MATH 200: Multivariable calculus, the common website.
Winter Term 2 2017/18
Individual section websites:
Exams and Marking
Course mark will be based on the Homework
Webwork (10%),
five inclass quizzes (15%), one common midterm exam (25%), and the final exam (50%).
The midterm will be on Tuesday February 13th at 6:30pm. Rooms will be
sectionspecific (please see below).
The final exam will cover the entire course.
The midterm 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:
All exams are closed book, but you can bring 1 formula sheet written on both sides. Calculators will not be permitted.
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 makeup midterm; dates and times of makeup midterms will be announced later.
If you anticipate having a valid conflict with the announced midterm
time, please send an email to math200dictator@gmail.com.
If you fail to notify the Instructorincharge of a conflict via this email before February 12, you may not be allowed to take the makeup exam, and your score will be 0.
Each Webwork assignment generally closes at 11:59pm on Wednesday
(occasionally, Tuesday or Thursday) 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 universitywide 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
 Homework assignments should be submitted online through
Webwork .
(Scroll down to the course named MATH200ALL_2017W2); or you should be
able to access it through Connect.
 The "Getting started with webwork" handout
 Please use
Piazza
as the main resource for help with webworkrelated and other questions.
It is a forum, which will be monitored by our TA, where you can post questions and answers about webwork.
Please use the "email instructor" button in webwork *only* if the question is not answered on Piazza, and you posted it and did not receive an answer.
Signup link for our class on Piazza.
Getting help
 In addition to your instructor's office hours, please take advantage of the
Math Learning Centre dropin 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 email math200dictator@gmail.com
Resources
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+xyy^2+3z=0, just type in "plot (x^2+xyy^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).
See review materials for the exams below the
"Announcements" section on this website.
Math
Learning Centre dropin tutoring.
Announcements:

The Alternate MIDTERM EXAMS for those who had conflicts and informed me
(or for those who were sick) will be on:
 Wednesday February 15, 4:306pm in MATX 1118
 Thursday February 16, 4:306pm in MATH 202.
 Checklist of immediate things to do:
 log in into Webwork and make sure it works for you (first assignment due on February 12th);
 sign up for Piazza ;
 check for conflicts with the evening midterm on February 13th.
If for some reason you cannot log in to Webwork, cannot sign up for Piazza, or have an exam conflict, please email
math200dictator@gmail.com
Review materials for the Midterm
The list of topics .
Final from 2003, with solutions . Look
*only* at problems 1 and 2.
Midterm 1 for Math 263, 2005. (Ignore
Problem 2).
Midterm 1
from 2007. (Ignore
Problem 2).
Midterm 1 from 2012 (this one
was too easy, though  you can expect a slightly harder exam this year
and it will cover more).
Midterm 1 from 2013 with solutions
(ours will cover more  see below for selected problems from Midterm 2
from the same year).
Midterm 2 from 2013 with solution
(only look at problems 1(a)(b), (c) and 3).
Midterm from 2015 (with solution)
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 3,4,5.
 April
2006: do problems 1,5.
 April
2007: do problems 1, 2(a),4.
 April
2009: do problems 1, 2.
 April
2010: do problems 1, 2(ii).
 April
2011: do problems 1, 2, 3.
 April
2012: do problems 1, 2, 3.

December 2005: do problems 1, 2, 5(a).
 December
2006: only problem 1.

December
2007: problems 1, 7.

