Fall semester 2013

- Text: James Stewart, Calculus (edition 7). Note: If you have Edition 6, it is also fine. (You will see chapter numbers listed for both editions below).

- Section 101 (Prof. Peterson)
- Section 102, Prof. Davila.
- Section 103 , Prof. Adams.
- Section 104 (Prof. Peterson)
- Section 105 (Prof. Gordon)
- Section 107 (Prof. Ollivier)

- Most homework assignments should be submitted online through Webwork . In individual sections, there may be occasional written homework. Please follow the communications by your instructor.
- The "Getting started with webwork" handout
- Please use Piazza as the main resource for help with webwork-related (non-conceptual) questions. It is a forum, which will be monitored by our TA, where you can post questions and answers about webwork. Please use the "e-mail instructor" button in webwork *only* if the question is not answered on Piazza, and you posted it and did not receive an answer. Sign-up link for our class on Piazza.

- In addition to your instructor's office hours, please take advantage of the Math Learning Centre drop-in tutoring. Do not wait till the exams -- if you feel uncomfortable with any of the material, talk to your classmates, talk to the instructor, and come ask questions at the Math Learning Centre.
- For all technical problems with webwork, Piazza registration, or exam conflicts, please e-mail math200dictator@gmail.com

- The final exam is on Monday December 16, 8:30am, in SRC (the Student
Rec. Centre).
- Sections 101 and 104 (Prof. Peterson) -- go to SRC A.
- Sections 102 and 103 (Prof. Davila and Prof. Adams) -- go to SRC B.
- Sections 105 and 10 (Prof. Gordon and Prof. Ollivier) -- go to SRC C.

- The UBC Math Club
is selling packages of old exams with solutions, the last two dates are
Thursday and Friday (Dec 11-12), 11am -- 1pm, in
the Math Annex room 1119. Please find UBC Math Club on Facebook for
up-to-date information.
### Review materials for the Final exam

The exam will primarily cover the following sections from the text: 12.2-12.5; 14.3 - 14.8 (except Lagrange multipliers with two constraints are not covered); 15.1 - 15.5 (except moment of inertia and probability in 15.5) and 15.7 - 15.9. Other sections included in the course outline but not listed here will not be examined explicitly, though they are needed for background.

Here are some handouts to help you review (please not that the "detailed list of topics" handout reflects my personal view of which topics are important; other instructors might have emphasized different topics). - The detailed overview of topics.
- By popular request, a table of integrals and useful integration techniques .
- You can access old final exams without solutions at: The Math department website . The Math Club sells solution packages, Thursday and Friday this week, 11am-1pm, in MATX 1119.
- Notes from the document
camera, from the review session by Julia Gordon,
Wednesday December 11, noon -2pm, in BIOL 2000.

### Review materials for Midterm 2

- The list of topics .
- Midterm from Math 263 in 2004. Ignore Problem 4.
- Final from 2003, with solutions . Look at problems 2,3,4.
- One more midterm (with solutions). Look at problems 1 and 2 only.
- You can see the past final exams for Math 200 at
The
Department website . Here is the list of relevant
problems from some of these exams:
- April 2005 : do problems 1,2,5.
- April 2006: do problems 1, 2,3,5.
- April 2007: do problems 2,3,4,5.
- April 2009: do problems 1, 2, 3.
- April 2010: do problems 1, 2, 3, 4.
- April 2011: do problems 2, 3, 4, 5.
- April 2012: do problems 2, 3, 4.
- December 2005: do problems 1, 2,3,4,5.
- December 2006: 1, 2, 3(a).
- December 2007: 2, 3, 6, 7.
- December 2008: 1,2, 3,4,5(a).

