## Thursday, May 21, 2015

I set grade boundaries this morning and submitted grades to the registrar's office. The pass rate for people who took the final exam is 83.5%!

As promised, I replaced your lowest exam score (if your final exam score is higher than your lowest score) and, afterwards, added 5 bonus points to your lowest exam score. The course evaluation rate reached 83% (still waiting to hear about that aluminum F-150).

The quartiles for your course scores are 74.6, 81.4, and 89.2. Slightly more than 50% of you (the 164 who took the final exam) have scores of 81.4 or higher, and slightly more than 25% of you have scores of 89.2 or higher.

 Each full size rectangle represents five brave calcunauts.

## Thursday, May 14, 2015

### exam 4 results

A total of 164 people took the fourth exam Tuesday afternoon. The average score is 69 and the quartiles are 60, 71, and 83.75. For comparison, last semester the average was 66.3 and the quartiles were 53, 72, and 84.

The median scores on the individual problems are:

 14/20 8/10 8/10 12/14 6/6 9/10 7/15 13/15

Scores were low on problem 7 because relatively few people integrated around all three boundary segments. This is difficult material; overall people did very well.

 Each full size rectangle represents three brave calcunauts.
 Each full size rectangle represents three brave calcunauts.
 Each full size rectangle represents five brave calcunauts.
 Each full size rectangle represents four brave calcunauts.

## Tuesday, May 12, 2015

### exam 4 solutions

Take a look at my solutions to this afternoon's exam. Please tell me if you find errors or unclear parts.

### exam 4 is over!

Exam four is history. The exam covers sections 16.1-16.9. 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 each mock exam.

Practice integration and partial differentiation. Know how to convert integrals to polar, cylindrical, or spherical coordinates. Know how to compute dot and cross products. Know how to compute the divergence and curl of a vector function.

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

If you bombed one or more of the earlier exams, consider that spaced practice and self-examination may produce better results than cramming.

The exam rooms have not changed:

• Section 20, Berry Center 138
• Section 21, Berry Center 138
• Section 22, Classroom Bldg 214
• Section 23, Geology (old part) 216
• Section 24, Classroom Bldg 214
• Section 25, Geology (old part) 216
• ### a proposal

Exam four covers all of chapter 16. The extensions of the fundamental theorem, which we started last week, are the heart of the course. Because I want you to concentrate on this material (and the line and surface integrals of chapter 16) as much as you can, I have a proposal for you. If your score on exam four is higher than at least one of your first three exams scores then I'll drop the lowest of your first three exam scores and double the weight of your fourth exam score.

I tried this last semester and it had a great effect; a number of people were able to raise their grades, the pass rate increased, and people who might have skipped the exam in other semesters stayed with the course to the end.

## Friday, May 8, 2015

### the mother of all review sessions?

I reserved CR 302 (upstairs in the classroom building) on Sunday afternoon from 1 to 3 pm. Bring questions.

### lecture 41, divergence theorem

I will complete the problem I was working on Wednesday. Turns out I made a mistake and $\vec{F}=\langle y,-z, x\rangle$ so that the curl $\vec{\nabla} \times \vec{F} = \langle 1,-1,-1 \rangle$. This correction vastly simplifies the flux integral. Woohoo!

We'll finish by looking at one final version of the fundamental theorem, the divergence theorem (16.9). You can find explanations for why the divergence theorem involves $\vec{\nabla} \cdot \vec{F}$ in the text (page 1129) and in my notes.

Don't go away 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.

## Wednesday, May 6, 2015

### lecture 40, stokes' theorem

I'll finish the flux calculation from Monday and then discuss 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.

## Monday, May 4, 2015

### evaluation disaster!

This evening the course evaluation response rate reached 38%. I fear this is not nearly enough to win the new Ford F-150 (King Ranch Edition!) the A&S Dean has promised to the instructor with the highest evaluation rate. And, I fear that the competition will be tougher this semester because the new truck is fabricated from high-strength, military grade, aluminum alloys.

