Course Info

Virtual format

This course will be offered virtually and using a "flipped classroom" model. Before each class, students are expected to read assigned sections of the lecture notes. (See the syllabus.) Course meetings will take place on Zoom, where students will have the opportunity to ask questions about the course material. DGDs will also take place on Zoom. (See below for more information on the DGDs.)

About the course

MAT 2122 is a course on calculus in multiple dimensions aimed at students majoring in mathematics or doing a joint degree with another subject. We will focus mainly on real-valued functions of multiple real-valued inputs. Many concepts will be discussed using the language of vectors and linear algebra, since this is the most natural setting for multivariable calculus. We'll see how much of the calculus you learned in previous courses generalizes to multiple dimensions. This will allow us to explore interesting new mathematics, such as integration over surfaces and three-dimensional regions. We'll also see higher dimensional analogues of the fundamental theorem of calculus.

Official course description

Derivatives as linear maps, the chain rule. The Clairaut-Schwarz theorem. Taylor's theorem. Implicit function theorem. Extrema, critical points. Lagrange multipliers. Double and triple integrals, Fubini's theorem, polar, spherical and cylindrical coordinates. Change of variables. Line integrals, Green's theorem. Parametric surfaces and surface integrals. Curl and Stokes' theorem, existence of potentials. Divergence and Gauss's theorem. Applications.


(MAT 1325 or MAT 1322), (MAT 1341 or CEGEP linear algebra with MAT 1341 as corequisite). The courses MAT 2122, MAT 2322 cannot be combined for units.

Reference material

Course texts

There are two main textbooks for this course. Both are open access and contain extensive exercises, with hints and solutions.

Lecture notes

Click the above header to download lecture notes for the course. They are a single file that may be updated as the course progresses. Students will be expected to read assigned sections of these notes before class. (See the syllabus.)

Additional references

If you're looking for additional references, you can try the books listed in the "Calculus" section on Another good (but not open access) book for this course is Vector Calculus by Marsden and Tromba.


You should be registered in the DGD associated to this course. The DGD is an important part of the course. It will take place on Zoom; the links are posted in Brightspace. It is led by the professor and supplements the material covered in the lectures. You will be given an opportunity to ask questions about the lectures. In addition, we will go through the recommended exercises that correspond to the lectures from the past week. To get the most from the DGDs, you should attempt the recommended exercises before the DGDs. That way, you can focus on clearing up any difficulties that you encounter. Please note that the Math Help Centre does not offer help for MAT 2122.

Course website

There are two main locations for information regarding the course:

  • This is the main course website. It will be updated regularly and contains important material for the course.
  • Brightspace. Grades will be posted on Brightspace.

Other resources