In the previous chapter we looked at evaluating integrals of functions or vector fields where the points came from a curve in two- or three-dimensional space.  We now want to extend this idea and integrate functions and vector fields where the points come from a surface in three-dimensional space.  These integrals are called surface integrals.

Here is a list of the topics covered in this chapter.

Parametric Surfaces  In this section we will take a look at the basics of representing a surface with parametric equations.  We will also take a look at a couple of applications.

Surface Integrals  Here we will introduce the topic of surface integrals.  We will be working with surface integrals of functions in this section.

Surface Integrals of Vector Fields  We will look at surface integrals of vector fields in this section.

Stokes’ Theorem  We will look at Stokes’ Theorem in this section.

Divergence Theorem  Here we will take a look at the Divergence Theorem.