December 2008: 1,2, 3.
You can also use the other exams picking out the problems on relevant
topics in the same spirit as above. (Please do NOT get scared by things we
have not yet covered and email me about it though).
(Approximate) weekbyweek course outline
Chapter numbers are from Apex Calculus unless otherwise specified.
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.
 January 35:
10.1 (only up to "Cylinders") : Threedimensional coordinate systems;
10.2: Vectors; basic operations with vectors; length of a vector, equation of a sphere in
space, unit vector in a specified direction.
Suggested problems:
10.1: 13, 7, 9, 12, 16
10.2:
15, 8, 11, 15, 20, 23, 27, 31
 January 812:
10.3 Dot product;
Using dot product to find an
angle between lines. Application to finding forces.
10.4 Cross product. Using cross product to find a vector orthogonal to two
given ones; cross product and area.
Quiz 1 on vectors.
Homework 1 due.
Suggested problems:
10.3: 13, 11, 15, 19, 31, 39.
10.4:
15, 9, 15, 27, 30, 31, 35, 39, 41.
 January 1519:
10.5 and 10.6 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.
Homework 2 due.
Suggested problems:
10.5: 7, 11, 21, 27, 31.
10.6: 1, 2, 9, 11, 14, 15, 17, 19, 25, 29, 32;
 January 2226:
10.1: Cylinders and quadric surfaces. Reading assignment: 9.1 (Conic Sections).
12.1 Functions of several variables. Domain and range. Level curves and level surfaces.
Quiz 2 on equations of lines and planes in space.
Homework 3 due.
Suggested problems:
10.1: 15, 17, 2326, 27, 32.
12.1: 16, 7, 11, 17, 19, 21, 23, 26, 27, 29, 31
 January 29  February 2
Brief dicsussion of limits and continuity for functions of two variables.
(reference: section 12.2 (we will not cover everything in this section; refer to lecture notes).
12.3, Partial derivatives; higherorder partical derivatives.
12.4 Differentials, tangent planes, and linear approximations.
Homework 4 due.
Suggested problems:
Section 12.3: , problems 14, 5, 13, 19, 29, 33.
Section 12.4: 7, 10, (find equation of tangent plane to z=f(x, y) at given point for 11, 12) , 13, 15, (find linear approximation for 17, 18 at the given point).
 February 59.
12.5 Chain rule and implicit differentiation; start 12.6  directional derivatives.
One additional topic to recall here: parametric equation of a segment connecting two points A and B.
Homework 5 due.
Quiz 3 on partial derivatives and differentials.
Suggested problems:
Section 12.5: 15, 9, 17, 21, 29.
 February 1216.
12.6 Directional derivatives and gradients, continued.
12.7 Geometric meaning of the gradient.
Tangent planes to level surfaces.
Tangent planes to graphs of functions of two variables, revisited.
Midterm
Homework 6 due.
Suggested problems:
Section 12.6, problems 16, 13, 15, 21, 23, 25, 27
Section 12.7, problems 17, 19, 21, 23
 February 26 March 2.
Section 12.8 Critical points: the second derivative test, absolute maximum and minimum values.
Lagrange multipliers (Secondary text #1, Section 14.8).
Homework 7 due.
Suggested problems:
Section 12.8, problems 14, 5, 7, 11, 13, 15, 17 (also 11, 13, 15, 19 from 14.7 in secondary text #1)
Section 14.8 (from secondary text #1) 5, 10, 11, 12, 13, 15, 17
 March 59.
14.8 Lagrange multipliers, continued. (two constraints not included). Starting integration: 13.1 (the definitions; area; integral of a function of two variables over a rectangle.
Iterated integrals (over a rectangle).
Fubini theorem (without proof).
Quiz 4 on critical points
Homework 8 due.
Suggested problems:
see above for 14.8, see below for 13.1
 March 1216:
Section 13.1: double integrals over general regions.
Interchanging the order of integration. Section 13.2.
A summary of
integration techniques from Math 101.
Homework 9 due.
Suggested problems:
13.1: 7, 9, 19, 21 (also see #3, 5, 10, 13, 15 from section 15.1 secondary text #1)
13.2: 14, 7, 9, 13, 17, 21, 25 (also see #17, 21, 23 from section 15.1 secondary text #1)
 March 1923:
13.3 Double integrals in polar coordinates.
13.4 Center of mass.
Quiz 5 on changing the order of integration in a double integral.
Homework 10 due.
Suggested problems:
13.3: 3, 4, 8, 13;
13.4: 1, 5, 6, 13, 24
 March 2630:
13.6 Triple integrals. Six different ways of writing a triple
integral as an iterated integral. Applications.
Triple integrals in cyindrical coordinates, see
14.4 (from secondary text #2)
Homework 11 due.
Suggested problems:
13.6:
5, 7, 9, 11, 13, 15, 19, 23.
 April 46:
Triple integrals in spherical
coordinates 14.4 (from secondary text #2); review.
Suggested problems:
14.4 (from secondary text #2): 11, 13, 15, 19, 22, 23
Homework 12 is due after the end of classes, depending on the date of the final exam.