## Wednesday, May 18, 2016

### total scores

Here are the total scores for the 143 people who took exam 4. The mean score is 77.7 and the quartile scores are 71.78, 79.28, 84.93; so half the scores are above 79.28 and half are below. I'll try to set the final grade boundaries this evening.

## Monday, May 16, 2016

### don't panic!

The grade you see on WyoCourses may not be your final grade, particularly if your total score lies just below a grade boundary. One big adjustment remains: Bang, Bryan, and I need to decide where to place the grade cutoffs.

Changes to the WyoCourses gradebook since the final exam:

2. (Monday, May 16) I uploaded your exam four score. Info about exam 4 is available at math2210.blogspot.com.
3. (Tuesday, May 17) I uploaded your adjusted midterm exam average. Everyone received an extra 5 points on one exam and, if your final exam score was high enough, your lowest midterm exam score was replaced with your final exam score.
4. (Tuesday, May 17) I uploaded scores for the week 14 discussion problem set.
5. (Tuesday, May 17) Dropped your two lowest discussion scores.

### exam four results

On Wednesday, May 11, 143 brave calcunauts took exam four. The mean is 63.8 and the quartile scores are 54, 65, and 76. Last semester the average was 69.8 and the quartiles were 62, 73, and 82. The median scores on the individual problems are:

 14/20 9/10 5/10 14/24 6/8 4/5 3/9 11/14

People did reasonably well on the core problems (2, 3, 4, and 5), the median score on those is 67.3%. Many people lost points on problem 3 because they used Green's theorem, even though the curve is not closed. And too many people had trouble with limits of integration in problems 4 and 5.

Problem 7 surprised me; only a few people were able to differentiate $\ln(r)$ and even fewer realized the fundamental theorem could be used to evaluate the line integral. I thought people would do well on this one because there were several homework/discussion/lecture problems that used the scalar function $r$.

## Wednesday, May 11, 2016

### solutions for exam four

Please let me know if you find any errors or confusing bits in my solutions to exam four.

(May 12, 11:40 am) I fixed the integrand in the solution to problem 5.
(May 14, 2:40 pm) Bang found an error in my cross product in problem 6. It's fixed.

### exam 4 approaches

Exam 4 is history. The exam covered sections 13.7, and 14.1-14.8.

Calculators and computers are not allowed at the exam. We will provide you with an equation sheet. You can find the equation sheet on the last page of the new mock exam.

The equation sheet does not contain the transformation equations for cylindrical coordinates, but you should know them by now.

Practice integration and partial differentiation. Know how to change variables in double and triple integrals. Know how to compute dot and cross products. Know how to compute the divergence and curl of a vector function. Know the cosine and sine of common angles like $0$, $\pi/6$, $\pi/4$, $\pi/3$, $\pi/2$, $\pi$, and $2\pi$ radians.

Your exam room is a function of the first three letters of your last name.
• Aar through Kla, go to CR 133
• Kle through Pow, go to Berry Center 138
• Put through Zzz, go to Geology 216
Leave an empty seat between you and the next calcunaut.

To practice for the exam, use your MyMathLab, discussion, and mock exam problems. Solutions are available for these problems. If you don't understand something ask questions in class, at your discussion section, during our office hours, or at the review session.

## Tuesday, May 10, 2016

### error found and fixed

Carissa Guynes found an error in my solution to problem 1 in the week 13 discussion problems. The error is fixed.

## Saturday, May 7, 2016

### so many theorems!

Here is an incomplete guide to using the integral theorems to compute line and surface integrals.

## Friday, May 6, 2016

### course evaluation rate

Nice work Caymen! The response rate stands at 84.87% and I'll add 5 points to one of your first three exams.

### sunday review

I reserved CR 302 from 3-5 pm for a review session. Bring questions. If the east doors are locked, try the west doors (the 9th St. side).

### loose ends, sections 14.7 and 14.8

I'll verify the divergence theorem by computing the flux of $\vec{F}$ across the closed surface that surrounds the solid region $E$ from last time.

elderly guy assembles and computes surface integrals

## Thursday, May 5, 2016

### need extra points?

Hey Calcunaut, I really need your help! Each year the A&S Dean awards the instructor with the highest course evaluation rate a vacation at her luxurious Jackson Hole chateau (see photo below). And, while the current response rate (44%) is pretty good by A&S standards, it may not be enough to win the prize. Competition may be tougher this year because she increased the length of the vacation to two nights.

To increase my chances of winning I have an offer for you: if the response rate exceeds 80% I'll add five points to one of your first three exam scores. Is it a deal? Be sure to tell your friends; the deadline is Sunday, May 8. If you've already responded, thank you.

### step schedule

If you go take the equation sheet with you. The tutors will thank you.

## Wednesday, May 4, 2016

### divergence theorem, section 14.8

I'll give a quick review of Stokes' theorem and finish the flux problem.

And, we'll look at one final version of the fundamental theorem, the divergence theorem (14.8). You can find an explanation for why the divergence theorem involves $\vec{\nabla} \cdot \vec{F}$ in my notes.

elderly guy yammers about the divergence theorem

You shouldn't leave the course thinking these theorems are only useful for avoiding a difficult line or flux integral. In my experience they are mainly useful for turning conservation laws into partial differential equations.

## Monday, May 2, 2016

### homework twenty-two

Pearson's MyMathLab website is sick, very sick. Check its status at status.pearson.com. I was able to extend the deadline for homework twenty-two to Wednesday night.

### stokes' theorem, section 16.8

Today we'll look at Stokes' theorem (16.8). Stokes is another extension of the fundamental theorem; it relates the flux across a surface to a line integral around the boundary of the surface. My notes give some details on how the integrals are related.

We'll verify Stokes' theorem by computing a surface integral and a line integral. We'll also look at some ramifications of the theorem.

## Friday, April 29, 2016

### surface integrals (part 2), section 14.6

After finishing any leftovers from Wednesday, we'll compute the flux of a vector field $\vec{F}$ across open or closed surfaces. The flux across the surface element $d\vec{S}$ is represented by the gray boxes. You can see that the flux is largest when $\vec{F}$ and $d\vec{S}$ are parallel, but decreases as the angle between the vectors increases. In detail, the flux is equal to the dot product between $\vec{F}$ and $d\vec{S}$.

## Wednesday, April 27, 2016

### surface integrals (part 1), section 14.6

First, a word on section 14.5. You want to be able to compute the curl and divergence of a vector function. You also want to know that if $\vec{F}$ is conservative then $\vec{\nabla} \times \vec{F} = \vec{0}$. There are examples in the book, on YouTube and in this week's discussion problems. We'll do some additional work with the curl and divergence next week, after we have discussed Stokes's theorem and the divergence theorem.

Today we'll work on integrating scalar functions over common surfaces. To save time I'll let you read about the vector and scalar surface area elements on your own.

The WyoCast recording system failed again.

This table contains some common surface area elements:

## Monday, April 25, 2016

### green's theorem and vector operators, sections 14.4 and 14.5

We'll verify Green's theorem, use it to play some tricks, and get to know some friends of the gradient vector.

The WyoCast recording system failed.

## Friday, April 22, 2016

### conservative vector functions, section 14.3 and 14.4

We'll will finish Wednesday's project and see why a vector function of the form $\vec{F}(x,y,z)=\vec{\nabla}f(x,y,z)$ is said to be conservative. The short story is that the fundamental theorem of calculus requires that energy (kinetic plus potential) be conserved if the force is conservative. And, this last statement explains why math rulz!

If there is time, we'll start work on the next version of the fundamental theorem, Green's Theorem in section 14.4. Green's Theorem links double integrals to line integrals.