Introduction

The famous triple peaks Eiger, Monch, and Jungfrau in the Swiss alps. The steepness at a point in a mountain range is measured by the gradient, a concept defined in this chapter.

In this chapter we extend the concepts and techniques of differential calculus to functions of several variables. As we will see, a function \(f\) that depends on two or more variables has not just one derivative but rather a set of partial derivatives, one for each variable. The partial derivatives are the components of the gradient vector, which provides valuable insight into the function’s behavior. In the last two sections, we apply the tools we have developed to optimization in several variables.