ABSTRACT
This chapter shows how the theory of curves in space, which has many applications, can be developed to great advantage by using vectors. It explores the integrals of vector functions are introduced by analogy with ordinary integrals, and explains the ideas of scalar and vector fields, together with the notion of a directional derivative and the gradient operator that play important roles in continuum mechanics, electromagnetic theory and elsewhere. The chapter deals with the definition of the divergence and curl vector operators followed by an introduction to conservative fields and potential functions. The divergence is an operation that when performed on a vector produces a scalar quantity, while curl is an operation that when performed on a vector produces another vector.
