Saturday, April 19, 2014

discussion, week 14

Only two weeks of classes left! This week's review problems cover the divergence and curl operators and will also help you parametrize surfaces. Surfaces, being two dimensional objects, require two parameters.

The quiz will cover line integrals; please know how to decide if a line integral is positive, zero, or negative from the graph of the vector function. You worked problems of this sort in homework 18.

Friday, April 18, 2014

Wednesday, April 16, 2014

lecture, wednesday apr 16

I'll start with the problem of the day (provided by Trevor Gray) and then dig into section 16.5, to look at some relatives of the gradient vector. These relatives, the curl and divergence, will appear in Stokes' theorem and the divergence theorem.

Audio and video.

If there is time I would like to start the discussion of how to parametrize surfaces (16.6).

Tuesday, April 15, 2014

discussion, week 13

The final exam is only four weeks away. We should practice line integrals. Problem 7 will take you back to chapter 12 and remind you that $\vec{A} \times \vec{B}$ is a magical vector.

This week's quiz is about the spherical coordinate system. There may be problems on the final exam where you need to integrate in spherical or cylindrical coordinates. 

Monday, April 14, 2014

exam 3 results

You may pick up your exam in your section meeting, or at my office. Your score on WebAssign is two points higher than the score recorded on your exam. This is not a mistake, but a correction for problem 1d which we thought was badly written.

This was a happy exam. A total of 142 calcunauts took the exam Thursday night. Two people will be taking a makeup exam at some point. The mean is 76.8 and the median is 77. The quartiles are 87, 77, and 70. So 75% of the class have scores of 70 or higher and 25% of the class have scores of 87 or higher. Pretty great! And these are the uncorrected scores.

exam 3 quartiles: 70, 77, and 87

lecture, monday apr 14

We'll construct Green's theorem (16.4) and then use Green's theorem to compute a line integral around a simple, positively oriented, closed curve in the $xy$-plane.

Weird, the audio wasn't working initially. Video and audio. April is an ok the cruelest month.

Friday, April 11, 2014

answers to exam 3

Luke Cloud found a mistake in problem 9. It is fixed.

Here is my first attempt at answers (and a few solutions) to exam 3.  We'll be using this as the answer key, so please let me know if you find a mistake.

lecture, friday apr 11

I'll wrap up section 13.3 today and, maybe, start on Green's theorem. Green's theorem is another extension to the fundamental theorem and provides another way to avoid computing a particular type of line integral.

Video and audio.

If the domain of $\vec{F} = \left<P,Q\right>$ is open and simply connected, and $P_y=Q_x$ then $\vec{F}$ is guaranteed to be conservative.

If the domain of $\vec{F} = \left<P,Q\right>$  is open but has one or more holes (so it is connected, but not simply connected) then $P_y=Q_x$ does not guarantee that $\vec{F}$ is conservative. 

Thursday, April 10, 2014

exam 3 is today

Exam 3 starts at 5:15 pm this afternoon, Thursday, April 10.  As the schedule promises, the exam covers sections 15.1 through 15.5 and 15.7 through 15.10. Remember, no calculators or other electronic devices are allowed at the exam.

This exam will cover the same topics covered by mock exams 3a and 3b.

This exam covers material from homework assignments twelve through fifteen and discussion problems from weeks 9 through 12.

Like last time, you'll take this exam with your discussion section. Space may be tight. Please leave backpacks and computers at home. Bring a photo ID.
  • Section 20 (Tues, 9:35) CR 133
  • Section 21 (Tues, 11:00) CR 133
  • Section 22 (Tues, 1:20) CR 314
  • Section 23 (Thurs, 9:35) BU Auditorium
  • Section 24 (Thurs, 11:00) BU Auditorium
  • Section 25 (Thurs, 1:20) CR 306

Wednesday, April 9, 2014

lecture, wednesday apr 9

More line integrals today (16.2) and we'll look at an escape hatch (the fundamental theorem of line integrals, 16.3) that allows us to compute line integrals of conservative force fields without doing any integration!

Rats! Video but no audio. It was a fresh battery too.

Monday, April 7, 2014

lecture, monday apr 7

Don't forget, there is an exam Thursday afternoon.

I'll summarize last week's line integrals of scalar functions and then look at another type of line integral that is used to calculate work.

Audio and video.

A quick note on the reverse parametrization, because a number of people in the noon section asked about it. It's not necessary for the type of line integral we did today, because there is no requirement that $dt \ge 0$. The reverse parametrization is necessary for the line integrals we did last week.

Saturday, April 5, 2014

discussion, week 12

As usual, no quiz this week, due to Thursday's exam. As in past weeks, the discussion problems are mainly old exam problems from chapter 15. No fair looking at the answers until you've worked the problems on your own.

Please let me know if you find a mistake.

Friday, April 4, 2014

lecture, friday april 4

I'll work some line integral examples where we integrate scalar functions along curves in $\mathbf{R}^2$ or $\mathbf{R}^3$. Toward the end of the hour On Monday we'll think about integrating integrate vector functions (force fields).

Audio and video.

solutions, week 11 discussion

I forgot to post these answers yesterday. As always, please let me know if you find a mistake.

Wednesday, April 2, 2014

lecture, wednesday apr 2

We'll take another stab at identifying vector fields (16.1) and then look at line integrals (16.2). We'll start with arc length calculations.

No audio! Video only.

Tuesday, April 1, 2014

mistake in discussion problems

Curtis alerted me to a mistake in problem 5. It has been fixed. The same mistake appeared in mock exam 3a, but that has also been fixed. What a week!

discussion, week 11

This week's problems include triple integrals in both cylindrical and spherical coordinates, and changes of variables for double integrals.

The quiz covers properties of iterated integrals and cylindrical coordinates.

Monday, March 31, 2014

lecture, monday, mar 31

I'll finish the change of variables problem (15.10) from Friday and then talk about several vector fields (16.1) we'll use in chapter 16. I passed out two vector field identification problems.

Video and audio. Let's hope I'm less senile Wednesday.

Saturday, March 29, 2014

spherical coordinates

I have been writing the spherical coordinates in a right-handed order: ($\rho$, $\phi$, $\theta$). To see why this is a right-handed order you need to think about the unit vectors $\hat{e}_\rho$, $\hat{e}_\phi$, and $\hat{e}_\theta$.

Our textbook, and the WebAssign problems too, use a different order: ($\rho$, $\theta$, $\phi$). Watch out for this in problem 6.

Friday, March 28, 2014

lecture, friday mar 28

I'll do one more triple integral in spherical coordinates (15.9), by calculating the polar moment of inertia of a half-ball. Then we'll go back and compute a double integral by performing yet another change of variables (15.10).

In the next two discussions you'll work on problems from 15.8 (cylindrical coordinates), 15.9 (spherical coordinates) and 15.10 (general transformations). With luck, everyone will be well prepared for the exam on April 10.

Audio and video. Wait a minute or two for the audio.