Math 253 - 2021S Summer Term 1, May–June 2021

Zitrus algebraic surface
Instructor in Charge:Colin Macdonald
Email:cbm (at) math ubc ca
Office:Hah, not likely!
Office hours:TBA on Canvas
Lectures: These will be live, and recordings will be available
Sections: Many

Information about the textbook, the topics, the marking scheme, and policies can be found in the Course Outline.
A rough syllabus is given below. The material below generally applies to all sections, unless other information has been provided by your instructor.

General information

This course is using UBC's Canvas system.


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.

Contacting your instructor

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.

Rough outline of course topics

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.