Here are some videos showing heat-wave in action. I set them to music instead of narration because I'd much rather listen to music than a rambling monologue.
This first video shows the heat-wave program solving various sheets, using both the heat- and damped-wave-equations. There is some scrolling and zooming, but it's done by hand and a little rough.
A scriptable UI with timing would lead to smoother video.
The next two videos illustrates how to use the scrollbars and sliders to rotate and zoom around the view. They also show a little of what you can do with the Slicing controls in the Draw tab.
(Another video showing scrollbar and slider controls.)
These last videos show heat-wave solving more heat- and wave-sheets, set to music.
As an aside, by making mistakes I discovered a few things while making these videos. First, if you're going to make screen-capture video, get a machine with lots of power and memory. I'm running Vista on an older machine with 1GB of memory and no graphics card, and I crashed many times. The video-capture software uses a lot of CPU and memory, and when it is constrained it produces jerky video with uneven timing.
The second lesson is that while there's a lot video-editing packages available, most of them are geared to home videos and not to demos and music. They're simple and easy, assuming all you want is to paste together a few clips and cut out the bad spots. They are not good for quick cutting, synchronizing video to music, or any kind of complicated editing.