### Review materials for Midterm 1

- A detailed list of topics is here . Please note: by accident a wrong file was posted in this place for a few hours on September 30. If you looked at it before noon on Sep.30, please clear the cache of your browser and reload this page to get the correct file. Sorry.
- A lot of practice problems from the Math 253 web page. Please note that in problem set 8, only problems 1 and 2 are relevant for this exam in our course.
- sample test (that was given earlier than ours, in one section last year), so our exam will cover more.
- Another earlier midterm
- A quiz covering some of the material on vectors. Please note that our exam, in addition to the kind of problems you see above, will cover 12.6 (quadric surfaces) and 14.1 -14.3 (you need to be able to find the domain of a function of two or three variables; to sketch contour plots -- this is the content of 14.1, and also have all the skills from 14.3 (partial derivatives).
- Some review materials from 2011 can be found here .
- Midterm 1 for Math 263, 2005. (Only Problem 1 and Problem 3a) and 3c) are relevant).
- Midterm 1 from 2007. Only Problem 1 is relevant.
- Midterm 1 from last year (this one was too easy, though -- you can expect a slightly harder exam this year). Problem 5 and Problem 3 b), c) are not yet relevant this year.
- Review
material from Section 107 website

## (Approximate) week-by-week course outline

Chapter numbers are given for Edition 7; the numbers from Edition 6 are in parentheses, when they are different. Please note that this is only an approximate outline; it may be updated as the course progresses. Please also check the individual sections' websites for more specific information about your lectures. Some illustrations and supplemental materials may be posted below the description of a week's lectures, please keep checking.- September 4-6:
12.1: Three-dimensional coordinate systems; 12.2: Vectors; basic operations with vectors; length of a vector, equation
of a sphere in
space,
unit vector in a specified direction.

Suggested problems: 12.1: 3, 5, 7, 9, 11, 13, 15, 21, 25, 27, 33, 35, 39, 41.

12.2: 5, 7, 13, 17, 19, 21, 25, 29, 33, 35, 37, 41, 51. - Sep. 9-13:
12.3 Dot product;
Using dot product to find an
angle between lines. Application to finding forces.
12.4 Cross product. Using cross product to find a vector orthogonal to two
given ones; cross product and area.

Homework 1 (on 12.1, 12.2, beginning of 12.3) due on Sunday September 15.

Suggested problems: 12.3: 1, 3, 5, 7, 9, 11, 15, 17, 21, 23, 25, 27, 39, 41, 45, 49, 55.

12.4: 3, 5, 7, 11, 13, 17, 19. - Sep. 16-20:
12.5 Equations of lines and
planes.
Symmetric and parametric equations of a line in space.
Equations for planes in space.
Equations for a line of intersection of two planes, etc.
Finding distances in space: distance from a point to a plane, etc.

Lines in space (demo by Joseph Lo).

Homework 2 (on 12.3, 12.4) due on Sunday September 22.

Suggested problems: 12.5: 3, 5, 7, 11, 13, 23, 25, 27, 29, 33, 35, 37, 51, 61,65, 67. - Sep. 23-27:
12.6 Cylinders and quadric surfaces. Reading assignment: 10.5 (Conic Sections).

Very nice interactive demos of quadric surfaces can be found here .

14.1 "Functions of several variables". (In edition 6, this is section 15.1). 14.3 "partial derivatives". One additional topic to recall here: parametric equation of a segment connecting two points A and B.

Homework 3 (on 12.5) due on Monday September 30.

Suggested problems: 12.6: 1, 3, 5, 7, 9, 11, 15, 19, 23, 25, 27, 29, 31

Please also read 10.5 and look at the following problems: 3, 5, 7, 13, 17, 21, 23, 25, 27, 29.

14.1: 1, 3, 7, 9, 11, 13, 15, 19, 25, 27, 33, 34, 39, 43, 47, 49, 53, 55, 65.

14.3: 1, 11, 13, 15, 17, 21,27, 29, 35, 43, 45, 49, 53, 55, 61,63, 69, 75,77,79, 81, 83, 89, 93. - Sep. 30- Oct. 4
14.3, Partial derivatives, continued (see above for suggested problems).
14.4 "Tangent planes
and linear approximations". Differentials. Review if time permits.

Here is a post on tangent planes and the meaning of partial derivatives, with great interactive pictures (by Joseph Lo). (you might have to log in with CWL to see it).

One more interactive demo of the tangent plane (by Joseph Lo).

Homework 4 (on 12.6 and 14.3) due on Sunday October 6.

