ANNOUNCEMENTS
MTH 255H — Winter 2012

3/23/12

Grades have been posted, but may not show up online until Monday.

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

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

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

2. (a) VI & VIII (b) V or VII (c) VII (d) V, VI, or VIII (e) VI or VIII (f) V & VII

3. (a) 0 (b) 60x³+42y (c) 10

4. (a) 243π cc/s (b) 243π cc/s (c) =H (d) Stokes' Theorem (e) 0

5. 64π

6. (a) False (b) False (c) False (d) False

EC: 2 ln(2)

3/16/12

Pictures of today's review can be found here and here.

3/15/12

I will hold office hours next week on Monday from M 1:30–3:30 PM.

I will also be available on Wednesday on a limited basis. Please email me in advance to make an appointment if possible, but feel free to drop by my office without one if necessary and see whether I am available.

3/14/12

The answers to the integrals in today's activity are 27*ln(2) and 81/2.

3/12/12

The final will be Thursday 3/22/12 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 (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.

3/9/12

Photos of the surfaces drawn on the board today can be found here and here.

3/5/12

The software I demonstrated in class today 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.

2/27/12

I may have written the equation of the paraboloid down incorrectly during class. The correct statement of the problem is:

Let P be the paraboloid 2x²+2y²+z=50. Find the flux of the vector field F=3r upward through P.

The correct answer is 5625π.

Can you think of more than one way to do this problem?

2/26/12

Here are some comments about Friday's activity ("The Fishing Net"). By all means address these points in your writeup.

• 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.

2/20/12

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.

2/15/12

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; ask me if you'd like to take a look at worked solutions.

1. −2

2. 17/10

3. 13/3

4. 1+e+π²/4

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

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

7. 8 grams

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.

• 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.

1/28/12

Some further advice on writing up homework assignments can be found here.

1/27/12

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.

1/26/12

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.

1/25/12

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.

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.

1/22/12

Due to the closures of OSU this past week, there are a couple of optional topics I will not cover during class:

• Directional Derivatives
• The Gradient in Curvlinear Coordinates

1/17/12

OSU is officially closed tomorrow morning until 10 AM; class is therefore canceled. I encourage you to work on this worksheet.

Weather permitting, I will come to the classroom tomorrow morning at 9 AM, and be available for questions. This would be a reasonable time to work on this worksheet, should you be so inclined (and able to get to campus).

This worksheet does not need to be turned in, but you should be prepared to discuss your results at the beginning of Friday's class. However, you will need to know the answers througout the remainder of the course, and should probably memorize them (after being sure they are right...).

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 full text, as well as access to most of its homework problems, are available through this CourseID. However, this traditional text is not a close match to the philosophy of this course, but you may nonetheless benefit from seeing other approaches to the same material.

1/14/12

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.

1/13/12

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.

1/10/12

Some of you may have noticed that my website originally had the wrong class schedule. We will follow the schedule of classes, so that Friday will be our early day.

1/9/12

A copy of my (slightly outdated) Study Guide for MTH 255 can be found 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.

1/8/12

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.

1/3/12

You may wish to read this note about textbooks, intended for students in the non-honors section of MTH 255. The honors section will make even less use of traditional textbooks; there is no need to purchase one unless you want to.

11/13/11

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.