[BUG] The Hill in a multivariate course

[Martin Jackson]

All,

I am preparing to make full use of the Bridge materials in my 
multivariate calculus course that starts next week.  This is a 
semester course (15 weeks) that covers vectors, vector-valued 
functions, derivatives of functions of several variables (partial 
der, gradients, etc), multiple integrals, and vector calculus.  We 
use Strauss/Bradley/Smith (3rd edition, Strauss added as an author to 
Bradley/Smith).

When  I look to lay out Bridge activities through the semester, I see 
a big gap between (Which Way is North?/Acceleration/Finding dr) and 
The Hill if I wait to do The Hill until gradients are covered.  I'm 
considering doing The Hill just after introducing functions of 
several variables (graphs,level curves).  Students would confront the 
ideas of slope and "direction of steepest ascent" before developing 
the conventional computational tools.  This will make all of the 
activity essentially open-ended.  I might revisit the activity after 
we have worked with gradients.

In looking at the schedule of activitites that Alex Smith shared with 
us last fall (his message of August 24, 2003), I see he put The Hill 
in a spot similar to what I intend.  I also note that Alex has The 
Valley split into two parts.  Alex, can you give us a bit more detail 
on this?

Alex also mentioned a gap in the Bridge activities when doing 
multiple integrals.  In previous semesters, I have had students do 
small-group activities to get the volume elements in cylindrical and 
spherical coordinates using geometric reasoning.

I would appreciate any thoughts on this use of The Hill.

Martin