Monday, February 8, 2016

lines in space, section 11.5

We'll review the properties of the cross product, and compute cross products that give the area of a parallelogram and a triangle. You'll look at additional examples in discussion this week.

It won't be long before we are integrating along lines and curves in $\mathbb{R}^3$. So, we'll return to the business of defining a line in space using a point and a vector. Examples will be worked.

low res video from section 01

Friday, February 5, 2016

cross product, section 11.4

We'll wrap up any remaining dot product examples and then define the cross product (11.4). We use cross products to compute areas and volumes in $\mathbb{R}^3$ and to construct new vectors that are perpendicular to two given vectors.

low res, better aim, section 01

Thursday, February 4, 2016

good to know?

All discussion sections meet in room 120 of the Enzi STEM Building. If you can't attend your scheduled section you are welcome to go to another; just be sure to mark your regular section on the worksheet.

  • Section 20, 9:35-10:50, Bryan Curtis, 33 calcunauts
  • Section 21, 11-12:15, Bryan Curtis, 33 calcunauts
  • Section 22, 1:20-2:35, Bang Huang, 31 calcunauts
  • Section 23, 9:35-10:50, Bang Huang, 16 calcunauts
  • Section 24, 11-12:15, Bryan Curtis, 32 calcunauts
  • Section 25, 1:20-2:35, Bang Huang, 16 calcunauts

Wednesday, February 3, 2016

dot and cross products, sections 11.3 and 11.4

We'll use the dot product (11.3) to compute the angle between two vectors and to project one vector onto another. If there is time we'll define the cross product (11.4).

low res, bad aim, section 01

Monday, February 1, 2016

nothing to see here, move along

We'll take a quick look at vectors in $\mathbb{R}^3$ (11.2) and find nothing new but the basis vector $\hat{k}$ which points in the positive z-direction. After a few examples, we'll move on to the dot product in section 11.3. Dot products are used to compute work (or change in kinetic energy), angles between vectors, and to project one vector onto another.

low res video from section 01

Saturday, January 30, 2016

exam four error

Nicole Pekarek pointed out an error on both the syllabus and course schedule. Exam four is still scheduled for Wednesday, May 11, but the correct time is 1:15 to 3:15 pm. The updated syllabus and schedule show the correct time. Thanks Nicole.

Friday, January 29, 2016

vector arithmetic, sections 11.1 and 11.2

We'll talk about how to add and, also, scale vectors geometrically. Then we'll discuss how to do vector arithmetic using basis vectors.

low res video from lecture 01

office hours set

Come visit our luxurious offices! And don't forget to check my calendar for nerdfests. 

Thursday, January 28, 2016

exam times fixed

Levi Wolfe noticed that exam times on the WyoCourses calendar were off by as much as 12 hours. Who starts an exam at 5:15 AM? The times are correct now. Thanks Levi.

Tuesday, January 26, 2016

distance and vector arithmetic (11.1 & 11.2)

We'll finish our previous discussion by assembling a distance formula for $\mathbb{R}^3$ and then using the formula to create spheres.

Then we will move on to vectors and vector arithmetic. Basic quantities such as position, velocity, acceleration, and force are represented by vectors. We will add vectors and also scale vectors.

If there is time we'll talk about basis vectors and how to express a general vector in terms of the basis vectors.  

Sunday, January 24, 2016

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.

This stuff will be useful throughout the semester. 

Thursday, January 21, 2016

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, T, and F from 3:30 - 5:00 pm, or by appointment. I'll post additional hours every week as my schedule permits. These hours are marked as nerdfests on the calendar.

I'll post office hours for the discussion leaders (Bang and Curtis) as soon as possible. Keep checking the link at the top of this page.


We are using the textbook Multivariable Calculus by Briggs, Cochran, and Gillett (2nd Edition, ISBN 978-0-321-96516-5) for the first time. You will have access to the electronic version of the book through MyMathLab.

If you want to buy a paper textbook try searching for multivariable calculus at your favorite bookseller; most multivariable calculus books cover the same topics and some of the older editions are a fraction of the price of the current edition.

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. Some of these examples may appear on the exam.


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

Tuesday, December 22, 2015

course scores

 I submitted course grades on January 2 so it's past time to update this section (Jan 12). The pass rate for those who took the final exam is 86.7% (181 out of 209). The pass rate for those who took the first exam is 78.7% (181 out of 230), indicating that 21 people dropped or disappeared from the course following exam one.

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 one of your midterm exams (the course evaluation rate reached 86%).

The quartiles for your course scores are 73, 80.4, and 87.4. Slightly more than 50% of you (the 208 209 who took the final exam) have scores of 80.4 or higher, and slightly more than 25% of you have scores of 87.4 or higher. Last semester the quartile scores were 74.6, 81.4, and 89.2.

Each full size rectangle represents five brave calcunauts.

Saturday, December 19, 2015

exam 4 results

We graded 208 exams this time. The average is 69.8 and the quartiles are 62, 73, and 82. One brave calcunaut has a perfect score! The mean and quartiles are lower than they were on the earlier exams, but this is difficult material and many of you had multiple exams last week. Last semester the numbers were similar: the average was 69 and the quartiles were 60, 71, and 83.75. You will have to scroll down to see the histogram.

The median scores on the individual problems are:


Overall, people did very well. But, many made problem 4 difficult by ignoring the given surface area element and others failed to show work. The algebra in problem 5 was a problem for some people.

Take a look at these beautiful solutions to problems 7 and 8. These folks were just getting warmed up and could have gone another 15 weeks.

click to embiggen!

Friday, December 18, 2015

exam 4 solutions

(12/19) Bang found mistakes in my answers to problems 3 and 6. They are fixed, but maybe Bryan will find more?

Have a look at my solutions to exam 4. As always, please let me know if you find mistakes or parts that are unclear.

Thursday, December 17, 2015

exam 4 approaches

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.

The equation sheet does not contain the transformation equations for cylindrical coordinates, but you should know them by now.

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.

  • Section 20, Business Auditorium
  • Section 21, Business Auditorium
  • Section 22, History 57
  • Section 23, Geology 216
  • Section 24, Geology 216
  • Section 25, History 57

  • 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.

    a fluxing magnetic field at t=38s!