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MATH 2310 3.00AF (Fall 2010)
Calculus of Several Variables
This course is designed to follow MATH 1300/1310, as the third semester
in the standard university-level calculus sequence. It studies the calculus
of functions in two and three dimensions, just as those earlier courses
examined one-dimensional functions. For a function y=f(x), either x or y
(or both) can be a vector. For example, if x is 1-dimensional
but y is 2-dimensional, this means that f parametrizes a curve in the
plane. While if x is 2-dimensional and y is 1-dimensional, the graph of
f is a surface in space.
In addition to curves and surfaces, topics include vector functions, partial
derivatives, gradients, polar coordinates, arc length, Lagrange multipliers,
optimization, as well as multiple integrals and their changes of variables.
If time permits, we will treat line integrals.
This is a required course for most honours and bachelor programs offered by
the Department of Mathematics and Statistics. After this course, the study
of calculus continues in MATH 3010.
Integral calculus, normally MATH 1310 3.00; Students may also enter
with MATH 1010 3.00 or MATH 1014 3.00; Students should have at least
a high-school level knowledge of vectors in two and three dimensions.
Course Credit Exclusions are:
MATH 2010 3.00 or MATH 2015 3.00
Department of Mathematics and Statistics
- Departmental office: N520 Ross Building, (416) 736-5250,
FAX: (416) 736-5757
- Undergraduate Program office: N502/503 Ross Building, (416) 736-5902
- Math/Stat lab: S525 Ross Building
MWF 12:30-1:20pm in CB 121
Wed. 2-3, Fri. 11-12
I will try to post a notice on the course webpage if other commitments make
it necessary to reschedule one or more office hour.
If you need to see me outside these hours, you are welcome to e-mail or call
me to try to arrange an appointment.
The Math department drop-in centre is located in S525 Ross.
Variously called the Math Lab or the MathStat Lab, it is staffed with TAs
who can help you with questions from the course. The hours are subject
to change, but the plan is that it will start operation by at least the
second week of classes, and will be open throughout the semester from
Monday to Friday
from 10:30 am to 3:30 pm.
It will be closed during reading week. Hours during the exam period will vary.
The text is basically the same as chapters 10-17 of the 6th edition of Stewart's
Calculus: Early Transcendentals, so if you already own that, you
may stick with it. We will be using the on-line homework facility WebAssign
tied to the textbook. The York bookstore will sell a bundle that includes
the text, solution manual, and WebAssign access. For those who already
own Stewart from
a previous course, it will be possible to purchase WebAssign access
separately, at a lower price.
Multivariable Calculus: Early Transcendentals by Stewart, 6th edition.
- Student solution manual to Stewarts's Multivariable Calculus
We will cover all of chapters 12-15. Background material from chapter 10 will be included when required. If time permits, we will cover the first 3 sections of chapter 16.
Note that the dates given for midterms and quizzes are tentative
- 20% First midterm exam (Wednesday October 27)
- 20% Second midterm exam (Friday November 26)
- 12% Quizzes (3 in total, held Wed. Oct. 6, Wed. Nov. 10, and
Wed. Dec. 8)
- 13% Assignments (via WebAssign)
- 35% Final exam (3 hours, to be held during the exam period)
- Assignments are computer-graded. Quizzes will be graded by
TAs. Exams will be graded by TAs and by the instructor, with the
TAs doing more of the midterm grading, and the instructor more
of the final grading.
- You are expected to do a minimum of 3-4 hours of homework per week.
You don't learn how to do math by reading about it, or by watching
someone else do it - you learn by struggling with problems
yourself. The lectures will prepare you to do that, but the real
learning in the course takes place while working problems (and more
problems). The assigned homework is the minimum that will get you
through the course. If you find it easy, you can get away with doing
that minimum. But whenever you run up against something on the assigned
homework, that you don't understand at first,
you should follow it up by doing additional
problems from the text, on the same topic.
- To get the most out of a lecture, you should
read ahead and try some related problems beforehand. Don't fall behind,
as each week builds on the previous one.
- All assignment, quizz, and exam marks should be interpreted
as raw scores and not 'percentages'. Cutoffs will be announced for
converting midterm scores into letter grades.
- There will be no makeup midterms or quizzes.
If you miss one due to illness (with an
acceptable note from your doctor), or some other valid reason then
your final exam will simply be counted for more. This will be done
by calculating an equivalent score for the missing work, based
on your ranking on the final. If a makeup final examination is
necessary, there will normally be a single sitting of that exam
in January 2011.
- Students are responsible for reviewing the
Student Information Sheet maintained by the university, which
outlines policies on academic honesty, access and disability,
religious observance accommodation, and student conduct.