University of British Columbia

Department of Mathematics

Department of Mathematics

Mondays, Wednesdays and Fridays, 9-10 at Buchanan A103.

Mondays and Wednesdays, 11-12 at Math Annex 1118.

If you need help, you should also consider the drop in tutoring.

This is an introduction to the calculus of several variables. The main topics are partial derivatives and multiple integrals - basically adding an extra dimension to first year calculus. Hence an appreciation of three dimensional geometry is essential.

Sections numbers refer to Stewart, Multivariable Calculus, 6e (for Early Transcendentals, substract 1 from the section numbers):

- Vectors, quadratic surfaces (Sections 13.1-13.6, 11.1, 11.3, 11.5)
- Partial derivatives, increments, chain rule (Sections 15.1-15.5)
- Taylor's Polynomials in 1 and multiple dimensions (Sections 12.10, 12.11)
- Directional derivative and Gradients (Section 15.6)
- Max/min, Lagrange multipliers (Sections 15.7-15.8)
- Double integrals (Sections 16.1-16.5)
- Triple integrals (Sections 16.7-16.8)

Early Transcendentals, or Multivariable Calculus by James Stewart Edition 6e.

Here's a summary of Taylor's polynomials, which should be used in conjunction with chapters 12.10, 12.11 and 15.7. Also look at the "Discovery project" the very end of 15.7 (after the exercises).

The final exam is scheduled for Saturday, April 16, at 3:30pm, in LSK 200. If you think you may have a conflict or a hardship (3 exams *within* 24 hours with Math being the middle exam) then you should contact Mar Ness (ness at math.ubc.ca) by email with your name, student number, and an explanation of the issue. You are also welcome to stop by the Math Office and speak to Mar.

The exam consists of 8 multi-part questions and will primarily cover the following sections from the text: 13.5; 15.3 - 15.8;16.2 - 16.8 (except probability in 16.5). Other sections included in the course outline but not listed here will not be examined explicitly, though they are needed for background. Invigilators will not be allowed to answer questions from students during the exam.

There will be 3 midterms, on Wednesdays, at regular class time and location. The dates for the midterms are January 26, February 23 and March 16. No make up midterms will be given. No books, notes, calculators, formula sheets, other human beings, etc. are allowed.

The first midterm will cover chapters 11.5, 13 and 15.1.

The second midterm will cover 15.1-4 (except for partial differential equations and the differential), 15.7 and Taylor's Polynomials (12.10 and 12.11, not including Taylor's series, only Polynomials, and my notes above).

The third midterm will cover 15.5, 15.6, 15.8, 16.1, 16.2 as well as Partial Differential Equations (in 15.3) and Absolute Max/Min problems under general domains (cover in 15.7 + Lagrange Multipliers).

Here are the midterms solutions, courtesy of Alyanna Uy: Midterm 1 Midterm 2 Midterm 3. These are not the only possible solutions, of course.There will be 4 mandatory homework assignments. The hand in dates are January 19, February 11, March 9 and March 30. The assignments will be posted on this webpage a week before the deadline.

Mandatory homework assignment no. 1 (due Jan 19) and its solution.

Mandatory homework assignment no. 2 (due Feb 11) and its solution.

Mandatory homework assignment no. 3 (due Mar 9) and its solution.

Mandatory homework assignment no. 4 (due Mar 30) and its solution.

Suggested exercises:

- section 13.1: 3,5,11,15,21,27,31.
- section 13.2: 5,9,17,23,31,35.
- section 13.3: 1,2,3,5,7,11,15,18,21,24,25,35,38,51,52,57,58.
- section 13.4: 3,5,7,13,17,19.
- section 13.5: 1,2,4,6,9,11,13,23,24,27,28,33,34,36,49,50,60,63,65,69,71.
- section 11.5: 3,7,9,15,17.
- section 13.6: 1,2,4,7,9,11,15,19,21-28,29,36.
- section 15.1: 1,3,8,9,11,13,17,27,28,30,31,32,34,35-38,41,43,46,55-60,61-64.
- section 15.2: 1,25,26,29-38.
- section 15.3: 1,5,7,9,15,17,19,21,25,33,35,41,57,63.
- section 15.4: 1,3,5,11,13,15,19,21.
- section 12.11: 3-10,13-22,25,26.
- section 15.7: 1,3,4,5,7,9,11,13,15,17,19,21,23,31,33,39,41,43,49,47,51,53.
- section 15.5: 1,3,5,7,9,11,13,15,21,23,25, 27,29,31,33,45,47,49,51,58.
- section 15.3: 71-77,81,83,85,87.
- section 15.6: 1,3,5,7,9,11,15,19,21,25,27,29,31,39,43,47,49,51,53,55,57.
- section 15.8: 1,3,5,7,9,11,13,18,19,25,29,33.
- section 16.1: 1,3,11,13.
- section 16.2: 3,5,7,9,11,13,15,17,23,25,27,31,35.
- section 16.3: 1,3,5,7,9,11,13,19,25,31,33,39,41,43,45,47,51,59.
- section 16.4: 9,11,13,17,19,21,23,25,29,31,35.
- section 16.6: 1,3,5,7,9,11,15,21,27,33.
- section 16.7: 5,7,9,11,15,17,19,21,23,27.
- section 16.8: 1,3,5,7,9,11,13,15,17,19,21,25,27,29,31,35.
- section 16.5: 3,5,7,9,11,13,15.

- Brian Seymour's Math 200 Resources include a lot of useful explanations, exercises with solutions, etc.
- Past exams.
- The graphing application I used in class is K3DSurf. I am not very familiar with it, I do not endorse it in any way and I do not take any responsibility whatsoever for what happens to your computer or your brain if you choose to use it. Having said that, it seems useful in visualizing 3D surfaces, it's free and nothing particularly bad happened to my computer or my brain in the few days I've used it.
- I also use Mathematica. It's a great software if you're interested in math. Many of it's features are also available for free at WolframAlpha.