ANNOUNCEMENTS
MTH 255H - Winter 2005

3/20/05

Sorry I didn't make it back in time for the final; answers are below. I also have an answer key, but won't have a chance to post it until next term; sorry. Grades will be submitted Monday (and will therefore probably not available online until Tuesday). You can collect your exam from me next term if you wish.

1. (a) roughly NNW (b) roughly (0,3/5) (c) 0

2. (a) Figs 2 and 4 are conservative; Figs 1 and 3 are not.

    (b) The (k-comp) of the curl is zero for Figs 2 and 4, positive for Fig 1, and depends on location for Fig 3.

    (c) The divergence is zero for Figs 1 and 3, positive for Fig 4, and depends on location for Fig 2.

3. -72π

4. -81π/2

5. 171π grams

6. (a) φ/r (b) 0 (c) 2π

7. 2π on the ellipse; 0 on the small circle

3/4/05

The software from today's class can be found here.

A live version of the windflow example can be found here; take a look at the "Streakline" and "Archive" links.

3/3/05

My last office hour will be Monday afternoon, 3/7.

After that, you may utilize Dianne Hart's office hours: 10-11 on 3/9, 10-11:30 on 3/11, and (probably) 8-10 on 3/14 and 3/15. The exact hours will be posted on her office door, Kidder 346.

Dr. Hart teaches the regular section of MTH 255, using the same text.

3/2/05

The final will be on Thursday, 3/17, at 9:30 AM 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 also wish to look at §16.4-§16.9, and §15.9 in Stewart, as well as the review section at the end of Chapter 16. There is also a nice review in §16.10.
• 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.

2/21/05

Formulas for gradient, curl, and divergence in rectangular, cylindrical, and spherical coordinates can be found here.

You can find a discussion of their derivation in the excellent book Div, Grad, Curl and All That by Schey.

2/18/05

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

2/11/05

The due date for the this week's homework assignment has been postponed until Wednesday, 2/16.

2/10/05

A PDF version of the transparency I showed today can be found here. 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.

2/5/05

Below are the answers to the midterm; an answer key is posted outside my office.

1. (a) zero (b) positive

2. Figure 1: conservative (II); Figure 2: not conservative (I)

3. 5/2

4. 0

5. 0

EC: 24 grams

2/4/05

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

2/3/05

There is a typo on page 24 of the study guide. The last term of Equation (I.1) should of course be (v_x w_y - v_y w_x) k.

1/28/05

The midterm will be Thursday 2/3/05 in class.

• The primary focus of the midterm is Lessons 5-7 (line integrals) in the Study Guide, which however incorporates material from the previous lessons; everything in the first 7 lessons is fair game.
• The relevant sections in the text (MHG) are Chapters 17 and 18. 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.
• You may also wish to look at §13.1-§13.4, §14.6, and §16.1-§16.3 in Stewart (Early Transcendentals), as well as the review sections at the end of Chapters 13, 14, and 16.
• 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).
• Wednesday's class will be devoted to review. Come prepared to ask questions!

1/19/05

I will be giving a talk on my research (applications of nonassociative algebrasto physics) this afternoon to 1st-year math grad students, which you may enjoy. 4 PM, Gilkey 104.

1/10/05

This week's homework has been posted on the homework page; due this Friday.

1/7/05

The library does now have the text on reserve.

1/6/05

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".)

1/5/05

JAVA applets which illustrate the geometry of the dot and cross products can be found at the sites below:

Dot product;

Cross product.

Further information about vectors, including the dot and cross products, can be found here.

1/1/05

Here are some further guidelines for the Group Activities:

• One member of each group will be asked to write up the day's activity.
• This report should be turned it in at the next class period.
• All members of the group should sign the cover page.
• The report will be graded on both content and presentation.

Some advice on writing mathematics can be found here. You may also be interested in this website which gives advice on writing a math essay, some of which is relevant to the presentation of short reports.

10/21/04

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.