[BUG] update

[Stuart Boersma]

This quarter I taught our third quarter calculus course.  We start with
series and work through multivariable functions, directional
derivatives, gradient, and optimization problems. I used the following
labs:
1. Which way is north?:  This lab went over very well.  the students
liked it.
2. Finding dr(vector): 
 a.  Since I didn't use the Acceleration lab, I added problem zero from
Acceleration to this lab.  When trying to give advice to the class as a
whole while they were working on this lab, the abundance of "r"s made
this tough (\vec r, \hat r, r the scalar, dr the scalar, dr the vector,
etc).  
  b. Many of my students didn't sketch r hat and theta hat with their
tails on the unit circle (many had their tips end on the circle).  Maybe
this should be made explicit in the directions?
c.  When they were asked to plot all four vectors (i,j,r hat, theta
hat) they again, didn't always put the tails at the same point.  Thus, I
don't think they really saw how all four vectors were related.

3. The Hill:
 a.  Many of my students had a hard time drawing a simple picture
representing the steepness of the hill.  Not really sure why...
 b. For the last problem, determining the correct k component can be
tricky (norm of grad or the norm squared).  If they realized that this
vector should be tangent to the hill and they recall how to find normal
vectors to surfaces using gradients, they could quickly check their
work.  I had one student do this (actually he found the k component by
making the corresponding dot product equal to zero).

On a related note: In the instructor's guide the directional derivative
is derived from the master formula as a rate of change with respect to
distance traveled (the puddle problem).  However, in the hill problem to
correctly interpret the "steepness" of the hill, you need to realize
that a directional derivative give the rate of change as a function of
distance traveled IN THE TOPO MAP (i.e. horizontal distance traveled). 
Right?  

Spring quarter I will teach the next class which will involve multiple
integration and vector calculus.

NSF deadline on Thursday, so gotta go...

Stuart.