ANNOUNCEMENTS
MTH 434/534 — Winter 2011

3/16/11

Exams are graded; course grades should go in tonight.

You can get your exam back from me next term.

I will offer an opportunity to go over the exam as a group during the first week of the term.

Perhaps Monday 3/28 at 5:30 PM? If that time does not work for you, let me know.

3/15/11

If you downloaded a copy of the class notes on or prior to 3/14, your copy may be corrupt.

The file size should be 449276 bytes. If it's not, please try again. (Sorry about that.)

3/14/11 (π Day = Einstein's Birthday)

A PDF copy of the class notes can be downloaded here.

It's still pretty rough; comments welcome.

3/13/11

I should be in my office tomorrow afternoon (Monday) from roughly 1–3 PM.

Other times may also be possible; email me or take your chances.

3/12/11

Two mathematicians are talking on the telephone. Both are in the continental United States. One is in a West Coast state, the other is in an East Coast state. They suddenly realize that the correct local time in both locations is the same! How is this possible?

Give up? Some hints can be found here.

3/8/11

The final will be Tuesday 3/15/11 from 2–3:50 PM in Weniger 304 (our regular classroom).

• The exam is closed book.
• The exam will cover everything discussed in class through Wednesday 3/9/11.
• The final will be slightly less than twice as long as the midterm, and will cover material from the entire course.
• Important new topics are the structure equations, curvature, and integration.
• Important old topics are exterior product (∧), Hodge dual (∗), and exterior differentiation (d).
• Other topics discussed in class this past week should be regarded as supplementary material which is good to know but not required.
• There should be time during Friday's class for a review; come prepared to ask questions.

3/7/11

The goal of this week's homework assignment is to make you think about integration. You should be able to perform the requested computations, with the possible exception of 2(b), and even in that case you should be able to state what answer you expect, and discuss whether or not you obtained it.

We will discuss these problems in class on Wednesday.

I neglected to mention that today's astonishing result, relating total Gaussian curvature to the Euler characteristic, is called the Gauss-Bonnet Theorem.

3/4/11

There will be an extra class meeting on Monday, 3/7, from 5:30–6:20 in Weniger 304.

I will use this class meeting to present at least one application of differential forms, most likely either a discussion of spinors and/or a discussion of Lagrangians.

Two updates to this afternoon's lecture:

• We wrote an incorrect formula for de_θ. The correct formula is de_θ = cosθ dφ = cotθ/r (r sinθ dφ). Since ds = r sinθ dφ along a line of latitude, we conclude that κ_g = cotθ/r so that κ_g = 0 forces θ=π/2.
• The argument that ∫dα=2π relies on the use of a small closed curve. More precisely, the vector fields e_i must be well-behaved throughout the interior of the curve. This condition excludes, for instance, the use of e_φ on a line of latitude. (To handle a line of latitude, either rotate the sphere so that it does not circumnavigate a pole, or use stereographic projection.)

2/23/11

There will be an extra class meeting on Monday, 2/28, from 5:30–6:20 in Weniger 304.

We will also meet the following Monday (3/7) at the same time and place.

MTH 437/537 will meet next term at 8 AM (most likely in Weniger 304).

2/16/11

Come to class tomorrow prepared to discuss scheduling for next term.

We are currently scheduled for MWF at 3 PM, which is a conflict with PH 575.

There is no "extra" class next Monday at 5:30 PM.

We will of course meet as usual on Monday at 3 PM.

2/15/11

Last week's reading assignment has been updated to include Flanders §4.4 and §4.6.

Don't forget to check frequently for updates to the online course notes.

2/12/11

My (old) Mathematica package wedge.m can compute ∧, d, and ∗, and should work on any computer running Mathematica, such as those in the MLC.

• Please note that this software has not been extensively tested!
• Some (old) instructions are available here, but they only tell you how to load the package on COSINe machines running Linux (e.g. app.science.oregonstate.edu).
• For other machines on campus, the package must be loaded from \\poole\Class Folders\Math-Dray. For instructions on how to do this under Windows, follow the Getting Started section of this document from another class (but don't start GSP). Start Mathematica, then load the package with a command of the form "<<\\poole\Class Folders\Math-Dray\wedge.m".

2/11/11

The midterm will be in class next Monday, 2/14, from 5:30–6:20 in Weniger 304.

