In Calculus I we moved on to the subject of integrals once
we had finished the discussion of derivatives.
The same is true in this course.
Now that we have finished our discussion of derivatives of functions of
more than one variable we need to move on to integrals of functions of two or
Most of the derivatives topics extended somewhat naturally
from their Calculus I counterparts and that will be the same here. However, because we are now involving
functions of two or three variables there will be some differences as
well. There will be new notation and
some new issues that simply don’t arise when dealing with functions of a single
Here is a list of topics covered in this chapter.
Double Integrals We will define the double integral in this
Iterated Integrals In this section we will start looking at how
we actually compute double integrals.
Double Integrals over General Regions Here we will look at some general double
Double Integrals in Polar Coordinates In this section we will take a look at
evaluating double integrals using polar coordinates.
Triple Integrals Here we will define the triple integral as
well as how we evaluate them.
Triple Integrals in Cylindrical Coordinates We will evaluate triple integrals using cylindrical
coordinates in this section.
Triple Integrals in Spherical Coordinates In this section we will evaluate triple
integrals using spherical coordinates.
Change of Variables In this section we will look at change of
variables for double and triple integrals.
Surface Area Here we look at the one real application of
double integrals that we’re going to look at in this material.
Area and Volume Revisited We summarize the area and volume formulas from