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

[Smith, Alexander J.]

I used the lab acceleration just today. I did not bother to introduce polar coords.and it worked just great.
Many students saw polar coords way back in precalc, or if not, this was a gentle intro. to polar
coords.
 
One thing that struck me as odd, however, is that the word "acceleration" is never used in
the lab titled "Acceleration"!
 
I was amused, however, to overhead students talking about centripedal  (sp?) acceleration, at
no impetus on my part. 
 
Alex

	-----Original Message----- 
	From: Tevian Dray [mailto:tevian at MATH.ORST.EDU] 
	Sent: Tue 9/9/2003 6:11 PM 
	To: Bridge Users Group 
	Cc: 
	Subject: Re: [BUG] Placement of labs "Acceleration" & "Finding dr" 
	
	

	> 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
	
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