• The exam is closed book.
• The exam will cover everything discussed in class through Friday 2/4/11.
• Important topics are exterior product (∧), Hodge dual (∗), and exterior differentiation (d).
• Integration will not be covered.
• Other topics discussed in class this past week should be regarded as supplementary material which is good to know but not required.
• There should be time during Monday's regular class (at 3) for a review; come prepared to ask questions.

2/8/11

Further information about the dot and cross products in orthogonal coordinates, including applications to electrostatics, can be found in this paper.

2/4/11

There will be an extra class meeting on Monday, 2/7, from 5:30–6:20 in Weniger 304.

We will also meet on most subsequent Mondays (2/14, 2/28, and 3/7) at the same time and place.

2/1/11

There does appear to be a scheduling conflict for next term, as PH 575 is scheduled for 3 PM and is required for physics graduate students.

We will therefore need to (try to) find another time, so please take a look at your schedule for next term and be prepared to discuss alternatives.

1/20/11

Time to start thinking about scheduling for next term. The default would be to continue at 3 PM. Please let me know as soon as possible if this is likely to be a problem.

1/18/11

Here are some comments about the first homework assignment:

Content:

• You should discuss the special case when some of the coefficients are zero.
• A geometric solution is fine!
• It is enough to translate your answer from Problem 1 to Problem 2; don't re-solve the same equations.
• i×j=k, but dx∧dy≠dz.

Presentation:

• Use complete sentences (most of the time).
• Show (the essential parts of) your calculations.
• Do use displayed equations — which should nonetheless be grammatically correct parts of sentences.
• Do restate the problem (preferably in your own words).

I have posted solutions to most of these problems (with slightly different numbering) here.

I should be in my office this afternoon from roughly 2–3 PM.

1/14/11

I have updated the online course notes, which now cover most of the topics we have discussed in class. I should be able to keep up with where we are in class for the remainder of the term, and will no longer announce future updates.

Please feel free to send me comments on these notes via email; constructive criticism is welcome! You can also post (anonymous) feedback directly on the book wiki, by clicking on the "discussion" tab at the top of any page, then on either the "edit this page" or "create this page" tabs.

1/13/11

Scheduling:

• There will of course be no class on Monday, 1/17, which is a holiday.
• There will be no class the week of 1/24–28.
• I would prefer to avoid a Monday evening class on the days the physics paradigms students have a final exam, which I believe to be 1/31 (Week 5) and 2/21 (Week 8).
• That leaves the following Mondays open for a class at 5:30 PM: 2/7, 2/14, 2/28, & 3/7

I therefore propose that we meet on those 4 Mondays at 5:30 PM.

Please let me know ASAP if any of these days will not work for you.
(An alternative might be longer sessions on fewer days.)

1/12/11

The pictures shown in class today are from Chapter 4 of Misner, Thorne, and Wheeler, a book intended for physicists. Weinrich's book presents an elementary treatment of many different types of vectors. Bachman's book provides a more mathematical treatment, emphasizing geometry, also with lots of pictures.

See the book list for further details about these books.

1/10/11

The library has placed many of the books on the book list on reserve.

You are strongly encouraged to browse through one or more of these books.
A brief description of each book is available on the book list.

1/6/11

The "vector space" V referred to in Problem 2 should really be the module Λ¹R³, the space of 1-forms in 3 dimensions.

1/5/11

There will be no class this Friday, 1/7/11.

We have tentatively agreed to reschedule 4 classes to Mondays at 5:30 PM, with the exact choice of dates yet to be determined. If you are not comfortable with this arrangement for any reason, now is the time to let me know. Also, if there are particular Mondays this term when you do not want to (or cannot) meet at that time, please let me know as soon as possible.

1/4/11

Course notes will be posted as they are written in wiki format here.

Partial notes from the first day of class can be found here.

1/3/11

The class will move to Weniger 304 effective Wednesday, 1/5/11.

We will meet today in Batcheller 150 as originally scheduled.

1/2/11

Due to conference travel, I will be out of town for four class periods this term. Rather than arranging for somebody else to give the lectures, I would prefer to reschedule those classes if possible.

This would only be for a total of 4 hours during the term, not every week. Most times during the day are likely to lead to conflicts for somebody in the class, with the possible exception of 8 AM. I am also willing to consider evenings and weekends, and of course Tu/Th as well as MWF.

Be prepared to discuss these options in class this week.

To get the ball rolling, I propose that we meet on four Fridays (to be determined) at 8 AM.

11/11/10

The course has been rescheduled to MWF at 3 PM.

10/23/10

There is a good chance the course time will be changed.

If you are considering taking this class, please contact me.
(It would be useful to know the times when you could not take the course.)