Mathematical Models in the Physical Sciences.
Prereq: MA 242; and MA 405.
( 11:45am - 1:00pm, Tuesday-Thursday, in HA 263 )

This course should be of interest to any undergraduate who is eager
to learn about differential forms. We will use differential forms
to rephrase the mathematics of MA 242 in a neat unified language.
The gradient, curl and divergence will be unified into the exterior derivative.
The generalized Stoke's theorem will be applied to reproduce the
Fundamental Theorem of Calculus, Stoke's, and Greene's Theorems.

As our central example, we will explore how Maxwell's equations
can be written in the language of differential forms. Lastly, we will
define geometry on a vector space. In particular, Minkowski space
will be seen to be the geometry which is consistent with Maxwell's equations.

No previous knowledge of physics is assumed and all mathematics beyond
MA 242 and MA 405 will be developed during the course. If you are
interested in differential geometry or general relativity this course
would be a good step in that direction. Differential forms are often
used in advanced mathematics. If one knew about differential forms
in a more down to earth context it would make those later courses
less formidable. That is essentially the mathematical-goal of this course.
We will develop the calculus of differential forms ( which can be a very
abstract discussion in general ) and link in a very concrete way to the
standard version of calculus of 3 variables.

Note: this course is currently listed as being taught by Dr. Fulp. If the paper work goes through
then hopefully I'll be teaching it under his supervision.

[Edited on March 21, 2006 at 2:00 AM. Reason : formatting.]

3/21/2006 1:56:41 AM

sounds cool

3/21/2006 2:14:02 AM

you want to register for the course... you feel the need to register for the course...

3/21/2006 2:15:28 AM

i talked to Dr. Fulp (best advisor EVER) about this class...looks interesting. I registered for it, so yay. You were also my 341 TA, and Dr. Fulp showed me some of your stuff so it looks like a safe class to take.

Funny you mention the Maxwell stuff -- we're deriving the differential forms for them in 574 right now.

3/21/2006 9:00:25 AM

Ah yes, the MA 341 Chukwu experience. That was fun. One of the more interesting and rewarding
jobs I've had here...

I guess you've had some ECE courses, this course might be very trivial to you at this point. I suppose I'll probably emphasize points no engineer would bother to deal with, so hopefully it will not be entirely a review.

You mentioned you are using differential forms in 574, which class is that?

Dr. Fulp is hard to beat as an advisor, no doubt. He's teaching a course on Lie Groups in the Fall
it should interesting.

I just checked the open section inquiry said 18 seats remain. 25-18 = 7 enrolled. Just a few more and we are in the clear... Join us, I implore you good citizens of TWW.

3/21/2006 7:58:47 PM

Quote :

" suppose I'll probably emphasize points no engineer would bother to deal with"

Careful with those hasty generalizations.

3/21/2006 8:26:21 PM

Nothing wrong with engineers generally, I just have different questions. It's why I left engineering, my motivations are quite different. I'm more interested in the mathematical structure of physical theory, as opposed to the technological applications of physical theory. Granted, no strict demarcation can be made between mathematics and engineering, but there are some general features that more often than not hold true.

I mean if there were no difference I suppose I would've stayed in engineering. I started in ECE here at NCSU a while back. Before that I had a 2-yr degree in electronics. My first semester I took circuits and digital ( I forget the numbers maybe ECE 211 and ECE 201 ... ) I did ok, but as the semester progressed I realized that they were not really focusing on the questions that interested me. On the other hand in my physics and mathematics courses it was pretty much wall to wall what I was looking for. So, I don't mean to put down engineering, it's just not for me. I have different questions.

Anyway, the generalization is one I make on the basis of much life experience. Doubtless there is some counterexample.

3/21/2006 9:19:08 PM

I think you took that too seriously. But anyway...
no doubt what you say holds for undergraduate engineering classes.

[Edited on March 21, 2006 at 10:01 PM. Reason : .]

3/21/2006 10:01:18 PM

Right, I agree. I wanted more than what engineering was offering me -- and that is why I added Applied Math as a second major.

I've used the differential forms of Maxwell's laws in antenna design and transmission lines, but they were just offered up on a plate and we were told how to use them. Deriving them has never been "needed", and thus it was omitted.

MA 574 is a modeling class taught my Dr. Tran and Dr. Smith -- it's great so far.

I'm kind of hoping for a smallish class..I think it would be more fun that way.

3/21/2006 10:53:52 PM

Oh yeah. You should have tests. Have *projects* instead. Yess...that would be better.

3/22/2006 5:11:06 PM

^should = shouldn't I'm guessing

I'm thinking probably there will be a test, a take home test, and a final. Plus homeworks. Haven't figured out all those sort of details quite yet... If we do have tests I'll give a review much like Dr. Fulp does so you'll know exactly what will be on it +/- epsilon.

I'd be interested to see the calculations you did with differential forms for the antenna class. I've always been a little interested in antenna's. I'd guess the calculations we'll be doing will be considerably less difficult. If you could point me towards the text you used it might be useful to me as I prepare for the course.

I wouldn't worry to much about the class getting to big, we shall see. Still need a few more folks to join us.

3/22/2006 8:28:00 PM

I think we made it. 25-12 = 13 registered.

3/29/2006 12:23:41 AM