Introduction

This fluid velocity vector field, from a study of turbulent flow, was produced using PIV (particle image velocimetry) in which the motion of tracer particles is captured by a high-speed digital camera.

In the previous chapter, we generalized integration from one variable to several variables. In this chapter, we generalize still further to include integration over curves and surfaces, and we will integrate not just functions but also vector fields. Integrals of vector fields are used in the study of phenomena such as electromagnetism, fluid dynamics, and heat transfer. To lay the groundwork, the chapter begins with a discussion of vector fields.