MTH 434/534 Announcements

ANNOUNCEMENTS
MTH 434/534 - Winter 2004

3/20/04
The exams are mostly graded, although I probably won't get course grades done until tomorrow. I'll post an answer key outside my office Monday morning at the latest.: (Yes, the exam was harder than I intended, but problem 3 should have been a straightforward translation between forms and vectors, and the integration by parts needed in problem 4 was a direct consequence of problem 3b...)

3/5/04
As mentioned in class today, it is important to choose 1-forms which are "nice". Since you want to differentiate it, it should be differentiable. In particular, it must have a well-defined value everywhere.

2/20/04
MTH 437 will cover much of the material which is in PH 429, with the exception of Coriolis forces. Physics majors who want to substitute MTH 437 for PH 429 should send a short email to the Physics Department Chair chair@physics.orst.edu requesting the substitution.

2/19/04
The previous suggested reading assignment has been corrected (again); should finally be right.

2/13/04
Strange but true: The 13th of the month is more likely to be a Friday than any other day of the week!

2/12/04
You may be interested in our article on Electromagnetic Conic Sections, which discusses the divergence and curl in orthogonal coordinate systems, with applications to electromagnetism.

2/5/04
The suggested reading assigment for this week has been corrected. (I had switched the two texts.)

2/4/04
You can find a list of some orthogonal coordinate systems here, based on the Schaum Outline: Mathematical Handbook of Formulas and Tables, Murray R. Speigel, McGraw-Hill, New York, 1968.

2/2/04

The midterm will be in class next Wednesday, 2/11.

The exam is closed book.
The exam will cover everything discussed in class through Friday, 2/6.
Important topics are exterior product (wedge), Hodge dual (*), and exterior differentiation (d).
Monday 2/9 will be devoted to review -- come prepared to ask questions.

2/1/04
I will be late for my office hour tomorrow (Monday, 2/2) due to a meeting; I hope to be back by 10:30.
There will be a linear algebra review session tomorrow (Monday, 2/2) at 2 PM in Weniger 377.

1/30/04
Some comments of possible relevance to the homework:: In rectangular coordinates, the standard basis for 1-forms, namely {dx,dy}, is already orthonormal. In curvilinear coordinates, this is not true. For example, polar coordinates in the plane lead to two nice bases: a coordinate basis, {dr,dphi} and an orthonormal basis {dr, r dphi}. Mathematicians tend to prefer the former; physicists usually use the latter. Be careful: The orthonormal basis vectors rhat and phihat correspond most closely to dr and r dphi, respectively, so if you're thinking of a vector "like" a rhat + b phihat, you need to write a dr + b r dphi; don't forget the extra factor of r.

1/28/04

Some additions to the ground rules for homework:

Please use scratch paper for scratch work, not your final writeup.
Please begin your answers with words, not equations.
If someone else acknowledges working with you, you should probably acknowledge working with them.

1/27/04
The definition of null vector should have added the restriction that v≠0; the zero vector does not count as null.

1/24/04
One more definition:: A null vector is a nonzero vector v with zero length, that is, g(v,v)=0.

1/21/04

Some of the concepts in the current homework assignment won't be covered in class until Friday.

Here's a quick summary for those of you who can't wait.

An inner product is a (nondegenerate, symmetric) bilinear map g(v,w) which takes 2 vectors to a number.
A unit vector u with respect to g satisfies either g(u,u)=1 or g(u,u)=-1.
The signature of g is the number of minus signs in the normalization of an orthonormal basis.
(Some authors define the signature to be the difference between the number of plus and minus signs.)

The standard example of an inner product is the dot product.

1/5/04
There will be no class this Friday, 1/9. My office hours on Thursday, 1/8, are also canceled.