Paul's Online Math Notes
Calculus III (Notes) / Surface Integrals   [Notes] [Practice Problems] [Assignment Problems]

If you were affected by the server issues last night I apologize. Over the years the traffic on the site has increased significantly and it's reaching the point that my server is having issues handling the heavy traffic that comes at the end of the semester. Luckily I've got a new more powerful server setup almost ready to go that should be able to handle the increased traffic for the foreseeable future. It is currently scheduled to "go live" on Wednesday, May 11 2016 at 10:30 Central Standard Time. Unfortunately this is the earliest possible day to do the switch over between servers.

In the mean time the website is liable to be somewhat unreliable during the peak usage times at night and for that I apologize.

May 5, 2016

Calculus III - Notes
Line Integrals Previous Chapter  
Curl and Divergence Previous Section   Next Section Parametric Surfaces

 Surface Integrals

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.

Curl and Divergence Previous Section   Next Section Parametric Surfaces
Line Integrals Previous Chapter  

Calculus III (Notes) / Surface Integrals    [Notes] [Practice Problems] [Assignment Problems]

© 2003 - 2016 Paul Dawkins