically in Python.
