Sunday, August 30, 2015

points, curves and surfaces, section 12.1

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 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.

In the last four weeks of the semester we'll integrate over various curves and surfaces in $\mathbb{R}^3$; you'll see this material over and over.

Friday, August 28, 2015

syllabus and course schedule

The syllabus for fall 2015 is mainly useful because it contains my contact info. My blog posts (scroll down) cover most of the syllabus topics.

Some elements of the fall 2015 course schedule may change, but the exam schedule is set in stone. Notice that the schedule contains reading and homework assignments.

need help?

One of the smartest things you can do is collaborate with other students on the homework. You will learn more 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, Bang or Bryan). It always seems backward, but the people who come to office hours usually end up with an A or B in the course.

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 8. Attendance is mandatory because quizzes and written assignments will be given. Quizzes will normally cover material from previous homework assignments.
9:35 to 10:50 am, CR 219 (Bang)
11:00 - 12:15 pm, AG 2018 (Bang)
1:20 - 2:35 pm, CR 142 (Bang)

9:35- 10:50 am, CR 142 (Bryan)
11:00 - 12:15 pm, CR 219 (Bryan)
1:20 - 2:35 pm, CR 215 (Bryan)

how to learn

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.

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.


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, discussion and exam scores:

total score = 0.15 * homework average + 0.05 * discussion 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, September 24 from 5:15 to 7 pm
  2. Thursday, October 22 from 5:15 to 7 pm
  3. Thursday, November 19 from 5:15 to 7 pm
  4. Wednesday, December 17, 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 December 17.

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 (Bang Huang and Bryan Curtis) as soon as possible. Keep checking 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. 

Friday, August 21, 2015


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.

If you decide to buy a physical copy of the textbook, consider buying an earlier edition. They are usually 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; 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.

In 2016 we will switch to a new book, Calculus, Early Transcendentals by Briggs, Cochran, and Gillett (2nd Edition, ISBN 978-0-321-96516-5), and a new homework system.


Twenty-three homework assignments await you. The first is due Wednesday, September 9 at 11:59 pm. If you are setting up a new WebAssign account there is a grace period (13 days) before you have to fork over money.

To connect to WebAssign follow these steps. If you are in lecture section 2 (10-10:50 am) your class key is uwyo 5914 9105. If you are in section 3 (noon-12:50 pm) your class key is uwyo 5030 5989. The period is not part of the key.

Monday, August 17, 2015

the semester begins

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

Thursday, May 21, 2015

course grades

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:


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. 

    conservative vector functions