Calculus Review

Abstract

Many techniques used in this text will require some knowledge of various levels of Calculus, especially multivariable Calculus. This chapter provides a refresher of relevant Calculus topics and may either be read carefully, skimmed, or visited as needed. Certainly the authors can work in the algebraic completion of the reals, namely do our analysis in Cn, or even a more abstract space; but as Optimization very often involves applications to real-world problems, they choose to do our work in this text in Rn. Though the result of the Intermediate Value Theorem seems intuitively obvious, its proof relies on the Completeness Property of the Real Numbers and can be found in a beginning Real Analysis text. The authors may use the ideas to find approximations of zeros of a function.