ABSTRACT
This chapter describes the idea of a derivative of a vector function and considers its geometrical as well as physical significance. It deals with vector functions defined in an interval which may contain one or both endpoints and which may be infinite. The concepts of linear dependence and orthogonality of vectors can likewise be carried over to vector functions. The study of curves and surfaces in space is greatly facilitated by the use of vector calculus. A curve that is represented in parametric or vector equation can be given one of two possible directions with respect to the parameter in a natural way. The torsion of a curve is a measure of the rate at which the binormal vector or the osculating plane rotates about the tangent vector as it moves along the curve. Many of the theorems on scalar functions concerning limits, continuity and derivatives can be carried over to vector functions in an almost straightforward fashion.
