ANNOUNCEMENTS
MTH 255 — Winter 2012

3/22/12

Grades have been posted, and should show up online tomorrow.

The average on the final was 66 out of 90, which was taken into account when assigning grades.

You can pick your exam from me next term if desired.

3/15/12

Brandon and I will hold office hours next week as follows:

Tevian: M 1:30–3:30 PM
Brandon: T 10–11 AM

3/12/12

The final will be Tuesday 3/20/12 from 2–3:50 PM in LPSC 125.

• 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.

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.

3/10/12

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.

3/5/12

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

3/1/12

The graphs of the vector fields for today's lab can be found here.

2/29/12

The answer I gave in class on Monday for the amount of chocolate on the paraboloid was missing the factor of 2π from the angular integration.

2/26/12

Here are some comments about Friday's activity ("The Fishing Net").

• Consider which terms, if any, will cancel in the final answer.
• Consider what happens if you construct your two dr vectors at other corners of the infinitesimal rectangle. (You may find this picture to be helpful.)
• A formula for the divergence div(F)=∇• F in rectangular coordinates can be found here.

If you're looking for a challenge, find dA on the triangular region considered in class earlier in the course, whose corners are at (1,0,0), (0,1,0), and (0,0,1).

How will you chop up the region?

A discussion of several alternatives can be found here, but try it yourself first.

2/24/12

My office hour today is canceled.

2/21/12

Mark your calendars:

On Friday 3/2 and Monday 3/5 we will meet in Weniger 212 rather than our usual classroom.

2/20/12

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.

2/13/12

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 in 2004 at the Brougham Bridge in Dublin, where Hamilton discovered the quaternion multiplication table in 1843, can be found here.

2/11/12

Below are the answers to the midterm; worked solutions are available for inspection in my office (or after class).

1. 17/10

2. 13/3

3. 1+e+π²/4

4. (a) conservative (b) not conservative

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

6. (a) false (b) false

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

2/1/12

The midterm will be Friday 2/10/12 in class.

Students with last names starting with A–L should come to our regular classroom, Bexl 321.
Students with last names starting with M–Z should go next door, to Bexl 323.

The primary focus of the midterm is line integrals.

• This material corresponds to Units 1–3 in the online textbook, and to Lessons 5–7 in the Study Guide (on CD).
• However, these sections incorporate material from previous sections, all of which is fair game.
• The most relevant sections in Briggs/Cochran are §15.1–§15.3.
• The most relevant sections in McCallum et al are §17.3 and §18.1–§18.3.
• Please bear in mind that the presentation in class differed somewhat from that in these texts.
• The Exercises at the end of each section in McCallum et al 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 blue or black ink.
• Wednesday's class will be devoted to review. Come prepared to ask questions!

1/26/12

The topo map for today's lab can be found here.

You do not need to print out a copy yourself.

1/25/12

The library has copies of two calculus texts on reserve.

In addition to the Briggs/Cochran text many of you may have used for MTH~254, they also have the previous text, by McCallum et al. This text 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.

The MLC also has copies of both of these texts.

1/23/12

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.

1/20/12

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

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

1/19/12

The topo map for today's lab can be found here.

You do not need to print out a copy yourself.

1/18/12

I left out the factor of π when differentiating sin(πxy) in class today...

1/17/12

Waitlists have now been turned off; waitlist information on OSU websites should be ignored.

If you are still trying to get into this class, make sure I know about it, and make sure you come to class this week.

1/17/12

Two of the recitation rooms have been moved:

• Sections 013 (2 PM) and 011 (4 PM) will now meet in Weniger 212.
• Section 012 (12 PM) is unchanged.

1/16/12

If you own a copy of the Briggs/Cochran text used for MTH 254, you may still have access to the accompanying online homework system, MyMathLab (also accessible through several other URLs). A generic MTH 255 course has been made available (by the publisher, not by me), which you are welcome to explore.

• The CourseID is osumath91039.
• The homework assignments associated with that CourseID are currently unavailable; this may change.
• If you do not have a valid access code, you should still be able to obtain temporary access (for roughly 2 weeks).

The entire text (Briggs/Cochran), including most of the exercises, are available at this CourseID. (The simplest way to access the exercises is probably via the "Study Plan" link.)

New material for this course is in Chapter 14, but it wouldn't hurt to review Chapters 11–13, especially Sections 11.1–11.4 and 12.6.

Please be aware that these problems are offered as an additional resource, and are not a required part of the course. Many of these problems do not reflect the philosophy of the course. Nonetheless, working these problems is likely to improve your mastery of the material.

1/13/12

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.

1/12/12

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.

1/11/12

A JAVA applet which illustrates the geometry of the dot product can be found here.

1/10/12

Are you interested in taking MTH 255 in a smaller class? Do you have a 3.25 GPA?

There are a few spots open in my honors section, MTH 255H, meeting MW 9–9:50 and F 8–9:50. This class is capped at 20 students, and there is no GTA, so I run the labs myself. You do not need to be in the Honors College, so long as you have that 3.25 GPA. If you are interested, contact me or simply fill out a request at the Honors College office (StAg 229).

1/8/12

A rough 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.

11/13/11

• Please read the note about the text materials for this course.
• 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.