- The final exam has been scheduled on April 12 (Saturday), at 12:00 noon, in MATH 104.
- Math final exam packs (usually, 5 past final exams with solutions) can be purchased from the UBC Math Club. There are no exams packs for Math 227, but Math 317 exams should be similar.
- I will have office hours before the final exam on Friday, April 11, 11-1 pm.
**Syllabus for Chapter 17**(these are the topics that we actually covered in class)- Section 17.1: k-forms (all of it). Practice problems: 1-8.
- Section 17.2: differential k-forms and exterior derivative. Skip "1-forms and Legendre transformations" and "Maxwell's Equations Revisited." Practice problems: 1-13.
- Section 17.3: Manifolds and integration. We used a slightly different (but equivalent) definition of a manifold. The important parts are "Integration in n dimensions" and "Parametrizing and integrating over a smooth manifold." Practice problems: 5, 6.
- Section 17.4: Oriented manifolds. The main part is "Integrating a differential form over a manifold" (in class, I also showed how this extends the "usual" line and surface integrals). Practice problems: 5, 6.
- Section 17.5: Generalized Stokes's Theorem. We skipped the proof and focused on the special cases in Examples 3, 4, 5. Practice problems: 3-6. (Use Stokes's Theorem, that's what it's for :) )

- Homework #5 solutions are posted here.
**Update re: practice problems**: We will be skipping some of the more computational exercises from Sections 16.4. 1-15 are good practice problems (4,6,11 are HW problems, 12 was done in class). You can skip 16-18 and 21-30.**Midterm 2 was on Wednesday, March 12,**and covered:- Surfaces, surface integrals, flux integrals: Sections 15.5 and 15.6
- Gradient, divergence and curl: Sections 16.1 and 16.2
- Green's Theorem: Section 16.3
*Please note that you do not need to memorize the identities in Theorem 3, Section 16.2, except for parts (g) and (h).*- A sample midterm is available here.
- Sample midterm solutions are posted here.

- Midterm 2 solutions are posted here
**Midterm 1 was on Wednesday, Feb. 5,**and covered the following:- Vector-valued functions: Sections 11.1, 11.3, 11.4, 11.5
- Vector fields: Sections 15.1 (without "Nonlinear systems and Liapunov functions", p. 864), 15.2 (without "Sources, sinks and dipoles", pp. 872-873), 15.3 and 15.4. (I expect to finish 15.4 on Friday.)
*We skipped Sections 11.2 and 11.6.*- A sample midterm (consisting of midterm problems from previous years) is available here.
- Sample midterm solutions are now posted.

- Midterm 1 solutions are posted here

- Math Bldg 200, (604) 822 4457, ilaba@math.ubc.ca
- Office hours: Monday 1-2, Wednesday 3-4, Friday 11-12, in MATH 200.
- The best way to contact the instructor is by email. Please note that email received on evenings and weekends will be answered on the next business day.
- If you cannot attend regular office hours due to schedule conflict, please make an appointment in advance. Drop-ins and same-day requests for appointments cannot always be accommodated.

**Vector-valued functions and curves (Chapter 11)**: curves, velocity, acceleration, arc length, curvature, tangent, normal, binormal, planetary motion.**Vector fields and line integrals (Sections 15.1-15.4):**vector fields, field lines, conservative fields, line integrals.**Surface integrals (Sections 15.5-15.6):**surfaces, surface area, flux integrals.**Integral theorems (Chapter 16):**gradient, divergence and curl, vector identities, divergence theorem, Green's theorem, Stokes' theorem, applications.**Differential forms (Chapter 17):**differential forms, exterior derivative, generalized Stokes' Theorem (if time permits).

Additional course related resources:

- Here are some videos on non-orientable surfaces:
- Basic facts about the Klein bottle
- Klein bottle, animated (there's much more under "related videos")
- Mobius strip, Escher-style

- Please read the UBC policy on Student Conduct and Discipline.
- Mathematics Learning Centre: The Math Department runs a drop-in tutorial centre for undergraduate Math courses, staffed by Graduate Teaching Assistants. This centre is located in Rooms 300, 301, and 302 in the Leonard S. Klinck (LSK) Building, and is open Monday through Friday, 9:00am to 7:00pm. Check the website above for any changes to hours and announcements. All tutors provide assistance with first- and second-year calculus and linear algebra and will attempt to help with any undergraduate Math course. In addition to regular assistance, the MLC offers Quick Help for students who are looking for fast support for minor snags. There is no charge for the services MLC provides.
- Past final exam database
- UBC Math Club, located in Math Annex 1119, sells math exam packages (old exams together with solution sets) for a nominal price before each final exam session.

[Mathematics Department] [University of British Columbia]