Welcome to the math222 course webpage! Here, you'll find info about the class and links to some helpful ressources. The page will be updated every week and it will serve as the main communication tool. If any link is broken, please let me know.

schedule

course

mtwr 11:00-13:30

Rutherford physics building, room 112

Please note that the courses take place in-person. Courses start officially on Thursday May 1st and end on Thursday May 29th (see key academic dates here).

course outline

The official course overview from the math department is the following :

Taylor series, Taylor's theorem in one and several variables. Review of vector geometry. Partial differentiation, directional derivative. Extreme of functions of 2 or 3 variables. Parametric curves and arc length. Polar and spherical coordinates. Multiple integrals.

You can find the up-to-date course outline here.

structure of the course

Below, the chapters are from Stewart's book Calculus : early transcendentals 9th edition.

• §1. Series (chapter 11)
• 1.1 Recap on sequences (lecture 1)
• 1.2 Series (lecture 1)
• 1.3 Convergence criteria (lecture 1,2)
• 1.4 Power series (lecture 2,3)
• 1.5 Taylor series (lecture 3)
• 1.6 Errors and remainder (lecture 4)
• §2. Vector geometry (chapter 12)
• 2.1 Recap on linear algebra (lecture 4)
• 2.2 Equations for $k$-planes in $\mathbb{R}^n$ (lecture 5)
• 2.3 Conics and quadrics (lecture 5)
• §3. Curves (chapter 13)
• 3.1 Definition and first properties (lecture 5)
• 3.2 Regular curves and arc length (lecture 6)
• 3.3 Curvature and torsion (lecture 6,7)
• §4. Differentiation (chapter 14)
• 4.1 Continuity (lecture 8)
• 4.2 Partial derivatives, gradient and chain rule (lecture 8,9,10)
• 4.3 Linearization (lecture 10)
• 4.4 Lagrange multipliers (lecture 10)
• §5. Integration (chapter 15)

references

books

The main reference for the class will be the 9th edition of Stewart's Multivariable calculus. On the website of McGill's library, you can find the 8th edition here and the complete text Calculus : early transcendentals of which our textbook is a subset here.

webwork

You can try out some exercises on the webwork which is accessible via MyCourses. These exercises will not be graded, but you will receive an automated feedback.

additionnal ressources

Grant Sanderson (also known under the pseudonym 3blue1brown) is a mathematician from Stanford who developped incredible expertise in math visualisation. He built a series of short videos about calculus which you can find here.

More ressources will be added in the future.

course calendar

The following calendar can give you a good impression of what's to come! Don't forget to scroll down to get some more precise info about quizzes and exams.

evaluations

There will be three quizzes (1h, 4% each), one midterm (2h30m, 33%) and one final exam (3h, 55%). Students attempting the quizzes automatically get full marks. Evaluations will all be closed book.

exams

As time goes, you will be able to find the pdfs of past exams here.

• quizzes : quiz 1, quiz 2, solutions to quiz 2
• midterm

lectures

• 01.05 chapter 11, sections 11.1 and 11.2.
  suggested exercises (numbering from the 9th edition) : 11.1.(3-16), 11.1.(17-22), 11.1.(27-62), 11.1.70, 11.1.76, 11.1.(78-84), 11.1.87, 11.1.95, 11.1.97, 11.2.(17-22), 11.2.(23-32), 11.2.(59-66), 11.2.69, 11.2.86, 11.2.90, 11.2.91

important info

The midterm will take place on Thursday May 15th from 11:05 to 13:05 at the McConnell Engineering Building, room 204.

office hours on wednesday, 14:15-16:45 at Burnside 1033

lectures

• 12.05 end of chapter 12, sections 12.4, 12.5, 12.6. chapter 13, sections 13.1, 13.2.
  suggested exercises (numbering from the 9th edition) : 12.5.(2-5), 12.5.(6-12), 12.5.13, 12.5.14, 12.5.15, 12.5.16, 12.5.17, 12.5.(19-22), 12.5.(23-40), 12.5.(45-47), 12.5.50, 12.5.(51-56), 12.5.(71-72), 12.5.(73-74), 12.5.75, 12.6.(3-8), 12.6.11, 12.6.(13-22), 12.6.(31-32), 12.6.(33-40) 13.1.(3-6), 13.1.(7-16), 13.1.(17-18), 13.1.(19-20), 13.1.(21-24), 13.1.(25-30), 13.1.(31-34), 13.1.35, 13.1.37, 13.1.38, 13.1.39, 13.1.40, 13.1.(50-54), 13.2.(3-8), 13.2.(9-16), 13.2.(17-20), 13.2.(21-22), 13.2.23, 13.2.24, 13.2.(25-28), 13.2.29, 13.2.43, 13.2.44, 13.2.(45-49), 13.2.(53-54).
• 13.05 chapter 13, sections 13.3.
  suggested exercises (numbering from the 9th edition) : 13.3.(3-8), 13.3.(9-11), 13.3.12, 13.3.13, 13.3.(15-16), 13.3.17, 13.3.18, 13.3.(19-24), 13.3.(25-27), 13.3.28, 13.3.29, 13.3.(46-49), 13.3.(51-52)
• 14.05 End of chapter 13, section 13.3. Frenet-Serret equations, fundamental theorem of the local theory of curves. Computation of the Frenet trihedron, curvature and torsion when $\overrightarrow{r}$ is not parametrized by arc-length.
• 15.05 midterm. You can find the pdf of the midterm here.

lectures

• 26.05
• 27.05
• 28.05
• 29.05 quiz 3