| Instructor in Charge: | Colin Macdonald |
| Email: | cbm (at) math ubc ca |
| Office: | Hah, not likely! |
| Lectures: | Some |
| Sections: | Many |
Information about the textbook, the topics, the marking scheme, and policies can be found in the
Course Outline.
A rough weekly syllabus is given below. The material below generally applies to all sections, unless other information has been provided by your instructor.
This course is using UBC's Canvas system.
I've been experimenting with live streaming my lectures, here's a
shorter one just for fun. Caution: volume is louder during
the part where I watch “Shrek” (sorry, didn't realize
it would capture the audio.)
Here's a longer example giving a little intro to contour plots (a
big part of this course so this one might be useful!)
We are the using the UBC textbook CLP-III Multivariable Calculus by Joel Feldman, Andrew Rechnitzer and Elyse Yeager. It is free and downloadable at no cost from the link above.
For additional practice problems or for alternate coverage of the material, we suggest APEX Calculus Volume 3 by Gregory Hartman (freely available) and/or "Multivariable Calculus, Stewart, 7th Edition" (traditional textbook).
There will be graded homework.
Optional problems: There will be suggested practice problems
from the book and other sources which will not be collected or marked
for credit.
You are encouraged to do lots of problems, this is the best way to
learn the subject.
There will also be optional WeBWorK, which will not count towards your
mark for the course. Initially its due date will be the same as the
required WeBWorK assignment. Answers will become available at the due
date. Optional WeBWorK is can also be accessed until the Final Exam.
Grade change requests: Any requests to reconsider grades (homework, midterm, etc) should include the regrade request form.
Email sent without "253" in the subject is very likely to be ignored.
There are listed roughly by week. Details to follow.
Introduction, three dimensional coordinate systems, vectors, dot product (textbook sections 1.1, 1.2).
Cross product, equations of lines and planes, equations of curves and their tangent vectors (1.2, 1.3, 1.4, 1.5, 1.6).
Cylinders and quadric surfaces, functions of several variables (1.7, 1.8, 1.9, 2.1).
Partial derivatives, chain rule, tangent planes, the differential and linear
approximation (2.2, 2.3, 2.4, 2.5, 2.6).
Linear approximation, tangent plane (2.5, 2.6)
Directional derivatives and gradient
Directional derivatives and gradient continued, Tangent planes via the normal, Maximum and minimum values, Lagrange multipliers.
Lagrange multipliers, double integrals over rectangles, iterated integrals
Iterated integrals continued, double integrals
Double integrals in polar coordinates, applications
Surface area, triple integrals
Triple integrals in cylindrical and spherical coordinates.
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