MATH 200: Multivariable calculus, the common website.
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).
Individual section websites:
Exams and Marking
Course mark will be based on the Homework (
Webwork +
occasional written homework in some sections) (10%),
two midterms (20% each) and the final exam (50%).
The two midterms will not overlap in the material covered.
The final exam will cover the entire course.
The midterms and the final exam will be common between all sections, and marked jointly.
No calculators, electronic communication devices, books, notes or aids of any kind will be allowed for exams. Students are required to bring ID to
all exams.
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, you will be allowed to take a make-up midterm; dates and times of make-up midterms will be announced later.
If you anticipate having a valid conflict with the announced midterm
times, please send an e-mail to math200dictator@gmail.com.
If you fail to notify the Instructor-in-charge of a conflict via this e-mail before October 4 and November 1, respectively, you may not be allowed to take the make-up exam, and your score will be 0.
Each Webwork assignment generally closes at 11:59pm on Monday
(occasionally, Sunday or Tuesday) night
(please look at the dates carefully in case there are some deviations).
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 the instructors or the
Mathematics Department.
Homework
- 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.
Getting help
- 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
Resources
Integractive graphic demos by Joseph Lo.
These are very helpful illustrations to some of the concepts we study in this course. The individual graphics from this site
will be linked from the relevant weeks in the week-by-week course description below.
You can use Wolfram Alpha -- it is a wonderful tool for plotting graphs of functions of two variables, for example. If you want to visualize, for example, the surface x^2+xy-y^2+3z=0, just type in "plot (x^2+xy-y^2+3z=0)".
A note about Webwork and Wolfram Alpha: there will be many problems in Webwork which require thinking and which Wolfram Alpha cannot do; for the more mechanical ones that it can do, if you just use the software and copy the answers, it detracts from your learning. You might get a few extra points for the webwork problem, but you'll certainly lose much more on the exam for not having that skill. So use this great software to your advantage (to help you visualize the objects we study, and to learn), not to your disadvantage (to cheat on Webwork).
"Math200 Playground", a UBC blog created in the Fall 2012 by Joseph Lo (you need to log in with your CWL).
Math
Learning Centre drop-in tutoring.
Announcements:
- 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.
There will be signs in place directiong you where to go in SRC.
Please arrive a little early to give yourself time to find the correct
place.
As usual, so not enter the exam area until invited.
You can keep your bags at your tables, but all the electronic devices need
to be turned off and in the bags. You are not allowed any access to your
bag durig the exam.
Having a cell-phone on your table will be considered cheating.
Please do not forget to birng ID -- IDs will be checked.
- 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.