MATH 200: Multivariable calculus, Section 107

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, starting the second week of September).
Instructor: Julia Gordon.
Where and when: Tuesday and Thursday, 3:30-5pm, at Buchanan A, room 104.

Instructor's office: Math 217.
e-mail: gor at math dot ubc dot ca
Office Hours: Wednesday 10 -- 11am; Thursday 11:30am -- 1:30pm.
Myrto's office hours: Monday and Wednesday, 11:15am -- 12:15pm, at Auditorium Annex 136. (Myrto is our TA).

Exams and Marking

Course mark will be based on the Webwork (10%), class participation (5%), two midterms (17.5% each) and the final exam (50%).

1st midterm: Thursday, October 11, in class

2nd midterm: Thursday, November 1, in class

The two midterms will not overlap in the material covered. The final exam will cover the entire course. The final exam will be common between all sections, and marked jointly. For additional information please see the section-specific information .

Policies:

Missing a midterm results in a score of 0, except with prior consent of the instructor or with a doctor's note. In these latter cases, a make-up midterm can be arranged, or you will receive no score from the missed exam, and your final exam will count for 67.5% of the grade.

Each Webwork assignment closes at 11:59pm on Wednesday or Monday night (please look at the dates carefully). No extensions are possible.

If for any reason you have to miss the final exam, it is the university-wide policy that you need to apply for "standing deferred" status through your faculty. Missed finals are not handled by me or the Mathematics Department.

Homework

All homework assignments should be submitted online through Webwork .
The "Getting started with webwork" handout

list of functions

You should also work on the suggested problems, posted at the main course page.
There will be pre-reading assignments, posted below in the "course outline" section as the course progresses.

here

Announcements:

The LAST office hours for concrete last-minute questions: Monday December 10, 10am -- noon.

Office hours last week: Monday December 3, 12-2pm; Friday December 7, 3-5pm. Both in my office, Math 217.

Review sessions:

Friday November 30, 5-7pm, in LSK 200. This session will be devoted to integration.
Friday December 7, 6-8pm, in GEOG 100. Notes from the document camera used in this session. (see below, under "Review materials" for comments related to these notes).

Please fill out the informal survey that will help us improve the course. Everyone's participation is really important for the future generations of students :-). Thank you.

Homework 10 due on Friday December 7 at 5:45pm (just before the review session) is now open.

Announcement from the Math Club: The UBC Math Club is now selling its exam packs to students. This is a great way to help prepare for the final exam. We have exam packs for math 100, 102, 104, 180, 184, 200, 215/255, 220, 221, 257/316, 300, 302, 307, and 317. The exam packs are available in the Math Annex room 1119 for $10 each during lunch and in the afternoon.

Please work on suggested problems on the main course website . For Edition 6, a list of suggested problems is here (please scroll down to it).

Not so new anymore: Math 200 Blog has a lot of useful tips and pictures! Please click here (you need to log in with your CWL).

Review materials for the Final exam

Official information from the main webpage: The exam consists of 10 multi-part questions and will primarily cover the following sections from the text: 12.5; 14.3 - 14.8; 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.

Please note: suggested problems on the main course website are a very good source for estimating the level of difficulty of the exam. I highly recommend them.

Review session on Friday December 7 was done by means of a document camera. Here are the resulting (unedited) notes. The session was mostly just me solving problems from old finals, especially from December 2011 final. For explicit questions, please see the final exams on the department website. I tried to label the problems clearly on the notes. One of them (that starts with a picture of a snowman) is not labelled -- it is part (a) of the problem 8 on December 2011 exam. We did not so much discusses the solution to this specific problem, but rather focused on how to set up a general integral over the intersection of these two spheres in spherical or cylindrical coordinates (cylindrical look much nicer here). If you are reading these notes and trying the problem, please note that in part (b), they have done some translations of parts of the snowman, which do not change the volume, but make the integrals simpler.

The items below are just my personal view of what is important:

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, generally, after lunch in Math Annex 1119. I was just told that their detailed hours are on Facebook, so find "UBC math club" on Facebook, and enjoy!

Remember that there will be the last review session, Friday December 7, 6-8pm, in GEOG 100. The last office hours for this term are on Friday 3-5pm, in my office math 217. Please remembr: the last webwork is due just before the review session on Friday. It is very helpful for preparation, too. The two sets of extra problems on webwork are probably a lot harder than the final exam problems. So do them last, only after you've done all else.

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 3,4,5.

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 2,3,4,5.
April 2007: do problems 2,3,4,5,6.
April 2009: do problems 2, 3, 4.
April 2010: do problems 1, 2, 3, 4.
April 2011: do problems 3, 4, 5.
April 2012: do problems 3, 4, 5.
December 2005: do problems 2,3,4,5,6.
December 2006: 1, 2, 3.
December 2007: 2, 3, 6.
December 2008: 3,4,5.

Review materials for Midterm 1

A detailed list of topics the midterm will cover is here .

sample test from Section 103.

Midterm from section 104

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 14.1, 14.3 and 14.4 (functions of two variables up to tangent planes and linear approximations).

Some review materials from 2011 can be found here .

Midterm 1 for Math 263, 2005. Ignore Problem 2 and Problem 3b).

