Course Description

Parametric equations and polar coordinates.  Vectors, vector functions and space curves.  Differential and integral calculus of functions of several variables.  Line integrals and surface integrals and classic vector calculus theorems. Examples from life sciences and physical science applications.  1st half of the course – geometry of 3d space, curves in 2d and 3d, multivariable differentiation.  2nd half of the course – double and triple integrals, line and surface integrals.  The course will have significant emphasis on computation.  In general, theorems will be stated without proofs, but with an indication of the mathematical ideas involved. No emphasis will be put on rigorous mathematical proofs.

Prerequisites

MAT135Y5/MAT137Y1/MAT137Y5/MAT157Y1/MAT157Y5, or

(MAT135H1/MAT135H5/MATA30H3/MATA31H3 and MAT136H1/MAT136H5/MATA36H3/MATA37H3).

Course Information

Note:  Office hours will be posted on the main  Quercus page  (http://q.utoronto . ca)

Homework - 6 biweekly WeBWorK problem sets - 15%

Quizzes - 12 Quizzes (10 highest graded) - 40%

Final (In-person) - Cumulative - 45%

Course Text

Multivariable  Calculus  : Stewart, James. 8th Edition.

Optional: The Fundamentals of Mathematical Analysis, G.M. Fikhtengolts, vol.1,2

Tutorials

Tutorials will begin the 2nd week of class (week of May 16).  The tutorials are 1 hour long, twice a week.  During each session, the TA will present relevant course material.

Quizzes

There will be a total of 12 quizzes throughout the semester, starting the first week.  These quizzes will consist of roughly 2-3 questions on the material that week.  These quizzes will be administered on the second day of one’s lecture section at the end of lecture that day.  These assessments will be will timed with some extra time in order to upload to Crowdmark. Uploaded work should be clearly presentable and readable for the graders. There will be no late submissions and no make-up quizzes, however the best 10 out of 12 will be used to calculate this portion of your Final Grade.

Homework Assignments

Homework will be submitted biweekly through WeBWorK on Fridays at 11:59 pm starting the first week.

Technical Requirements

In order to participate in this course, students will be required to have:

(1) Reliable internet access. It is recommended that students have a high speed broadband connection (LAN, Cable, or DSL) with a minimum download speed of 5 Mbps.

(2) A computer satisfying the minimum technical requirements (https://www.viceprovoststudents.utoronto.ca/ covid-19/tech-requirements-online-learning/)

∗ If you are facing financial hardship, you are encouraged to contact your college or divisional registrar https://future.utoronto.ca/current-students/registrars/ to apply for an emergency bursary.

Final exam

In-person final exam is handled by the Faculty of Arts and Science, and is planned to take place during the period of Aug. 17 - 30 (exact time and location to be determined close to the exam period).

Topics list

1. Geometry in R3 :  Cartesian coordinates, vectors, dot product, cross product, equations of lines and planes, distances.

2. Curves in 2D and 3D: parametric curves, arc length, curvature. Polar coordinates. Areas and length. Motion in space. Conic sections and quadratic surfaces.

3. Functions in 2 and 3 variables:  limits and continuity;  partial derivatives, gradient, chain rule, directional derivatives, differential, tangent planes, linear approximation. Applications.

4. Minimum and maximum of functions in several variables, local extremas, Lagrange multipliers. Applications.

5. Double and triple integrals, surface area, volumes, change of variables. Applications.

6. Vector fields, line integrals, Green’s theorem, curl and divergence, surface integrals, Stokes’s theorem. Appli- cations.

Email policy

Any email to the instructors should contain “MAT235” in the subject line. Please use your“@mail.utoronto.ca”or “@utoronto.ca”email address. You can usually expect a response within 48 hours. If the answer to your question is  found in the syllabus, then you might not receive a response.