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Re: vector components and notation



(Oops. I thought sending styled mail would serve my purposes in this
post, but it appears that the result was hopelessly garbled with
other tags. I'll try again using manually inserted tags where
needed.)

At 6:14 PM -0400 9/16/02, Bob LaMontagne wrote:

One of the reasons that I have used Serway (Physics for Scientists
and Engineers) is because I feel he is one of the few authors who
really presents the concept of components correctly and also very
clearly explains the concept to the student. ...

I have problems with Serway's approach because the notation is
inherently inconsistent. He defines <i>A</i> as the magnitude of
<b>A</b>. He then defines the *vectors* <b>A</b>_x and <b>A</b>_y.
Logically, therefore, <i>A</i>_x and <i>A</i>_y would be the
*magnitudes* of the vectors <b>A</b>_x and <b>A</b>_y. But in the
next breath they are defined instead as the ordinary signed scalar
components of the vector <b>A</b>.

While I like the idea of being able to talk about *vector* components
as well as *scalar* components, I think it almost inevitably leads
either to notational awkwardness or inconsistency, both of which are
potentially confusing to students.

John
--
A. John Mallinckrodt http://www.csupomona.edu/~ajm
Professor of Physics mailto:ajm@csupomona.edu
Physics Department voice:909-869-4054
Cal Poly Pomona fax:909-869-5090
Pomona, CA 91768-4031 office:Building 8, Room 223