ANNOUNCEMENTS
MTH 255H — Winter 2008

3/18/08

I will submit grades as soon as I can, but may not be able to get to it until the end of the week.

You should be able to see your course grade online the day after I submit them.

Feel free to drop in next term to pick up your exam, or just to chat.

3/17/08

Here are some suggestions for review:

• Make sure to look through the Check your Understanding problems at the end of each chapter.
• Make sure you understand each piece of the bathtub problem (§20.4:34) from the last homework, and preferably multiple ways of approaching each part.
• See if you can set up dA (the vector area element) on a paraboloid. For instance, try doing the second question on the Stokes' Theorem lab (Lab 8) for a paraboloid, and make sure you get the same answer as for the other integrals in that lab.
• Go over the midterm!
• Try some of the Excercises and Problems in §16.7 on change of variables.

3/14/08

I expect to be in my office on Monday, 3/17, from 10–11:30 AM and 1:30–3:30 PM.

Other times can be arranged via email.

3/9/08

The final will be Tuesday 3/18/08 from 2-3:50 PM in StAg 233 (our regular classroom).

• 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.

3/5/08

The summary page we constructed for today's lab can be found here.

The right-hand margin is missing, but should be fairly easy to reconstruct.

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

2/29/08

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 in the library (but checked out ...). You can also look at my copy in my office.

2/27/08

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.

2/25/08

JAVA versions of the vector fields I showed in class can be found here.

2/13/08

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.

2/7/08

As mentioned in class yesterday, graphs of some important vector fields can be found here.

2/6/08

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

• This site has a nice photo of a real planimeter, together with a detailed explanation of how they work.
• The applet I used in class is available here.
  The counter won't start until you pass through "Start" (the first time — it will stop the second time), so you'll first need to load one of the shapes from the menu at the left, although there is no need to trace that shape. You can reset the counter by clicking on the number in the top left corner. (This planimeter is programmed to give a nonnegative answer, that is, it corrects for the direction in which you start.)
• Finally, a general page with links to further information can be found here

2/3/08

The midterm will be Friday 2/8/08 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).

1/28/08

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.

1/25/08

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.

1/18/08

You are encouraged to read the appropriate sections of the Study Guide, which I follow fairly closely.

You may wish to skim the lesson on Line Integrals before next week's classes.

Here are some of the slides from today's class. In each case, the first picture shows the (3-d!) graph of a function z = f(x,y), and the second shows the combined (2-d!) graph of the level curves and gradient of f.

1/11/08

Please work through today's handout (Calculating Line Elements) on your own.

Be prepared to tell me on Monday what dr is in spherical coordinates.

1/7/08

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".)

10/25/07

If you already have the complete Calculus text by Hughes Hallett et al (not merely their Single Variable text), you do not need to purchase the McCallum et al text; for our purposes, these books are identical.

You have the full book if it includes Chapters 17–20; the Single Variable book ends with Chapter 11.

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

The criteria I will use to evaluate written work can be found here.

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.

This schedule assumes Thursday recitations, which we don't have. You won't be far off if you assume that those activities will occur in our class on the preceding Wednesday.

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