Wednesday, January 28, 2015

no office hours

I won't have office hours on Wednesday, January 28. My next office hours are 10-noon, Thursday.

Tuesday, January 27, 2015

lecture 2, vectors

I'll give a quick overview of Monday's talk and then assemble the distance formula for $\mathbb{R}^3$ and investigate the equation for a sphere. Then we will move on to vectors and vector arithmetic (12.2). Basic quantities such as position, velocity, acceleration, and force are represented by vectors. We will add vectors and scale vectors.

Sunday, January 25, 2015

lecture 1, points, curves, and surfaces

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

Also, we'll talk about how to measure distances between points in the various spaces. All of this material is in section 12.1 of the text and much of this material will appear on all four exams.

Monday, January 19, 2015

syllabus and course schedule

The syllabus for spring 2015 is mainly useful because it contains my contact info. My blog posts for August (scroll down) provide more details about topics covered in the syllabus. Some elements of the spring 2015 course schedule may change, but the exam schedule is set in stone. Notice that the schedule contains reading and homework assignments.

need help?

The difficulty level of this course is somewhere between hard and trivial. Anyone who understands single variable calculus can learn multivariable calculus, but it may take considerable effort. Asking for help is not a sign of weakness.

One of the smartest things you can do is collaborate with other students on the homework. You will learn more if you collaborate, and it will take less time compared to working alone. But, and this is important, always write up detailed solutions to the homework problems on your own. Writing up your own solutions is the single best way to test your understanding of the material and to embed the material in your brain.

Ask questions if you don’t understand something, especially during lecture and discussion. Your classmates will be grateful; they have the same question. And, please, come ask questions during our office hours (or make an appointment with me, Andrew or Curtis).

You can also get help at the Mathematics Assistance Center, with the engineering honor society Tau Beta Pi, and at the new STEP Tutoring Center at Coe Library.

discussion sections

Discussion sections will begin on Tuesday, September 9 February 3 (thanks Stephen!). Attendance is mandatory because quizzes will be given. Quizzes will normally cover material from previous homework assignments.
9:35 to 10:50 am, CR 103 (Curtis)
11:00 - 12:15 pm, CR 105 (Curtis)
1:20 - 2:35 pm, CR 142 (Andrew)

9:35- 10:50 am, CR 118 (Curtis)
11:00 - 12:15 pm, CR 103 (Andrew)
1:20 - 2:35 pm, AG 1030 (Andrew)

how to learn, how not to learn

A bunch of books appeared last year that are directed at those of us who forget what we've read as soon as we turn the page. All these books have similar prescriptions and are backed, to some extent, by observations of actual humans. This particular list of ten things to do and ten things not to do is by an engineering professor who was once a mathphobe. If you are curious, she teaches a MOOC on how to learn things.

It's easy to fool yourself into thinking you understand the course material. Test yourself by working random homework problems. Don't just look at current problems, look at problems from past chapters also. Can you work these problems correctly without referring to notes or books? It takes time to understand the material at this level; you won't get there by doing homework problems at the last minute or by cramming before an exam.


We assume you are able to differentiate and integrate functions of one variable, and solve algebra and trigonometry problems, even if you were shipwrecked on a deserted island, without access to computers, calculators or books.

classroom behavior

The document Students and Teachers - Working Together, produced by the UW College of Arts and Sciences, has information on our mutual responsibilities.

academic honesty

The University of Wyoming is built upon a strong foundation of integrity, respect and trust. All members of the university community have a responsibility to be honest and the right to expect honesty from others. Any form of academic dishonesty (see UW Regulation 6-802) is unacceptable to our community and will not be tolerated.

Please, don't copy from others or allow others to copy from you. Academic dishonesty hearings are time consuming and can get you kicked out of school.


You will be able to check your total score and course grade in WebAssign as soon as the first due date passes. Your total score is a weighted average of homework, quiz and exam scores:

total score = 0.15 * homework average + 0.05 * quiz average + 0.80 * exam average

We are sticking with the old grading system (no $+$, no $-$). Your course grade is determined by your total score: $[89.5,\infty)$ is an A, $[79.5,89.5)$ is a B, $[69.5,79.5)$ is a C, $[59.5,69.5)$ is a D, and $(-\infty,59.5)$ is an F. You need a course grade of C or higher to use this course as a prerequisite for higher level math courses.


