[BUG] The Hill in a multivariate course

[Tevian Dray]

This is a nice discussion!  We realize that we don't yet have a complete set
of activities for multivariable calculus, so this discussion is timely.

I like the idea of doing the Hill activity early, although it may need to be
modified somewhat so as to not emphasize the gradient so much.

As far as splitting the Valley activity, some of you will recall that an
earlier version refers only to the Master Formula, and not to line integrals.
This seems to correspond at least roughly to the split Alex made.
You can find the older version in the Winter 2003 activities available at
	http://www.math.oregonstate.edu/bridge/labs

Regarding Martin's comment about having students work on finding volume
elements in cylindrical and spherical coordinates, we have a worksheet which
does something similar, namely deriving expressions for dr vector.  You can
find this worksheet either in the Instructor's Guide (unnumbered pages 17-20)
or on the supplemental homework page for last term at OSU:
	http://oregonstate.edu/~drayt/MTH255/Fall03
(It's the link labeled "Vector Differentials".)

I typically assign this worksheet for homework, but Corinne has used it as an
in-class activity, which students seem to really like.  We are planning some
minor changes, however, primarily to minimize the confusion caused by
second-order terms along the particular paths shown.

Tevian