To increase my chances of winning the truck, I am offering to increase one of your first three exam scores by 5 points if you spend a few minutes to fill out a course evaluation for Math 2210.

I'll be given a list of those calcunauts who evaluated the course after the evaluation period closes on this weekend. The evaluations are anonymous and will not be released to me until well after the grade submission deadline.

## Sunday, May 3, 2015

### lecture 39, surface integrals, part 3

I'll start by talking about oriented surfaces and the flux of a vector field across those surfaces. Then we'll use our surface area elements from Friday to compute fluxes across two closed surfaces. One integration will be easy; the second will take some time.

This is the last of the new material. On Wednesday and Friday we'll look at the final versions of the fundamental theorem. These theorems will give us a chance to do more surface integrals and to revisit line and triple integrals.

### discussion, week 14

This week's quiz is very difficult. You'll need to know how reversing the direction of a curve affects line integrals (remember, they come in two flavors). You'll need to understand that line integrals are path dependent unless the vector function is conservative. And, you'll need to know how to tell if a given set of parametric equations satisfy the Cartesian equation of a surface.

This week's problems concern surface integrals.

## Friday, May 1, 2015

### lecture 38, surface integrals, part 2

We'll parametrize cylinders and spheres and then compute moments of inertia for cylindrical and spherical shells (16.7). We'll assemble the new surface area elements in a way that bypasses the individual Jacobian determinants we used Wednesday.

## Wednesday, April 29, 2015

### lecture 37, surface integrals

Integrating over surfaces is similar to integrating over curves; a change of variables is necessary. Surfaces are two dimensional so we are back to double integrals and Jacobian determinants.

We'll parametrize planes, paraboloids, cylinders and spheres and compute some surface areas (16.6). Our parametrizations use two parameters because surfaces are two dimensional. I'll skip over some of the details; look at my notes if you want to see those details.

Surface integrals are complicated because the regions of integration are 2-dimensional surfaces that live in $\mathbb{R}^3$. A change of variables is usually required.

## Monday, April 27, 2015

### homework changes

I edited homework assignments 20, 21, 22, and 23 this afternoon and changed their due dates to better fit our schedule. My edits may cause trouble for the people who have started those assignments. Contact me if you have problems.

### lecture 36, div, grad and curl

We'll wrap up the Green's Theorem (16.4) example from Friday and then compute the curl and divergence of several vector fields (16.5). We'll see that the curl of a gradient field $\vec{\nabla} \times \nabla f= \vec{0}$ and that the divergence of a curl field $\vec{\nabla} \cdot (\vec{\nabla} \times \vec{F}) = 0$. The first equation shows that conservative fields are irrotational. The second equation shows that incompressible fields can be generated from vector potential functions.

## Sunday, April 26, 2015

### discussion, week 13

The quiz problems will remind you of problem 1 on assignment 18. All you have to do is figure out if, on average, the wind is in your face (W<0), from the side (W=0), or at your back (W>0) as you trek along.

Discussion problems include line and double integrals and gradient's two siblings: curl and divergence.

## Thursday, April 23, 2015

### lecture 35, green's theorem

We'll ponder our odd results from Wednesday and then move on to discuss Green's Theorem (16.4), a new extension of the fundamental theorem of calculus. Green's theorem relates a double integral over a region in the plane to a line integral around the boundary of the region. We'll verify Green's theorem and then use the theorem to perform some neat tricks.

## Wednesday, April 22, 2015

### lecture 34, line integrals

First, a bit of review. Then we'll continue with Monday's example and integrate the components of the force field to get a potential function.  We'll also evaluate the line integral in the problem in order to verify the fundamental theorem for line integrals. Then we'll look at a vector field you are likely to see in an E&M or fluid mechanics course. It seems to break the rules, but not really. Along the way we'll construct a map for those brave enough to venture into section 16.3.