| Date | Topics |
| T 9/6 | Review of continuity. Little "o" notation. Approximation by a constant. Sequential criterion of continuity. |
| R 9/8 | Differentiability. Carathéodory's definition. Approximation by a linear function. Sequential criterion. |
| T 9/13 | Continuity and differentiability of vector valued functions. |
| R 9/15 | Separate and joint continuity. |
| T 9/20 | More on continuity. Directional and partial derivatives. |
| R 9/22 | Fréchet derivative. Jacobian matrix. |
| T 9/27 | Caratheodory's criterion. Chain rule. Second order derivatives. |
| R 9/29 | Hessian matrix and its symmetricity. |
| T 10/4 | Quadratic approximation. |
| R 10/6 | Inverse function theorem for single variable functions. |
| T 10/11 | Inverse function theorem. |
| R 10/13 | Inverse function theorem. Implicit function theorem in two dimensions. |
| T 10/18 | Curves. Tangent line. Tangent vectors. |
| R 10/20 | Vectors and covectors. Coordinate transformations. |
| T 10/25 | Manifolds. Implicit function theorem. |
| R 10/27 | Applications of the implicit function theorem. Implicitly defined manifolds. |
| M 10/31 | Midterm exam, 18:05-19:05, Stewart Biology S1/4 |
| T 11/1 | The preimage theorem. Level surfaces. The orthogonal group. |
| R 11/3 | Tangent spaces of manifolds. Critical points. Local extrema. |
| T 11/8 | Conormal spaces. Lagrange multipliers. |
| R 11/10 | Bounded and closed sets. Weierstrass' existence theorem. |
| T 11/15 | Hessian test. The Riemann integral. The fundamental theorem of calculus. |
| R 11/17 | Fubini's theorem. Negligible sets. Jordan content. |
| T 11/22 | Linear transformations. |
| R 11/24 | Change of variables. Oriented curves. Line integrals. |
| T 11/29 | Oriented curves. Green's theorem. Stokes' theorem. |
| R 12/1 | Divergence theorem. |
| R 12/15 | Final exam, 18:00-21:00. |
Instructor: Dr. Gantumur Tsogtgerel
Prerequisite: MATH 133 (Linear Algebra and Geometry) and MATH 222 (Calculus 3) or consent of Department.
Restriction: Intended for Honours Mathematics, Physics and Engineering students. Not open to students who have taken or are taking MATH 314.
Topics:
An in-depth study of certain Calculus 3 topics, as well as some new topics,
including surfaces, manifolds, vector fields, and integration of vector fields.
Calendar description: Partial derivatives; implicit functions; Jacobians; maxima and minima; Lagrange multipliers. Scalar and vector fields; orthogonal curvilinear coordinates. Multiple integrals; arc length, volume and surface area. Line integrals; Green's theorem; the divergence theorem. Stokes' theorem; irrotational and solenoidal fields; applications.
Homework: 4-5 written assignments.
Exams: A midterm and final.
Grading: Homework 20% + MAX{ Midterm 20% + Final 60% , Final 80% }