ANNOUNCEMENTS
MTH 255H — Winter 2013

3/23/13

The final exams have been graded; the average was 79 out of 90. (Well done!) Course grades will be uploaded this afternoon (but may not be visible until Monday). You can get your exam from me by stopping by my office next term, where you can also see worked solutions to the final.

3/17/13

I should be in my office Tuesday afternoon from roughly 2:30 to 4, and again Wednesday from roughly 10 to 2 with a short lunch break.

3/15/13

Below are the answers to the midterm; ask me if you'd like to take a look at worked solutions.

1. (a) III (b) I (c) IV (d) II

2. 0

3. −8/3

4. 8/3

5. 0

6. 1+1/4+e

7. Figures 1 & 4 are conservative; Figures 2 & 3 are not.

8. 8 grams

In some cases, alternative answers with suitable justification received at least partial credit.

3/11/13

Photos from class showing the derivation of the 2-dimensional Jacobian from dr₁×dr₂ can be found here and here.
Photos from class outlining two approaches to solving today's problem can be found here and here.

Further discussion can be found in the online text.

3/11/13

The final will be Thursday 3/21/13 from 9:30–11:20 AM 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 (with slightly more than 50% new material and slightly less than 50% old.)
• The old material is described below in the midterm announcement.
• The new material emphasizes surface integrals, divergence, curl, and the corresponding theorems.
• This material corresponds to the last two units in the online text.
• 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.
• Friday's class will be devoted to review; come prepared to ask questions.

Here are some suggestions for review:

• Make sure you understand each piece of the bathtub problem 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 for a paraboloid, and make sure you get the same answer as for the other integrals in that lab.
• Go over the midterm!
• The Exercises at the end of each section in the text by McCallum are an excellent skills check, and the Check your Understanding questions at the end of each chapter are an excellent review.
• Try some of the Exercises and Problems on change of variables in §16.7 of that text, or seek out such problems in another text.

3/9/13

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.

3/8/13

There was a minor typo in the current homework assignment, which has been fixed:

The denominator in the second term in part (a) should be (z²+a²)².

3/4/13

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

2/28/13

The library does have two copies of the alternate text by McCallum, Hughes Hallett, et al on reserve.

If you have trouble finding it in the catalog, the call number is VR 195.

2/27/13

Formulas for the divergence (div(F)=∇•F) and curl (curl(F)=∇×F) in various coordinates can be found here.

2/18/13

A PDF version of the slide 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.

2/17/13

There will be no class this Friday, 2/22/13.

2/11/13

Some further information about the quaternions can be found at MathWorld or on Wikipedia, and some further information about the octonions can be found on Wikipedia or on my website.

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.

2/2/13

Wednesday's class will be devoted to review.

• There will not be an activity.
• Bring questions and sample problems!
• Feel free to bring your (old) calculus text as a source of problems.

2/1/13

The midterm will be Friday 2/8/13 in class.

• The primary focus of the midterm is on line integrals, which however incorporates material from earlier in the term; everything covered in class is fair game.
• This material corresponds to the first three units in the online text, with an emphasis on Unit 3.
• The Exercises at the end of each section in the text by McCallum 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 in black or blue ink.

1/30/13

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

I will use this software for further demonstrations later in the term.

Here is a photo from class showing the relationship between written, symbolic, and graphical definitions of work.

1/26/13

The homework assignment due Monday has been changed:

The assignment has been divided into two pieces, one due this Monday (1/28), the other due next Monday (2/4).

If you have already completed the original assignment, you may submit that instead for possible credit on both assignments.

1/25/13

With apologies, there is an undefined term in this week's homework assignment.

The circulation of a vector field around an oriented closed path is defined here.

This week's suggested reading has been updated accordingly.

1/23/13

The rotatable images of vector fields I showed in class today are available here.

Another 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.

You can make your own rotatable images of vector fields using Maple or Mathematica, both of which are available in the MLC computer lab.

I have put sample files showing how to do this in the folder \\poole\ClassFolders\Math-Dray\MTH255 which you should be able to access from any campus computer. The files are PlotVF.nb (Mathematica) and PlotVF.mws (Maple). (The Maple file is written for the old interface, but should also open in the newer, java-based interface. Further information about connecting to poole using Windows is available here, but you should be able to connect from any OS.)

You can also run Mathematica, but not Maple, using the OSU Virtual Computing Lab (Umbrella).

If you already have Remote Desktop installed, you should be able to connect to Umbrella by clicking on the files umbrella6.rdp (Windows) or umbrella.osx.rdp (Mac) in the poole folder listed above.

1/22/13

The library has copies of the calculus text (Briggs/Cochran) currently used in other sections on reserve.

The MLC also has copies of the previous text, by McCallum et al., which has excellent, conceptual problems.

• Our course primarily covers Chapters 18–20, as well as some review material from Chapters 13, 14, and 17.
• The "Check your understanding" problems at the end of each chapter are strongly recommended.

A list of suggested problems from the Briggs/Cochran text (and from another instructor, not me) can be found here.

These problems are offered as an additional resource, and are not a required part of the course.

1/17/13

Further discussion of the hill activity can be found in this article (by a former MTH 255 TA who is now a math professor), as well as in this followup article.

1/16/13

Here are some suggestions for improving the presentation of your written work:

• Restate the problem in your own words.
• Use (mostly) complete sentences (with the math included as grammatically correct parts).
• Don't write a book — keep it short and sweet.
• Don't use scratch paper; use blue or black ink (or pencil).
• Don't use a multicolumn format.

The goal of your writeups should be able to understand them 5 years from now without any additional information.

Further information is available at the top of the homework page, and also here.

1/11/13

You can find out more about the reasons we will use the "physics" convention 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)

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.

1/9/13

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 Wikipedia, and there are some online maps available here.

1/5/13

An online copy of my (slightly outdated) Study Guide for MTH 255 can be found here; a PDF version is available here.

The Study Guide provides a somewhat more traditional treatment of the material we will cover than the approach used in class, which more closely reflects our online book.

1/3/13

A revised schedule has been posted, and will be kept reasonably up-to-date.

This supercedes the automated version referred to in the older announcement below.

Main readings are listed on the schedule, but see also the recommended readings on the homework page.

Feel free to supplement these readings with other content from the Bridge Book, and/or from any (vector) calculus text you are comfortable with.

11/13/12

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.