Hi guys,

Here's some junk from your office visit, in case you find it useful. I added a few things.

For problem 12.7.24, we wanted to look at the extreme values of the function    on the unit disk  .

Here's a basic plot of the function on the square .

One question was, how can we isolate our region (the unit disk) of this plot, graphically? Here is one easy way that I didn't mention, but that is occasionally useful. We are looking for maximum and minimum values, so wem look where it is darkest and lightest.

We can make this prettier by using different functions for the shading. Here's an easy one.

But we want 3D. Let me first turn off an annoying message.

Here's our function, plotted only inside the unit disk. This does a pretty good job of illustrating things.

Here's the perimeter of the section of our surface.

Let's superimpose it on our original plot.

Gee whiz. The points lie right on the surface, so Matt has a hard time combining them. We'll fudge it and lift the z values ever-so-slightly.

If we are really geeked out we can check our computed extreme values. (These don't look very good.)