MTH 255 Announcements

ANNOUNCEMENTS
MTH 255 - Fall 2005

12/9/05
We have finished grading the exams, and grades will be posted shortly. They should be available online by Monday morning at the latest.: You can get your exam from me by coming to my office. I will be in my office sporadically next week, or you can wait until next term.

12/6/05
Below are the answers to the final; an answer key has been posted outside my office.: 1. (a) 0 (b) 12x+60y³ (c) 5; 2. conservative, potential function is sin(x)+yz+x²cos(y)e^z; 3. Figures 2 & 4 are conservative; Figures 1 & 3 are not.; 4. (a) negative (b) depends on location (c) zero (d) positive; 5. 162 π; 6. -32 π; 7. 32 π; 8. (a) False (b) False (c) False; 9. 16/9
In some cases, alternative answers with suitable justification will receive at least partial credit.

12/4/05
The last part of the sample change-of-variables problem as originally posted is too hard and has been changed.

12/2/05
A sample change-of-variables problem is available here.
In addition to the simple surface elements I reviewed in class today, you should also know how to find surface elements for more complicated surfaces.: One good example would be to find the surface element on a paraboloid (such as z=r²), another would be to do the flux integral in part (d) of this week's homework.

11/29/05

The final will be on Tuesday, December 6, at 12 PM in Weniger 149 (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.

11/21/05
I will spend Wednesday's class demonstrating some software used to analyze vector fields; no new material will be covered. The online schedule has been modified accordingly.

11/14/05
You are strongly encouraged to work additional Exercises in §20.1-§20.4 in order to gain practice calculating divergence and curl, and in using the Divergence Theorem and Stokes' Theorem.

11/11/05
A copy of the formula sheet I showed 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 available at the library.

11/9/05
JAVA versions of the vector fields I showed in class today can be found here.

11/2/05
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.

10/28/05
Some further information about the quaternions can be found at MathWorld or at the Wikipedia, and some further information about the octonions can be found at the Wikipedia or on my website.: A link to some pictures I took last summer at the Brougham Bridge in Dublin, where Hamilton discovered the quaternion multiplication table in 1843, can be found here.

10/27/05

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

10/26/05
Below are the answers to the midterm; an answer key will be posted outside my office later this week.: 1. (a) False (b) False; 2. Figures 1 & 2 are conservative; Figures 3 & 4 are not.; 3. (a) zero (b) positive (c) zero; 4. 0; 5. -8/3; 6. 14/3
In some cases, alternative answers with suitable justification will receive at least partial credit.

10/21/05

The midterm will be Wednesday 10/26/05 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!

10/12/05
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.

10/6/05
The library does now have a copy of the 3rd edition of the text on reserve.: If you use this copy, be careful to get the correct homework problems, as many of the problems in the 4th edition are different.

10/5/05
You can find out more about the reasons for the choices discussed in class today for the names of the spherical coordinates in our paper:: Spherical Coordinates, Tevian Dray and Corinne A. Manogue, College Math. J. 34, 168-169 (2003)
a copy of which is posted on my bulletin board. The short answer is that most students will need to switch conventions at some point during their education, so this might as well be done sooner rather than later.

9/29/05
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".)

9/28/05
A JAVA applet which illustrates the geometry of the dot product can be found here.: You may also be interested in the website of the Vector Calculus Bridge Project, which describes some of the reasons why this course is taught the way it is, and which among other things contains a link to the applet above.

9/27/05
This week's homework assignment has also been posted in PDF format. I will try to do this with all the assignments for the benefit of those with the older edition of the text.

9/26/05

Make sure to read the note about the text.

Make sure to read the grading policy.

Good things to review: