Introduction

The first three sections of this chapter develop some additional uses of integration, including two important physical applications. The last section introduces Taylor polynomials, the higher-order generalizations of the linear approximation. Taylor polynomials illustrate beautifully the power of calculus to yield valuable insight into functions.

This NASA simulation, depicting streamlines of hot gas from the nozzles of a Harrier Jet during vertical takeoff, is based on a branch of mathematics called computation fluid dynamics.