Please let me know if you find errors or unclear bits in my solutions to exam 4.

# math 2210

## Thursday, December 18, 2014

## Wednesday, December 17, 2014

### a note on webassign grades

I decided to wait and add the 5 bonus points (the course evaluation rate reached 85.12%!) after exam 4 is graded and the substitution has been made for the lowest of the first three exams. This way everyone will benefit from the 5 points.

I'll also add in the final quiz score when those are graded.

I'll also add in the final quiz score when those are graded.

## Saturday, December 13, 2014

### exam 4 is history!

Exam four is over. The exam covers sections 16.1-16.9.

Section 20, AG 1032
Section 21, GE 216
Section 22, AV 212 (Aven Nelson Building)
Section 23, AG 1032
Section 24, GE 216
Section 25, AV 212 (Aven Nelson Building)

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.

### Be careful, The exam rooms have changed!

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.

### final grades

If you click on Grades on your WebAssign homepage you'll see four numbers. The first, your overall score, is the important one; it determines your course grade. The overall score is a weighted average of your three category scores:

This is the midterm exam category score that WebAssign will show after exam four scores are entered.

If your fourth exam score, call it X again, is higher than your lowest exam score, say E2, then your midterm exam category score will be

The fourth exam score replaces the lowest exam score.

WebAssign does not permit conditional calculations of this sort. WebAssign will only show your minimum midterm exam category score and, therefore, your minimum overall score. But you are a quantitative person. You can compute your true overall score using the formulas shown above.

overall score = 0.8 * exam score + 0.15 * homework score + 0.05 * quiz score.

At midsemester I proposed deleting your lowest score from the first three exams and then doubling the weight of the fourth exam. This adjustment will occur only if your fourth exam score is higher than one of your earlier scores. So, the calculation of your midterm exam category score depends on your fourth exam score.

If your fourth exam score, call it X, is lower than your other exam scores (E1, E2, and E3) then your midterm exam category score will be

exam score = 0.25 * E1 + 0.25 * E2 + 0.25 * E3 + 0.25 * X.

This is the midterm exam category score that WebAssign will show after exam four scores are entered.

If your fourth exam score, call it X again, is higher than your lowest exam score, say E2, then your midterm exam category score will be

exam score = 0.25 * E1 + 0.25 * E3 + 0.5 * X.

The fourth exam score replaces the lowest exam score.

WebAssign does not permit conditional calculations of this sort. WebAssign will only show your minimum midterm exam category score and, therefore, your minimum overall score. But you are a quantitative person. You can compute your true overall score using the formulas shown above.

## Friday, December 12, 2014

### lecture 41, fundamental theorems

We'll continue to play with the Stokes' (16.8) and Divergence (16.9) theorems. The problem sets might lead you to believe these theorems are only useful for simplifying integrations. In my experience the theorems are mainly useful for turning conservation laws into partial differential equations.

## Thursday, December 11, 2014

### discussion problem solutions

Here is the final set of solutions. Please let me know if you find mistakes.

### all hail tyson ridell!

Tyson Ridell found an error in my solution for problem 2 of the week 13 discussion problems. I believe it is fixed.

## Wednesday, December 10, 2014

### lecture 40, fundamental theorems

I'll finish verifying Stokes' theorem and then talk about the divergence theorem. We'll use the divergence theorem to get a quick answer to problem 23 on homework 22.

### all hail tylynn smith

Tylynn Smith found a mistake in the way I defined quiz 6 in the WebAssign gradebook. The mistake is fixed and her classmates are jubilant.

## Tuesday, December 9, 2014

## Monday, December 8, 2014

### discussion week 15

This week we'll parametrize some surfaces, and compute several surface integrals, a line integral, and a curl.

The quiz deals with properties of line integrals and surface parametrizations.

The quiz deals with properties of line integrals and surface parametrizations.

### lecture 39, stokes' theorem

Stokes' theorem (16.8) is yet another extension of the fundamental theorem of calculus. It relates the flux of $\textrm{curl} \, \vec{F}$ across a surface to the circulation of $\vec{F}$ around the boundary of the surface. Stokes' theorem is a great excuse to compute more flux and line integrals. And, Stokes' theorem will show us that $\textrm{curl} \, \vec{F} = \vec{0}$ if $\vec{F}$ is conservative.

Use this file to speed your way through surface integrals and to practice computing $dS$.

Use this file to speed your way through surface integrals and to practice computing $dS$.

## Saturday, December 6, 2014

### all hail stephen kristy!

Stephen Kristy found a most foul error in my solutions to the week 13 discussion problems (problem 1). The error is fixed (12/6).

### evaluation disaster!

This afternoon the course evaluation response rate reached 40%. While that rate is pretty good by A&S standards, I fear it's 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. Consequently, I am offering to

I'll be given a list of those calcunauts who evaluated the course after the evaluation period closes on December 14. The evaluations are anonymous and will not be released to me until well after the grade submission deadline.

**increase one of your 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 December 14. The evaluations are anonymous and will not be released to me until well after the grade submission deadline.

## Thursday, December 4, 2014

### lecture 38, surface integrals

We'll finish computing the moment of inertia of the spherical shell and then turn to flux integrals.

The flux of $\vec{F}$ across the surface $d \vec{S}$ is largest (compare the volumes of the the gray boxes) when the two vectors are aligned. The flux is computed with a scalar triple product, combining a dot product (the obvious one shown here) and a cross product (buried inside $d\vec{S}$).

The flux of $\vec{F}$ across the surface $d \vec{S}$ is largest (compare the volumes of the the gray boxes) when the two vectors are aligned. The flux is computed with a scalar triple product, combining a dot product (the obvious one shown here) and a cross product (buried inside $d\vec{S}$).

## Tuesday, December 2, 2014

### lecture 37, surface integrals

We'll compute the surface area of the plane we parametrized last time. If you are curious about the origin of the surface area differential, $d\vec{S}$, you'll have to look at the discussion problems for week 13 or this longer handout.

Also, we'll parametrize and compute properties (surface area and moment of inertia) for a cone and a sphere.

Also, we'll parametrize and compute properties (surface area and moment of inertia) for a cone and a sphere.

## Sunday, November 30, 2014

### lecture 36, parametric surfaces

The first day back is a reasonable time to talk about where we have been and where we are going. We'll build a map.

The good news is only three sections remain and only one of the three contains new material (16.7). We'll wallow in surface integrals (16.7) this week and then wrap up the final versions of the fundamental theorem next week. The end is near.

We'll start 16.7 by parametrizing some familiar surfaces. Surfaces are two dimensional and so require two parameters. On Wednesday and Friday we'll use these surface parametrizations to compute surface integrals in the same way we used curve parametrizations to compute line integrals.

The good news is only three sections remain and only one of the three contains new material (16.7). We'll wallow in surface integrals (16.7) this week and then wrap up the final versions of the fundamental theorem next week. The end is near.

We'll start 16.7 by parametrizing some familiar surfaces. Surfaces are two dimensional and so require two parameters. On Wednesday and Friday we'll use these surface parametrizations to compute surface integrals in the same way we used curve parametrizations to compute line integrals.

### discussion, week 14

This week we use Green's theorem to compute a line integral, compute the curl and divergence of several vector functions, and parametrize a surface; some old stuff and some new stuff.

The quiz deals with line integrals; the problems are similar to problem 1 on assignment 16. If you used the trial and error method to answer problem 1 go back and understand the problem.

The quiz deals with line integrals; the problems are similar to problem 1 on assignment 16. If you used the trial and error method to answer problem 1 go back and understand the problem.

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