**The final exam is on April 30 (Wednesday) at 8:30 am, in ESB 1013.**The exam will be cumulative and will cover all course material (Chapters 13 and 16 of the textbook). In addition to the material already covered on the midterms, this includes Sections 16.8 and 16.9.- Office hours before the final exam:
- Section 201 (Prof. Laba): Wednesday April 23, 2-3; Friday April 25, 2-3; Tuesday April 29, 2-4.
- Section 202 (Prof. Au-Yeung): TBA

- Math final exam packs (usually, 5 past final exams with solutions) can be purchased from the UBC Math Club.
- Homework 5 solutions are posted here.
- Midterm 2 solutions:
**Homework 4 solutions**are posted here.**The second midterm exam on March 19**will cover Sections 16.3-16.7 of the textbook:- Section 16.3: Conservative fields and path independence of line integrals
- Section 16.4: Green's theorem
- Section 16.5: Curl and divergence
- Section 16.6: Parametric surfaces, normal vectors, tangent planes, area (note: we skipped "surfaces of revolution", p. 1127)
- Section 16.7: Surface integrals of functions and vector fields
- Recommended problems from Section 16.7: 5-32 (see Student Solutions Manual for solutions)
- A practice midterm (covering the same material, about the same length and the same level of difficulty) is available here. Solutions are posted here.

**The midterm exam on February 12**covered material up to (and including) Section 16.2 of the textbook:- Chapter 13: Sections 13.1-13.4. (Skip Kepler's laws, pp. 891-893 - last part of Section 13.4.)
- Chapter 16: Sections 16.1-16.2.
- Recommended problems from Section 16.1: 3, 5, 21, 25 (see Student Solutions Manual for solutions)
- Recommended problems from Section 16.2: 3, 7, 9, 15, 19, 21, 33, 41, 43 (see Student Solutions Manual for solutions)

- Midterm 1 solutions:
- A practice midterm (covering the same material, about the same length and the same level of difficulty) is available here. Solutions are available here.

- Section 201: Prof. I. Laba, MWF 2:00-2:50, LSK 201 (note that LSK is also known as CSCI)
- Section 202: Prof. E. Au-Yeung, MWF 12:00-12:50, Buchanan A202

- Math Bldg 200, (604) 822 4457, ilaba@math.ubc.ca
- Office hours (tentative): Monday 1-2, Wednesday 3-4, Friday 11-12, in MATH 200.

- ESB 4112, (604) 822 8746, enricoauy@math.ubc.ca
- Office hours: Thursday 1:00-2:30pm, in LSK 303C.

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 usually be accommodated.

**Vector valued functions of one variable (Chapter 13):**Parameterized curves, velocity, acceleration, arc length. Includes curvature, normal and binormal vectors, tangential and normal components of acceleration.**Vector valued functions of several variables (Chapter 16):**vector fields, line integrals, conservative fields, fundamental theorem of line integrals, Green's theorem, gradient, curl, divergence, parameterized surfaces, suface area, surface integrals, Stokes' theorem, divergence theorem.

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

- A short file explaining flux integrals (supplementing Section 16.7 of the textbook)
- An intuitive explanation of Stokes's Theorem

- 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]