ANNOUNCEMENTS
MTH 255H — Winter 2007

3/22/07

I expect to be in my office tomorrow from 9–3. I hope to have the exams graded by mid-morning.

3/17/07

Due to popular request, I'm posting two further problems involving change of variables:

• Suppose that x=½(u²−v²) and y=uv.
  Find the area of the region bounded by the curves u=1, u=2, v=1, and v=3.
• Find the area of the region bounded by the curves xy=1, xy=2, xy²=1, and xy²=2.
  Then integrate y² over the same region.

3/16/07

I will be in my office until noon on both Monday 3/19 and Tuesday 3/20.

I expect to arrive by 9:30 AM, and most likely earlier.

Other times are possible by arrangement.

I will also check my email regularly this weekend.

3/10/07

The final will be during the regularly scheduled time: Wednesday 3/21/07, from 6-7:50 PM, in Kidder 280.

• The final will be slightly less than twice as long as the midterm, and will cover material from the entire course.
• The old material is described below in the midterm announcement.
• The new material emphasizes Lessons 8-13 (surface integrals and applications) in the Study Guide, as well as the related material in Lesson 14.
• The relevant sections in the text are Chapters 19 and 20. Please bear in mind that the presentation in class differed somewhat from that in the text; we covered topics in class that are not in the text, and there is material in the text which we did not cover.
• If you are looking for extra problems to practice on, the Review Exercises and Check your Understanding questions at the end of each chapter are especially good.
• You may bring two 3″×5″ index cards (both sides) of handwritten notes, or the equivalent, as well as the handout containing the formulas for divergence and curl in spherical and cylindrical coordinates.
• Other rules are as announced below for the midterm.

3/8/07

The software I demonstrated in class today can be found here.

3/1/07

A copy of the formula sheet we used in class today, showing how to express gradient, curl, and divergence in rectangular, cylindrical, and spherical coordinates, can be found here.

You can find derivations of these formulas in the excellent book Div, Grad, Curl and All That by Schey, which is on reserve at the library.

JAVA versions of the vector fields I've been showing pictures of in class can be found here.

2/19/07

The answer to the paraboloid problem discussed in class today is 5625π.

We discussed this problem in cylindrical coordinates. Try it in rectangular coordinates.

Here are two related problems you may want to try:

Find the surface area of the paraboloid. (Assume x and y are in millimeters.)

Find the total amount of chocolate on the paraboloid if the density of chocolate is σ=2(x²+y²) g/mm².

2/13/07

You may want to take another look at the transparency I showed earlier, in the context of line integrals, which illustrates how to relate mathematical text, equations, and pictures.

2/10/07

Some further information about the quaternions can be found at MathWorld or at the Wikipedia.

A link to some pictures I took in 2004 at the Brougham Bridge in Dublin, where Hamilton discovered the quaternion multiplication table in 1843, can be found here.

2/9/07

If you'd like to learn more about using planimeters to measure area, here are some online resources:

• Planimeter 1
• Planimeter 2
• Planimeter 3
• Planimeter 4

2/2/07

The midterm will be Wednesday 2/7/07 in class.

• The primary focus of the midterm is Lessons 5-7 (line integrals) in the Study Guide, which however incorporate material from the previous lessons; everything in the first 7 lessons is fair game.
• The most relevant sections in the text (MHG) are §17.3 and §18.1-§18.3. Please bear in mind that the presentation in class differed somewhat from that in the text; we covered topics in class that are not in the text, and there is material in the text which we did not cover.
  A table of the relevant sections in the text can be found on the inside front cover of the study guide.
• The Exercises at the end of each section in MHG are an excellent skills check, and the Check your Understanding questions at the end of each chapter are an excellent review.
• The exam is closed book, and calculators may not be used.
• You may bring a 3″×5″ index card (both sides) of handwritten notes;
• Please write your exams in pencil or black ink (blue ink is OK).
• Monday's class will be devoted to review. Come prepared to ask questions!

1/31/07

A nice example of a vector field is provided by the current wind patterns in the San Francisco Bay, which you can find here; take a look at the "Streakline" and "Archive" links.

1/30/07

The circulation of a vector field around a closed curve is defined on page 880 of the text to be the line integral of the vector around the curve.

1/24/07

A figure similar to the one I drew on the board today can be found here. It involves flux (which we'll talk about later), rather than work, but the idea of "diagramming equations" is similar. This picture was drawn by Kerry Browne as part of his PhD thesis in Physics Education here at OSU, entitled Student Use of Visualization in Upper-Division Problem Solving.

1/12/07

Lab writeups will normally be due the next day.

Since I didn't announce that yesterday, please turn the first lab in Wednesday, 1/17.

The first homework assignment was due 1/11...

Pictures of cylindrical and spherical coordinates similar to the ones shown in class today can be found in the worksheet due next week.

1/11/07

You can use this website to determine the magnetic deviation (angle between true north and magnetic north) for any location. You will need to know the latitude and longitude -- or the zip code. (Enter a zip code, press the button labeled "Get Location", then press the button labeled "Compute".)

You can find out more about magnetic declination at this site. Especially interesting are the links to online maps available in the section on determining the declination. (Search for "On-line Isogonic charts".)

1/10/07

A practice problem involving differentials can be found here.

1/2/07

The criteria I will use to evaluate written work can be found here. We will discuss the goals of this course, including these criteria, on Monday.

11/19/06

My standard grading scheme is outlined here. I reserve the right to make small changes to these rules.

Please read the guidelines on the homework page, which also apply to the writeups for the group activities.

A rough schedule for MTH 255 can be found here. Please use this as a guide only.

You are encouraged to browse the website of the closely related Vector Calculus Bridge Project.