We'll have four exams. Make sure your schedule is clear for the following dates and times.
  1. Thursday, February 19 from 5:15 to 7 pm
  2. Thursday, March 12 from 5:15 to 7 pm
  3. Thursday, April 16 from 5:15 to 7 pm
  4. Wednesday, May 12, 3:30 – 5:30 pm
Each exam makes up 20% of your final grade. Notes and calculators are not allowed at the exams, but you will be provided with a list of equations. Look at the mock exams to see the types of questions, range of topics, and equation sheet. Exam problems are based on examples from the lecture and text, and from WebAssign and discussion problems.

To pass exam 4 you'll need to master most of the material covered on the first three exams. Please be careful; this course doesn't end until 5:30 pm on May 12.

office hours

My official office hours are M, W, and F from 3:30 - 5:00 pm, or by appointment. I'll post additional hours every week as my schedule permits. These hours appear as nerdfests on my calendar.

I'll post office hours for the discussion leaders (Curtis Nelson and Andrew Herring) as soon as possible. Check the link at the top of this page.

Use our office hours; make yourself known. It might make a difference if you are near a grade boundary at the semester's end. 


We use the textbook Calculus, Early Transcendentals by James Stewart, 7th Edition, ISBN 978-0-495-96224-3. You will have access to the electronic version of the book through WebAssign.

Should you buy a physical copy of the textbook? That is up to you and your credit card balance. Earlier editions of the book can be bought for a fraction of the price of the current edition. To me, the differences between editions are minor.

I won't have time in lecture to cover everything in the book; you will have to read the book (or ebook) and attend your discussion section to pick up the missing topics. We often use examples from the text as exam problems.


Twenty-three homework assignments await you. The first is due Saturday, January 31 at 11:59 pm. To connect to WebAssign follow these steps. If you are in lecture section 1 (10-10:50 am) your class key is uwyo 1898 3538. If you are in section 2 (noon-12:50 pm) your class key is uwyo 6616 1891. The period is not part of the key.

If you are setting up a new WebAssign account there is a grace period (13 days) before you have to fork over money.

a shiny new semester

I hope you enjoy math 2210; it is a fascinating and useful combination of geometry and calculus that never fails to excite me.

The semester is fourteen weeks long. The first ten weeks are mostly preparation for the final four weeks. In the last weeks of the semester you will integrate vector and scalar functions over curvy domains (curves and surfaces) that live in two or three dimensional space. You will also use four generalizations of the fundamental theorem of calculus to compute integrals of vector functions.

Wednesday, December 24, 2014

course grades

I set the grade boundaries today, so the grade you see in WebAssign will be your course grade. The pass rate is 80% for the 157 calcunauts who took the final exam.

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 85.12%!).

The quartiles for the total score are 70.5, 78.8, and 88.6. Slightly more than 50% of you (the 157 who took the final exam) have scores of 78.8, and slightly more than 25% of you have scores of 88.6 or higher. In this histogram each full sized rectangle represents 3 brave calcunauts.

Saturday, December 20, 2014

exam 4 results

We graded 157 exams in the last 3 days! The average is 66.3 and the quartiles are 53, 72, and 84. Slightly more than 50% of you have scores of 72 or higher. And, slightly more than 25% of you have scores of 84 or higher. No one has a perfect score but five people are very close.

The median scores for the individual problems are:


The T/F questions remain challenging and too many people did not realize you compute surface area by adding up little bits of $dS$ across the surface. Also, too many people were unable to see that the surface in problem 7 projects to a disk of radius $\sqrt{2}$ in the $xy$-plane.

Each full size rectangle in the top histogram represents 5 brave calcunauts.

Thursday, December 18, 2014

exam 4 solutions

Please let me know if you find errors or unclear bits in my solutions to exam 4. Remember, there is more than one way to solve problem.

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.