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MATH 2310 3.00AF (Fall 2010)
Calculus of Several Variables with Applications
Course Outline


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

Course Webpage:

Instructor/Contact Information:

Tom Salisbury Department of Mathematics and Statistics


MWF 12:30-1:20pm in CB 121

Office hours:

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.

Math Lab

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.

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

Other information: