Vectors and functions

Many mathematical properties possessed by functions of several variables are couched in geometric terms and with reference to elementary set theory. In this introductory chapter I will revisit some of the concepts that will be needed in later chapters. For example, vector calculus springs naturally from vector algebra so it is appropriate to begin the review with the latter topic. This is followed by a short review of elementary set theory, which will be referred to throughout the book and will indeed help establish many foundation concepts in both the differential and integral calculus. Coordinate systems and the notion of level sets are also discussed. Once again, both topics find application in differential and integral multivariable calculus, as well as in vector calculus.