[BUG] Placement of labs "Acceleration" & "Finding dr"

[Tevian Dray]

> In my 3rd quarter Calculus class I was planning on using the labs
> "Acceleration" and "Finding dr" shortly after introducing the ideas of
> Vectors (Chapter 13 in Hughes-Hallett et al).  I thought this would
> provide a nice introduction to the polar basis vectors as well as seeing
> vectors used at the "differential level".  Two concerns:
> 1.  Polar Coordinates are not even mentioned in this text until chapter
> 16 for use in multiple integrals.
> 2.  Parameterized curves (the language used in the "Acceleration" lab)
> are not introduced until even later (Ch. 17). 
> 

My suggestion would be to skip the Acceleration lab altogether, but possibly
to use its warmup problem to introduce polar (coordinates and) basis vectors.
I would personally do this in lecture, rather than making it part of the group
activity, but I could imagine it being done either way.

This avoids having to introduce parametric curves too early (part of your
concern A), while ensuring that the vector differential dr is covered before
the gradient (your concern B).  As for doing the Acceleration lab later
(concern C), I don't think it's necessary, especially if you are using polar
basis vectors at least occasionally anyway.  On the other hand, if this
material is in a different class (your Calc IV), it might be a good review.

This does of course require you to introduce polar coordinates early.  I see
no problem with that -- Section 16.4 in HH is only about how to use polar
coordinates in double integrals, and clearly assumes prior knowledge of polar
coordinates themselves, which are reviewed in Appendix B.

Tevian