Midterm 1 from 2007. Ignore Problem 2.

(Approximate) day-by-day 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 will be updated as the course progresses, and supplementary material, pre-reading assignments and other notes will be posted here as well.

Thursday, Sep. 6: 12.1: Three-dimensional coordinate systems.

Sep. 11: 12.2: Vectors; basic operations with vectors; length of a vector, equation of a sphere in space, unit vector in a specified direction.
Sep. 13: 12.3 Dot product; defined cross product. Using dot product to find an angle between lines. Application to finding forces.

Sep. 18: 12.4 ("Cross Product") continued; start 12.5 ("Equations of lines and planes"). Using cross product to find a vector orthogonal to two given ones; cross product and area. We also talked about a way to write an equation for a line in a plane, using its normal vector. This helps understand equations of planes in space.
[Homework 1 covering 12.1 -- 12.4 due on Sep. 19]
Pre-reading assignment due Thursday Sep. 20: 12.5.
Thursday Sep. 20: 12.5 "Equations of lines and planes"). We talked about equations of planes in space; and then parametric and vector equations for lines. Then there was a group activity on finding distances in space.

Tuesday Sep. 25: 12.5 "Equations of lines and planes". The lecture started with a discussion of the activity from the end of last class. If you missed the class, please look at it and think about all the problems, especially Problem 3 (Problems 1 and 2 provide hints for Problem 3). Then reviewed the whole Section 12.5; in particular, talked about symmetric form of the equations of a line. Please see the blog entry about symmetric equations of lines (you'll need to log in). Just started Section 12.6 "Cylinders and quadric surfaces".
Webwork 2 covering 12.5 due Wednesday October 26, 11:59pm.
Pre-reading assignment due Thursday Sep. 27 10.5 (Conic Sections).
Thursday Sep. 27: 12.6 ("Cylinders and quadric surfaces"), started 14.1 "Functions of several variables". (In edition 6, this is section 15.1)

Tuesday October 2: 14.3 (15.3 in Edition 6) "Partial derivatives".
Written homework due in class on Thursday October 4. Webwork 3 due on October 8.
Thursday October 4: 14.3 (15.3 in Edition 6) "Partial derivatives" -- continued. Please make sure you read the textbook from "Interpretations of partial derivatives" to the end of 14.3. In lecture, we started 14.4 ("Tangent planes and liner approximations"), and discussed the material you can see here .

Tuesday October 9. Finished 14.4 "tangent planes and linear approximations", started 14.5 "Chain rule" (respectively, sections 15.4 and 15.5 in the 6th edition). For Chain rule, we only did the case when two functions of one variable, x(t), y(t) are plugged into a function f(x,y) of two variables.
Thursday October 11. Midterm 1. The Solutions

Tuesday October 16. Section 14.6 (or 15.6) "Directional derivatives and gradients". Covered most of it, except for the geometric meaning of the gradient in three dimensions, and tangent planes to level surfaces.
Thursday October 18. Joseph Lo finished 14.6, and went back to 14.5 to finish that section -- the about all other cases of the chain rule. There was an activity on gradients and level curves, etc. It will be graded. The Solutions to the activity.
Here is the very useful blog post about the meaning of directional derivatives as slopes.

Tuesday October 23. Talked about implicit differentiation (the end of Section 14.5); and a bit more about gradients and directional derivatives.
Here is the blog post on gradients and directional derivatives.
Started Section 14.7 (critical points.). In order to find critical points, you often need to solve systems of nonlinear equations.
Here is the blog post with very helpful methods of doing it, and examples.
Webwork 5 due on Wednesday October 24.
Thursday, October 25: Section 14.7, continued: the second derivative test; absolute max and min values.

Tue, October 30: 14.8 (Lagrange multipliers). There was an in-class group activity on 14.7-14.8.
Solutions to the activity (on the blog).
Review session for Midterm 2: Tuesday October 30, 6-7:30pm, in GEOG 200.
Webwork 6 was due on Monday November 5.
Thursday, November 1: Midterm 2. Solutions.
Tuesday, Nov 6: Finished some remaining questions from 14.7 and 14.8: in particular, Lagrange multipliers with two constarints, and a discussion of when an absolute max or min still has to exist even if the domain is not closed and bounded. 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).
A summary of integration techniques from Math 101.
Thursday, Nov. 8: 15.3 Double integrals over general regions. Changing the order of integration.

Tuesday, Nov. 13: 15.4 Double integrals in polar coordinates.
Additional reading: 10.3 ("Polar coordinates"; in the old edition it is 11.3) in addition to 15.4.
The blog post on polar coordinates (we discussed this in lecture).
[Homework 7 due on November 14]
Thursday, Nov. 15: 15.5 Applications of double integrals: moments, centre of mass, moment of inertia. A few words about probability.

Tuesday, Nov. 20: 15.7 Triple integrals. Six different ways of writing a triple integral as an iterated integral. Applications.
Homework 8 due on Wednesday November 21
The last three classes: Triple integrals in spherical and cylindrical coordinates (sections 15.8, 15.9 in the new edition); this is sections 16.7, 16.8 in the old edition!)
The last webwork is due on Friday December 7, at 5:59pm