ANNOUNCEMENTS
MTH 255H — Winter 2011

3/19/11

Exams are graded; course grades have been submitted

You can get your exam back from me next term.

3/13/11

I should be in my office tomorrow afternoon (Monday) from roughly 1–3 PM.

Other times may also be possible; email me or take your chances.

3/12/11

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.

3/9/11

The area of the region in today's activity is 27 ln(2), and the final integral should evaluate to 81/2.

Make sure you are able to obtain these answers using a method involving Jacobians.

The slide we constructed during today's class can be found here.

3/8/11

The final will be Wednesday 3/16/11 from 6–7:50 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.

3/7/11

This week's homework assignment, originally due today, will be accepted until the start of class on Wednesday. This assignment is an important capstone experience, and should definitely be attempted. As always, please contact me if you have questions.

Assignments turned in by 5 PM this afternoon (Monday) will be corrected and handed back on Wednesday. Slip them under my office door if I'm not there.

3/4/11

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

3/2/11

Today's handout with formulas for divergence and curl in various coordinates systems can be found here.

2/28/11

I have added a discussion of compatible orientations for Stokes' Theorem to the online text.

The slide we constructed during today's class can be found here.

2/25/11

It was brought to my attention today that I may have written an incorrect definition of curl on the board on Wednesday. Just in case, below is the correct statement:

The component of curl(F) in the direction n at a point P is the limit of the circulation of F around a loop perpendicular to n, divided by the area of the loop, as the loop shrinks to the point P.
In symbols: ∇×F·n |_P = lim_C→P ∫_CF·dr/area(C)
In words: (Oriented) curl is circulation per unit area

2/24/11

Friday's class is canceled!

• Further information is available here.
• You should still be able to complete the homework due Monday. If you get stuck, I will accept it until Wednesday, but be prepared to ask questions Monday, either in class or during my office hours.

2/23/11

The slide we constructed during today's class can be found here.

2/21/11

Comments on the homework assignment due today:

• You should be able to do the second problem without explicit integration! (You do not need to compute dA...)
• My claim in class that today's lecture would help was incorrect.
• Feel free to have another go (and/or to ask me for help), and (re)submit on Wednesday.

Please bring the "Divergence" worksheet that was handed out today to class on Wednesday.

2/18/11

• The slide we constructed during today's class can be found here.
• The answer for the flux through the paraboloid discussed in class is 1875π.
  Can you get this answer in polar coordinates? In rectangular coordinates? Can you set up the integral needed to compute the amount of chocolate on the paraboloid if the density of chocolate is σ?
• A discussion of the surface element for graphs of functions can be found here.

2/16/11

Here are some comments about the writeup for today's activity ("The Fishing Net"):

• You are strongly encouraged to discuss which terms, if any, will cancel in the final answer.
• For possible extra credit, you may wish to 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.)
• You do not need to include a discussion of the Divergence Theorem in your writeup.
• You may nonetheless attempt part (b) if you wish, for possible extra credit.
• The Divergence Theorem states that ∫div(F) dV = ∫F • dA.
  (The RHS must be integrated over the boundary of the domain on the LHS.)
• A formula for the divergence div(F)=∇• F in rectangular coordinates can be found here.

The correct answer to the last problem on the most recent homework assignment (flux through a cylinder) is 72π. Make sure that you are able to obtain this answer.

Feel free to submit another writeup if you would like me to check your work.
(These writeups will be corrected but not graded.)

2/15/11

If you're looking for a challenge, find dA on the triangular region considered in class yesterday (and 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.

2/14/11

The slide I showed in class today, which illustrates how to relate mathematical text, equations, and pictures, can be found here.

2/7/11

You are encourage to rewrite your answers to any midterm questions on which you received a score of 5 or less, and turn them in to me by Wednesday, 2/9.

Resubmitted answers will be corrected, but will not affect your grade.

2/1/11

Tomorrow'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.

1/30/11

The midterm will be Friday 2/4/11 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 black ink (blue ink is OK).

1/27/11

Due to a communications mixup, the McCallum text is not yet on reserve in the library, but should be within a few more days.

A copy is also available for use in the MLC (Kidder 108).

1/26/11

The midterm is scheduled for next Friday, 2/4/11.

Further information will be posted soon.

1/25/11

Corinne will hold office hours on W 1/26 from 3–4 PM and Th 1/27 from 4–5 PM in Weniger 493.

My office hours are canceled this week...

1/20/11

By popular request, here are some practice problems you may wish to try.

• A list of recommended problems (by another instructor) from McCallum et al, the text used last year at OSU, can be found here. (All of the Exercises are good practice, and most of the Problems reinforce conceptual understanding — some of our homework problems come from this book!)
• A list of recommended problems (by another instructor) from Briggs/Cochran, the text currently used at OSU, can be found here.

I am arranging to place a copy of the McCallum text on reserve; it should hopefully show up later this week.
(The Briggs/Cochran text is already on reserve for MTH 255.)

If you took MTH 254 at OSU last term, you may still have access to MyMathLab, which allows you to work online versions of (almost) all of the problems in Briggs/Cochran.

You can figure out roughly where we are in McCallum et al by looking at the table at the beginning of the (old) study guide. (See the announcement dated 1/4.)

1/19/11

With apologies, I failed to correctly save the figure constructed in class showing the discussion of today's activity.

The vector field applets shown at the beginning of class can be found here.

The pretzel in this week's homework assignment, due Friday, is a 1-dimensional object, like a curved (edible) stick, and not a 2-dimensional object (such as a cookie in the shape of a quarter circle).

1/18/11

I should be in my office this afternoon from roughly 2–3 PM.

1/14/11

Here are some comments about writing I made in class a few days ago.

• Use complete sentences (most of the time).
• Show (the essential parts of) your calculations.
• Do use displayed equations — which should nonetheless be grammatically correct parts of sentences.
• Do restate the problem (preferably in your own words).
• Yes, it's a "lab report", but no, the goal is not to record every step you took. ("First, we did …") Rather, the goal is to present a clear discussion of your calculations and conclusions.
• Include pictures!

1/12/11

The final screen shot of today's onscreen presentation is available here.

An interesting discussion of the shortest path to the top of the hill can be found in these two published articles: Article 1 and Article 2.

1/7/11

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)

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.

1/5/11

The final screen shot of today's onscreen presentation is available here.

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.

1/4/11

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.

1/2/11

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.

10/12/10

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.