## Tuesday, November 25, 2014

I'l be passing out exams at my office between 9 and noon this morning. I posted solutions Friday afternoon; scroll down to find them.

If you are wondering, I wasn't able to upload exam scores last night due to the slowness of either WebAssign or my network connection.

## Monday, November 24, 2014

### exam 3 results (revised)

We graded 162 exams over the weekend, including one without a name! The average is 77.4 and the quartiles are 68.75, 78, and 88. Slightly more than 50% of you have scores of 78 or higher. And, slightly more than 25% of you have scores of 88 or higher. One person has a perfect score.

The median scores for the individual problems are

 16/20 10/10 8/10 12/16 12/12 8/8 6/8 6/8 5/8

The T/F questions remain challenging. Many people sailed through problem 4 but others did not plot the region of integration or failed to see they needed to integrate in the $z$ direction first.

Each full size rectangle in the top histogram represents three brave calcunauts.

### lecture 35, green's theorem

We'll finish assembling Green's theorem (16.4), our latest version of the fundamental theorem, and then use it to smite a vicious line integral. Green's theorem can be used with both conservative and nonconservative vector functions. But the curve used in the line integral must be simple (non intersecting) and closed.

We'll also look at the divergence and curl operators (16.5); they are close cousins of the gradient operator.

## Sunday, November 23, 2014

### math as art

Many people do amazing work on these exams, but check this out. Her graph even has the correct proportions.

## Friday, November 21, 2014

### exam 3 solutions

The person (or group) finding the most mistakes in my solutions to exam 3 will win a valuable prize!

### lecture 34, line integrals, part 4

I'll clean up some of the mess today by reminding you that $\vec{F}(t) \cdot \vec{r}'(t)$ involves a projection of $\vec{F}$ onto a tangent vector. We'll also look at some fallout from the fundamental theorem for line integrals (16.3) and start a new version of the fundamental theorem for simple closed curves (16.4).

I'll post solutions to the exam this afternoon. There are no discussion sections next week, but you may be able to pick up your exam at my office Tuesday afternoon.

## Thursday, November 20, 2014

### exam 3 is history!

Exam three starts at 5:15 pm this afternoon (Thursday, 20 November). The exam covers sections 15.1-15.5 and 15.7-15.10.

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 your integration and partial differentiation.

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.

Your exam room = f(your discussion section). You will share the room with Calculus II students. Be sure to leave an empty seat, or a Calc II student, between you and the next Calc III student.

• Section 21, CR 129
• Section 22, CR 133
• Section 24, CR 129
• Section 25, CR 133
• ## Wednesday, November 19, 2014

### ruh, roh

Curtis found an error in my solution to problem 13 in this week's discussion problems. The error is fixed.

### lecture 34, line integrals, part 3

We'll wrap up the magnetic field example and then turn to some simpler toy problems in section 16.2. We'll also look at the fundamental theorem for line integrals from section 16.3. The fundamental theorem gives a simple way to compute the line integral of a conservative vector field. Conservative vector fields are related to scalar potential functions by $\vec{F}(x,y,z)=\nabla f(x,y,z)$.

## Monday, November 17, 2014

### lecture 33, line integrals

Today we'll work on the second type of line integral, the one where we integrate $\vec{F}(x,y,z) \cdot d\vec{r}$. Again, we'll use parametric equations to transform the integral so that it depends only on $t$. In one example we'll see that the value of the integral is not influenced by the parametrization we apply to the curve. I'll work the spherical coordinate system into another example.

## Saturday, November 15, 2014

### discussion week 12

These problems will show you whether you understand the material in chapter 15, if you use them carefully.

For double integrals sketch the region of integration. For triple integrals in Cartesian coordinates sketch the region of integration for the two outermost integrals. For triple integrals in cylindrical and spherical coordinates plot the cross section of the solid region in the $rz$ half plane. Be sure to label all boundaries and shade in the region of integration.

The solutions don't provide any explanation, so talk to Curtis, Andrew or me if you have questions. We will, of course, start by asking you to plot the appropriate region of integration.

Please let me know if you find any sketchy looking bits.

## Thursday, November 13, 2014

### lecture 32, line integrals

We'll figure out how to integrate a scalar function along a space curve. Integrals of this type are used to compute lengths of curves, and the masses, center of masses, and moments of inertia of wires (one dimensional mass distributions).

Section 16.2 covers two types of line integrals. For now, just look at examples one through three.

### discussion problem solutions

Tell me if you find errors in these solutions. I'll make you famous.

## Tuesday, November 11, 2014

### lecture 31, vector fields

After ten weeks of preparation we are ready to take on vector calculus. Please take a quick look at section 16.1. You'll be happy to see our old friend the gradient vector.

We'll identify the graphs of several toy fields and create radial and tangential vector fields that mimic gravity, electric, and magnetic fields. Soon (Monday?) we will be integrating these vector fields along curves. And later, after the break, we will compute the flux of these same vector fields across surfaces.

### afternoon office hour cancelled

The scheduled Tuesday afternoon nerdfest is cancelled due to cold weather.

## Monday, November 10, 2014

### discussion, week 11

This week we write triple integrals in cylindrical coordinates and solve double integrals by changing variables.

The quiz deals with double integrals and cylindrical coordinates.

### lecture 30, integrating by changing variables

I'll finish the final spherical coordinate problem and then work a problem from section 15.10. In this section we solve problems using more general transformations.

The early part of section 15.10 is needlessly scary. A safe place to start reading is the redlined box on page 1044.

## Friday, November 7, 2014

### lecture 29, spherical coordinates

Please skim through section 15.9 over the weekend. Figures 1 through 5 are helpful for understanding how the spherical coordinate system works. Figure 8 is a stunning illustration of the volume element $dV$. It would be fun to compute the volume using vectors and a scalar triple product (combination cross and dot product).

We'll compute the mass and moment of inertia of Wednesday's ice cream cone, and maybe, start a new example.

## Thursday, November 6, 2014

### discussion problem solutions

There was a typo in problem 5 in the original problem set; the right half plane is $x \ge 0$, not $y \ge 0$. The typo is fixed in these solutions. Let me know if you see any new mistakes.