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Re: another math question

Justin asks:

-----Original Message-----
From: Justin Parke [mailto:FIZIX29@AOL.COM]
Sent: Tuesday, June 11, 2002 11:43 AM

I am wondering if, when I introduce vector operators like the gradient,
divergence, and curl, I
should go beyond just rectangular coordinates and include cylindrical and
spherical as well. We >do discuss these coordinate systems in terms of
equations of surfaces etc but none of the
textbooks employ them in vector analysis and I don't understand why. From
a physics standpoint
(like in electrostatics) performing these operations in spherical
coordinates is sometimes
preferred over rectangular.

But if none of the calculus textbooks do this then perhaps I am overlooking
a good reason why it >ought not be done.

Thoughts?

Would it be useful? Perhaps, if they can get to an understanding of what
grad, div, and curl are measuring. But most students come to me with
nothing but a formula and no underlying conceptual base. I'd rather they
had a working conceptual understanding, with some ability to calculate in
Cartesian coordinates than simply memorize a set of formulas. We can always
help them to extend that basic understanding with specific applications in
curvilinear coordinates.

*********************************************
"In my opinion, we don't devote nearly
enough scientific research to finding a
cure for jerks."
--Calvin and Hobbes
********************************************
George Spagna
Department of Physics
Randolph-Macon College
P.O. Box 5005
Ashland, VA 23005-5505
phone: (804) 752-7344
FAX (804) 752-4724
e-mail: gspagna@rmc.edu
http://www.rmc.edu/~gspagna/