| Date | Topics |
| T 9/3 | Review of continuity. Continuity of vector valued functions. |
| R 9/5 | Separate and joint continuity. Differentiability of vector valued functions. |
| T 9/10 | Partial and directional derivatives. Jacobian matrix. |
| R 9/12 | Gradient. Differentiability of multivariate functions. |
| T 9/17 | Chain rule. Tangent plane. Injectivity and surjectivity. |
| R 9/19 | Coordinate systems and frames. Smooth curves. |
| T 9/24 | Smooth surfaces. Univariate inverse function theorem. |
| R 9/26 | Inverse function theorem. Implicit function theorem. |
| T 10/1 | Implicitly defined curves and surfaces. |
| R 10/3 | Critical points. Gradient test. |
| T 10/8 | Weierstrass' existence theorem. |
| R 10/10 | Quadratic approximation. Hessian test. |
| T 10/15 | Optimization on curves and surfaces. Lagrange multipliers. |
| R 10/17 | Diagonalization of symmetric matrices. |
| M 10/21 | Midterm exam. On Webwork, between 06:00–23:59. |
| T 10/22 | The Riemann integral. |
| R 10/24 | Fubini's theorem. Change of coordinates in 2D. |
| T 10/29 | Change of coordinates in 3D. Surface area. Surface integrals. |
| R 10/31 | Line integrals. Conservative fields. Scalar potential. Curl in 2D. |
| T 11/5 | Irrotational fields. Green's theorem. |
| R 11/7 | Curl in 3D. Flux. Kelvin-Stokes theorem. |
| T 11/12 | Flux in 2D. Stream function. Divergence. Vector potential. Solenoidal fields. |
| R 11/14 | Gauss-Ostrogradsky theorem. Archimedes' principle. De Rham diagrams. |
| T 11/19 | Dual diagrams. Hodge duality. |
| R 11/21 | Electrostatics. Poisson equation. Laplace operator. Fundamental solutions. |
| T 11/26 | Magnetostatics. Maxwell's equations. Faraday's tensor. 4-potential. |
| R 11/28 | Helmholtz decomposition. Gauge transformations. |
| R 12/5 | Final exam, 09:00–12:00, Tomlinson Fieldhouse, Rows 36–38. |
Instructor: Dr. Gantumur Tsogtgerel
Prerequisite: MATH 133 (Linear Algebra and Geometry) and MATH 222 (Calculus 3) or consent of Department.
Restriction: Not open to students who have taken or are taking MATH 314 or MATH 358. Not intended for Honours Mathematics students.
Calendar description: Partial derivatives and differentiation of functions in several variables; Jacobians; maxima and minima; implicit functions. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line and surface integrals; irrotational and solenoidal fields; Green's theorem; the divergence theorem. Stokes' theorem; and applications.
Topics.
The following is one way to arrange the topics into groups.
Homework: 4-5 Webwork assignments and 2-3 written homework assignments.
Exams: A midterm and a final.
Grading: Webwork 20% + Written assignment 20% + MAX { Midterm 20% + Final 40%, Final 60% }