Suggested problems: 14.4: 1, 3, 5, 11, 13, 17, 19, 21, 25, 29, 31, 33, 35, 37, 39, 41. - Oct. 7-11.
Midterm 1 with solutions
(covering Chapter 12 and
14.1-14.3 -- October 7, 6:20-7:45pm).

14.5 "Chain rule"; start 14.6 (respectively, these are sections 15.5 and 15.6 in the 6th edition).

Homework 5 (on 14.4 and beinning of 14.5) due on Tuesday, October 15.

Suggested problems: 14.5: 1, 3, 5, 7, 11, 13, 17, 19, 21, 23, 35, 39, 41, 43, 47, 49, 53. - October 14-18.
14.6 (or 15.6) "Directional derivatives and gradients", continued.

Directional derivative and gradient -- interactive demo.

Implicit differentiation (if not covered earlier). Geometric meaning of the gradient. Tangent planes to level surfaces. Catch-up on sections 14.5-14.6.

Suggested problems: 14.6: 3, 5, 7,9, 11, 15, 19, 21, 25, 27, 29, 31, 33, 41, 45, 49, 53,55,61.

Homework 6 on 14.5 and the beginning of 14.6 due Monday October 21. - October 21-25.
Section 14.7 (or 15.7) Critical points: the second derivative test, absolute maximum and minimum values.

Homework 7 on the rest of 14.5 -14.6 due Monday October 28.

Suggested problems: 14.7: 1, 3, 5, 7,9, 11, 13, 15, 29, 31, 35, 39, 41, 45, 49, 51, 53,55. - October 28 -- November 1
14.8 Lagrange multipliers (two constraints not included).

Homework 8 on 14.7 due November 3.
Suggested problems:
14.8: 1, 3, 5, 7, 9, 11, 15, 17, 21, 27, 31, 35, 43.
- Nov 4-8:

Monday, Nov. 4: Midterm II covering Sections 14.4-14.7. Midterm with solutions.

15.1, 15.2. Integral of a function of two variables over a rectangle: the definition. Iterated integrals (over a rectangle). Fubini theorem (without proof). Start 15.3: double integrals over general regions.

A summary of integration techniques from Math 101.

Suggested problems: 15.1: 1, 3, 11, 13;

15.2: 3, 5, 7, 9, 11, 13, 15, 17, 23, 25, 27, 31.

Homework 9 on 14.8 and 15.1-15.2 due Tuesday November 12. - Nov. 11-15:
15.3 Double integrals over general regions. Changing the order of
integration.
15.4 Double integrals in polar coordinates.

Additional mandatory reading: 10.3 ("Polar coordinates"; in the old edition it is 11.3) in addition to 15.4. Start 15.5 (Applications) if possible.

Polar coordinates demo

Suggested problems: 15.3: 1, 3, 5, 7, 9, 15, 17, 23, 29, 35, 37, 43, 45, 47, 49, 51, 59, 62, 65.

15.4: 9, 11, 17, 19, 21, 23, 25, 29, 31, 37, 39.

Homework 10 on 15.3-15.4 due November 18. - Nov. 19-23:
15.5 Applications of double integrals: mass and density, centre of mass,
moment of inertia if time permits. Probability not included.

15.7 Triple integrals. Six different ways of writing a triple integral as an iterated integral. Applications. (This is section 16.6 in the old edition).

A triple integral demo (a must-read!)

Suggested problems: 15.5: 3, 5, 9, 11, 13, 15.

15.7: 1, 3, 5, 7, 9, 11, 15, 21, 27, 33, 41.

Homework 11 on 15.5 and beginning of 15.7 due on November 25. - Nov. 26-30:
15.8 Triple integrals in cyindrical coordinates (this is 16.7 in the old edition!).
Triple integrals in spherical
coordinates (section 15.9 in the new edition; 16.8 in the old edition!); review.

Suggested problems: 15.8: 9, 11, 15, 17, 19, 21, 25, 27, 29.

15.9: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 25, 29, 31, 35, 46.

Homework 12 is due after the end of classes, depending on the date of the final exam.

- September 4-6:
12.1: Three-dimensional coordinate systems; 12.2: Vectors; basic operations with vectors; length of a vector, equation
of a sphere in
space,
unit vector in a specified direction.