[BUG] notation
Tevian Dray
tevian at math.oregonstate.edu
Mon Mar 17 14:58:34 PDT 2008
On the one hand, dr-vector is d(r-vector), so it should presumably be
written with an arrow over r-vector, or typeset with r, but not d, in
bold. This correctly emphasizes that "zapping with d" is a scalar
operation, which can be applied to the position vector.
On the other hand, dr-vector is a fundamental geometric object in its
own right, the infinitesimal vector displacement, which surely should be
written as "dr" with an arrow over the whole thing, or typeset all in
bold.
The point is surely that these two ways of writing dr-vector emphasize
different viewpoints, and that it is a theorem that these viewpoints
turn out to be equivalent. But what about dA-vector, which is *not* d
of anything (a common student misconception), much less "d(A-vector)",
and which should therefore surely be written as "dA" with an arrow, or
typeset all in bold.
So which is best? Emphasize that dr-vector is fundamental by *not*
writing it as d(r-vector), thus also de-emphasizing the parametric
viewpoint (I regard this as an advantage) but also de-emphsazing the key
role played by differentials (I regard this as a disadvantage)? Abuse
the notation by writing d(A-vector), probably reinforcing a common
student misconception? Not worry about consistency at all? Explicitly
introduce both dr-vector and d(r-vector), then pick one (but which)?
Just thinking out loud here; comments welcome.
Tevian
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