Vectors and Functions

Typically, a first course in calculus comprises of the study of real-valued functions of one real variable, that is, functions f : D → R, where D is a subset of the set R of all real numbers. We shall assume that the reader has had a first course in calculus and is familiar with basic properties of real numbers and functions of one real variable. For a ready reference, one may refer to [22], which is abbreviated throughout the text as ACICARA. However, for the convenience of the reader, relevant facts from one-variable calculus will be recalled whenever needed.