[BUG] RE: dr and coordinate systems - BUG Digest, Vol 4, Issue 4

[Larry Tankersley]

Tevian,
  The bright students progress and err on their own. Our task is to prepare
the average and somewhat challenged students. In their cases, the anchoring
topics are crucial. For the applications in physics, the necessary anchors
include a review of coordinate systems including specific detailed
treatments of cylindrical and spherical coordinates. In each system, the
position vector, the line element and the basic representation of a vector
as components multiplying each of the coordinate directions must be
presented. The coordinate direction derivatives are the capstone to a full
introduction to the systems. (Generalized curvilinear systems need not be
presented.) In every facet, the goal is to ** visualize ** the situation as
well as to be able to compute the desired result. The visualization provides
the bridge to the application in many instances. I recommend problems that
require the students to sketch line elements, coordinate 'cubes', ... .

The line element dr or d'el' is so central that its representations and
development should be revisited frequently.

I have attached notes on coordinates and a visitation to dr as examples.
Both are due for edits.
                              Larry

Prof Larry Tankersley
U S Naval Academy Physics
572C Holloway Road
Annapolis MD 21402
(410) 293-6653  Office
(410) 293-3729  FAX
tank at usna.edu
 

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Subject: BUG Digest, Vol 4, Issue 4

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Today's Topics:

   1. starting slow (Tevian Dray)


----------------------------------------------------------------------

Message: 1
Date: Mon, 10 Apr 2006 21:40:15 -0700
From: Tevian Dray <tevian at math.oregonstate.edu>
Subject: [BUG] starting slow
To: Bridge Users Group <bug at science.oregonstate.edu>
Message-ID: <20060411044015.669697D9 at octini.math.oregonstate.edu>

I had an interesting conversation today with a student from my honors class
last term.  This student had always been good at math, and had developed the
habit of skipping class, not doing homework, but studying hard for, and
doing well on, exams.  Wound up with an A- in my class, quite respectable
under the circumstances, but not the desired, or expected, grade.

I explained that vector calculus was not easy to learn through last-minute
memorization of formulas, especially the way I teach it.  The response was
to
point out that I had warned the class at the beginning that we would start
out
slowly, spending lots of time on the basics (vector differentials, "review"
of
dot product and gradient), then using the same tools over and over again.
Yes, the student said, that was exactly true -- having been in class for the
first couple of weeks, the later material made sense, even trying to learn
it
on one's own.

While I am not pleased to think of this argument being used as an excuse to
miss class, I do think it is a strong statement in favor of spending the
extra
time at the beginning to develop those basic ideas.

I mentioned this story to the current TA, who has been with the course all
year long, with 3 different instructors.  Yes, he said, with one instructor
in
particular, who didn't spend as much time on the vector differential at the
beginning, the entire term was full of discussions which boiled down to how
to
compute dr.  In other terms, where this was emphasized from the start, such
computations were much less of a problem.

Tevian



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