ANNOUNCEMENTS
MTH 255H — Winter 2014

3/20/14

The final exams have been graded; course grades should be visible online tomorrow.
Stop by my office next term if you'd like to get your exam back.

3/19/14

Below are the answers to the final; see me next term if you'd like to take a look at worked solutions.

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

2. (a) 0 (b) 6xy²+2x³ (c) 1

3. Lots of possibilities...

4. (a) FALSE (b) FALSE

5. 0

6. 1125 π

7. (a) 4r³φ − 4r²z (b) 0 (c) 162 π

8. small circle: 0; large circle: 2π; ellipse: 2π

9. π/12 (401^3/2-1)

3/15/14

I expect to be in my office on Monday 3/17 from roughly 8:30–11:30 AM and 12–2:30 PM. If you want to see me after 2:30, please contact me to set up a time.

I will consider making appointments on Tuesday if necessary, especially for folks who have other exams Monday afternoon or Tuesday morning. And I always respond to email inquiries.

3/14/14

Happy Pi Day — and Happy Einstein's Birthday!

• As mentioned in class earlier this week, MIT's OpenCourseWare multivariable and vector calculus may be a useful resource when reviewing course material. it can be found here.
• Pictures of the board from today's class, showing the review material, can be found here and here.

3/11/14

The final will be Wednesday 3/19/14 from 12–1:50 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 somewhat more than 50% new material and somewhat 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.

3/9/14

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.

3/7/14

Lab writeup for Monday:

Write up a description of your group's work on this week's activity ("Stokes' Theorem").

You should evaluate at least one surface integral explicitly; additional surfaces, and a comparison of your results, is optional but highly encouraged.

3/5/14

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

3/1/14

Reminder: Your lab writeup for last week's activity ("Fishing Net") is due on Monday.

Do try to answer the last question — yes, we'll discuss it in class.
You should also attempt the first (but not yet the second) homework problem.

2/27/14

My office hour on Friday 2/28 is canceled.

2/26/14

Lab writeup for Monday:

Write up a description of your group's work on this week's activity ("Fishing Net").

You probably can't answer the last question until after Friday's lecture.

2/24/14

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".

Examples of how to chop the triangle we considered in class today can be found here.

2/21/14

Pictures of the board from today's class, showing the flux computation for the rotated square, can be found here and here.

2/19/14

Lab writeup for Friday:

Write up a description of your group's work on this week's activity ("Cone").

You are encouraged to include more than one way of determining dA, although one method is sufficient.

2/18/14

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.

2/16/14

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. −2

3. 11/5

4. 12

5. 5/4+e

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

7. (a) zero (b) positive (c) zero

8. 4/5 grams

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

2/12/14

Some of the problems in Briggs/Cochran (see previous announcement) expect you to know how to describe lines and circles.

• Circles around the origin can be converted to polar coordinates.
• Circles elsewhere can be handled similarly — just add the vector from the origin to the center of the circle!
• Lines through the origin have the form y=mx (or x=const).
• Other lines can be expressed using point/slope or slope/intercept form.

All of these cases can be handled using "Use what you know"!

2/10/14

The relevant sections from Briggs/Cochran (on reserve in the library if you don't have a copy) are §14.1–§14.3.

The Basic Skills questions are good practice, but skip the ones on normal and tangential components, averages, flux, and streamlines.

2/6/14

There will be no class tomorrow, 2/7. (OSU is closed both today and tomorrow.)

This should not affect next Friday's midterm.
This week's homework is now due on Monday, and the review will be on Wednesday.

2/5/14

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

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

2/4/14

The midterm is currently scheduled for next Wednesday, 2/12/14, in class.
The midterm is currently scheduled for next Friday, 2/14/14, 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.
• Monday's Wednesday's class will be devoted to review — be prepared to ask questions about topics with which you are having difficulty.

2/3/14

Lab writeup for Wednesday:

Write up a description of your group's work on this week's activity ("Wire").

You should attempt the first two problems — the second problem should be easy once you've done the first.
You may attempt to answer the third question for extra credit if you wish, but this is optional.

1/31/14

With apologies, my office hour today will again end at 11 AM, rather than 11:30 AM.

I am available at 1 PM.

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

This photo is actually from last year; can you spot the (slight) difference?

1/30/14

Lab writeup for Friday:

Write up a description of your group's work on this week's activity ("Valley").

• By all means include your evaluations of indefinite integrals if your group approached the problem that way initially, but make sure to (also) include a computation involving definite integrals.
• You may wish to speculate (without computing anything) about the answer for the first path.

Note that this week's homework is not due until Monday.

1/29/14

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 RemoteApps.

1/27/14

You do not need to write up today's activity ("Chocolate").

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.

1/24/14

Lab writeup for Monday:

Write up a description of your group's work on this week's activities ("3d Hill" and "Hill").

• For the "Hill" worksheet, it is sufficient to write up one of the points A–D;
  you do not (also) need to write up your work on points E or F.
• Make sure to give units with your answers! (You may want to briefly explain why these units are correct.)
• For the "3d Hill" worksheet, it is sufficient to write a short paragraph contrasting what you did for this activity with what you did for the the second activity. (You might therefore want to put this discussion at the end of your writeup.)
• Make sure to include the requested diagram for Question 2 of the "Hill" activity (or equivalently from Question 3 of the "3d Hill" activity).

1/23/14

With apologies, my office hour tomorrow (Friday, 1/24) will end at 11 AM, rather than 11:30 AM.

I should be available for appointments later in the day.

The schedule has been updated.

1/22/14

You do not need to write up today's activity ("The Puddle").

1/19/14

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.

(Please write on only one side of each page, and do not staple your pages together.
Please also do not use pages torn out of notebooks; they jam our scanner.)

The goal of your writeups should be to 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.

1/18/14

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.

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

1/17/14

You do not need to write up today's activity ("Calculating Line Elements").

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.

1/15/14

Two standard calculus textbooks are on reserve in the Valley Library, including Briggs/Cochran (the current text in MTH 255) and Hughes Hallett (the previous text).

You are strongly encouraged to use one or both of these books regularly as a source of practice problems. The Hughes Hallett text in particular has "Exercises", which are more-or-less routine, "Problems", which are more conceptual, and "Check Your Understanding" questions at the end of each chapter, which are True/False questions that can be surprisingly difficult. See me if you are having difficulty choosing appropriate problems.

1/13/14

Lab writeup for Wednesday:

Write up a short description of your group's work on this week's activity ("Which Way is North?").

• 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.

11/29/13

Make sure you read the note about textbooks.

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 is automatically generated, and assumes Thursday recitations, which we don't have.

There will be no class meetings during Week 1.

Recommended readings are listed on the homework page, and will also be listed on the schedule when available.

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

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.

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