MATH_V 217 101 2026W1 Multivariable and Vector Calculus

MATH 217 Multivariable and Vector Calculus

Contact information

Course Structure

Lectures will be held in person:

  • Tuesdays and Thursdays, 9:30–11:00 a.m. P.A. Woodward Instructional Resources Centre (IRC), Floor 1, Room G.
  • Wednesdays, 11:00 a.m.–12:00 p.m. Mathematics Building (MATH), Floor 1, Room 100.
  • Jim Bryan office hours: Tuesdays, 11:00 a.m.–12:00 p.m., Math 226.
  • TA office hours: TBA.

Learning Materials

  • Main texts: CLP-3 Multivariable Calculus and CLP-4 Vector Calculus, by Joel Feldman, Andrew Rechnitzer, and Elyse Yeager. These locally developed texts and their companion problem books are available here.
  • I will post my lecture notes under Pages → Notes.
  • I will post practice midterms and finals before each midterm and the final exam.
  • Piazza: Access the course Piazza page through Canvas. The teaching team will answer questions there.

WeBWorK

Weekly WeBWorK assignments will appear on the Assignments tab in Canvas. A new assignment will normally open each Tuesday and will be due two Mondays later at 11:59 p.m. Always access each WeBWorK assignment through its link in Canvas so that grades sync correctly.

Assessment of Learning

There will be weekly WeBWorK assignments and two midterms. Two midterms are currently scheduled, although this may change. The course grade will normally be given by the better of the following two schemes:

  • 50% final exam + 35% midterm grades + 15% WeBWorK grade; or
  • scaled final-exam grade minus 10.

Please note that grades may be scaled.

Course Policies

  • There will be two midterms during the term. There are no make-up midterms. Missing a midterm for a valid reason normally results in the weight of that midterm being redistributed to the remaining midterm and final exam. Any student who misses a midterm must submit the Department of Mathematics self-declaration form to the instructor within 72 hours of the midterm date. This policy conforms with UBC Vancouver Senate Academic Concession Policy V-135.

Learning Outcomes

Here is a list of learning outcomes: skills.pdf.

Schedule of Topics

The following is our expected progress through the course. Each full week contains roughly four lecture hours. The schedule is provisional and may be adjusted as the term progresses.

Weeks 0 and 1 (September 9–17): introduction, coordinates, vectors, dot and cross products, lines and planes (CLP3: 1.1–1.5).

Week 2 (September 22–24): curves, tangents, arc length, and sketching surfaces (CLP3: 1.6–1.9).

Week 3 (September 29–October 1): functions of several variables, partial and higher-order derivatives, equality of mixed partials (CLP3: 2.1–2.3), tangent planes and linear approximation (CLP3: 2.5–2.6), and the chain rule (CLP3: 2.4). There is no class on September 30.

Week 4 (October 6–8): directional derivatives and the gradient (CLP3: 2.5–2.7), and classification of critical points (CLP3: 2.9).

Week 5 (October 13–15): maxima and minima, and Lagrange multipliers (CLP3: 2.9–2.10).

Week 6 (October 20–22): double integrals, volumes, and double integrals in polar coordinates (CLP3: 3.1–3.2). The first midterm is tentatively scheduled in class for Thursday, October 22.

Week 7 (October 27–29): applications of double integrals, triple integrals, and triple integrals in cylindrical and spherical coordinates (CLP3: 3.3–3.7).

Week 8 (November 3–5): vector fields, line integrals, and path independence (CLP4: 2.1–2.4 and 1.6).

Midterm break (November 9–11): no classes.

Week 9 (November 12): parameterized surfaces and surface integrals (CLP4: 3.1–3.5).

Week 10 (November 17–19): surface integrals continued; gradient, divergence, and curl (CLP4: 4.1). The second midterm is tentatively scheduled in class for Thursday, November 19.

Week 11 (November 24–26): the divergence theorem, Green’s theorem, and Stokes’ theorem (CLP4: 4.2–4.4).

Week 12 (December 1–3): differential forms (CLP4: 4.7) and review.

Final exam: TBD.