## Monday, January 23, 2017

### no discussion sections this week

Due to bad weather, the discussion sections will not meet this week (January 23-27).

### lecture 1: points, curves and surfaces

We'll talk about some common objects (points, curves and surfaces) and the spaces ($\mathbb{R}$, $\mathbb{R}^2$, and $\mathbb{R}^3$) they live in. Our goal is to figure out how many Cartesian equations are required to describe the different objects in the different spaces. Also, we'll talk about how to measure distances between pairs of points in the various spaces.

Believe it or not, this stuff will be useful throughout the semester.

## Sunday, January 22, 2017

### office hours

Office hours are an important part of the course; if you are not using them you are not fully participating in the course.

My official office hours are M, W, and F from 3:10 - 5:00 pm, or by appointment. I'll post office hours for the discussion leaders (Bang and Andrew) as soon as possible. Keep checking the link at the top of this page.

### the etext is full of examples and problems ...

if you can find it. To make your way from the WyoCourses course page to the HTML version of the textbook, look for these links:
1. MyLab and Mastering
2. MyMathLab with Pearson eText Course Home
3. Course Tools
4. HTML eBook
5. alternate version of your eBook
6. HTML version of your textbook
Shame on you Pearson, shame on you!

### text

We use the textbook Multivariable Calculus by Briggs, Cochran, and Gillett (2nd Edition, ISBN 978-0-321-96516-5). Don't freak out, the chapters in this book might be included in the text you used for Calculus I and II. If not, you can access the electronic version of the book through MyMathLab.

The textbook (either ebook or paper) is an integral part of the course. If you are not using it you are missing out on a large number of worked examples that will help you solve homework problems. Some of these examples may appear on the exam.

### mymathlab

You can reach MyMathLab through WyoCourses. And, there is a permanent link to MyMathLab in the list of links on the right side of this page.

If you paid for access to MyMathLab in Math 2200 or 2205 you will not have to pay for access this semester. If you haven't paid for access, don't worry; you can signup for temporary access and then purchase a license when the trial period ends.

### a shiny new semester

This course is all about differentiating and integrating functions of two and three variables. Along the way, we'll play with a variety of curves and surfaces that live in three dimensional space. We'll figure out how to compute slopes on these objects and, eventually, how to integrate vector and scalar functions over the objects. In the final weeks of the semester we'll work with generalizations of the fundamental theorem of calculus that tie together different types of integrals. It is a fascinating and useful combination of geometry and calculus that never fails to excite me.

## Sunday, December 18, 2016

### total scores

Here are the total scores for the 214 people who took exam 4 (and are not suspected of academic dishonesty). The mean score is 80.2 and the quartile scores are 73.8, 81.5, 87.7; so half the scores are above 81.5 and half are below. These quartile scores are similar to those we saw in 2015.

## Saturday, December 17, 2016

### exam four results

Last Tuesday afternoon 216 brave calcunauts (and one interloper) took exam four. Three calcunauts with medical excuses will take a makeup exam next semester. The mean is 70.3 and the quartile scores are 61, 74, and 84. For comparison the results from the past two semesters are:

Spring 2016: mean 63.8, quartiles 54, 65, 76.
Fall 2015: mean 69.8, quartiles 62, 73, 82.

Strange but true: someone not enrolled in the course took the exam and scored a 42.

## Wednesday, December 14, 2016

### if only we could all write so well (part 4)

Check out these beautifully organized solutions. No one who graphs this surface or its domain could possibly mistake the region of integration for a disk or a square.

click to embiggen

## Tuesday, December 13, 2016

### exam four solutions

Here are my solutions to exam four. I await your corrections.
1. I added some details to several solutions and fixed an error in the first solution to problem 5. 12/14 (noonish).
2. I fixed the equation for the surface in problem 7. 1/14 (5 pm).

### 85.09% is greater than 75%

After the final exam is graded I'll add 5 points to one of your first 3 exams. My thanks to the 194 brave calcunauts who did an evaluation.

### exam 4 approaches

Exam 4 starts at 3:30 pm on Tuesday, December 13. The exam covers sections 14.1-14.8. Calculators and computers are not allowed at the exam. We will provide you with this equation sheet.

The equation sheet does not contain the transformation equations for cylindrical/polar coordinates, but you should know them by now, along with the formulas for $dA$ and $dV$.

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 how to parametrize circles and lines. 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.

• Aaa through Iri, go to CR 302
• Jag through Rac, go to CR 306
• Rai through Zzz, go to CR 310

• We are again sharing the rooms with Calculus II students. Make sure you are not sitting next to another Calculus III student.

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, or during our office hours.

## Sunday, December 11, 2016

### closed and open surfaces

From a Wikipedia article on surfaces. Closed surfaces (left) have no boundaries. Open surfaces (right) have closed boundary curves (in red).

## Saturday, December 10, 2016

### so many theorems!

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

### weekend challenge

We know that curl $\vec{F}$ is $$\vec{\nabla} \times \vec{F} = \langle \frac{\partial R}{\partial y}-\frac{\partial Q}{\partial z}, \frac{\partial P}{\partial z}-\frac{\partial R}{\partial x}, \frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}\rangle.$$ Is it true that $$\textrm{div}(\textrm{curl} \, \vec{F}) = \vec{\nabla} \cdot (\vec{\nabla} \times \vec{F})= 0?$$ Assume that the scalar functions $P$, $Q$, and $R$ are so smooth that all their derivatives are continuous.

## Friday, December 9, 2016

### lecture 41: divergence theorem

I'll give a quick review of Stokes' theorem and then move on to our final extension 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.

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.

## Wednesday, December 7, 2016

### lecture 40: stokes' theorem

Today we'll look at Stokes' theorem (14.7). 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.

## Tuesday, December 6, 2016

### step schedule

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