On August 21 I am planning to perform a major update to the site. I can't give a specific time in which the update will happen other than probably sometime between 6:30 a.m. and 8:00 a.m. (Central Time, USA). There is a very small chance that a prior commitment will interfere with this and if so the update will be rescheduled for a later date.
I have spent the better part of the last year or so rebuilding the site from the ground up and the result should (hopefully) lead to quicker load times for the pages and for a better experience on mobile platforms. For the most part the update should be seamless for you with a couple of potential exceptions. I have tried to set things up so that there should be next to no down time on the site. However, if you are the site right as the update happens there is a small possibility that you will get a "server not found" type of error for a few seconds before the new site starts being served. In addition, the first couple of pages will take some time to load as the site comes online. Page load time should decrease significantly once things get up and running however.
In this section we are going to relate surface integrals to
triple integrals. We will do this with
the Divergence Theorem.
Let E be a
simple solid region and S is the
boundary surface of E with positive
Let’s see an example of how to use this theorem.
Example 1 Use
the divergence theorem to evaluate
Let’s start this off with a sketch of the surface.
The region E for
the triple integral is then the region enclosed by these surfaces. Note that cylindrical coordinates would be
a perfect coordinate system for this region.
If we do that here are the limits for the ranges.
We’ll also need the divergence of the vector field so
let’s get that.
The integral is then,