- Final exam solutions are here.
- The final exam is on December 21, 8:30 AM, in IBLC 182 (Irving K. Barber Learning Centre). I am sorry but I am not able to accommodate requests for early exam sittings.
**Office hours during the exam period**: Mondays and Wednesdays, 1-2 pm, in MATH 200. These are for both of my classes, but on Dec. 5 and 7, priority will be given to Math 320 students, as their final exam is on Dec. 8th.- The mathematics department maintains a past final exam database. The final exam in our class should be similar to previous years, but shorter due to the very limited grading time available after Dec. 21.
- Here is the 2014 final exam, with solutions. Please note that Q4 covers material that was not included in this year's Math 226.
- Homework #6 solutions are posted here.
- For your review and practice, all past homeworks and solutions are posted here.
- Recommended practice problems from the textbook are posted here. This page also includes a list of topics for the final exam. The exam will be cumulative (it will cover all topics from class, including the early material), but with more emphasis on the more recent part.
- All unclaimed assignments, up to and including HW6, are available for pickup outside my office, MATH 200.
- Solutions to Midterm 2 are available here.
**Midterm 2 is on Friday, Nov. 4, in class.**It will cover material from Chapter 12, specifically:- Section 12.1: Functions of several variables, their graphs and level curves.
- Section 12.2: Limits and continuity, including proving existence of limits from the definition.
- Section 12.3: Partial derivatives
- Section 12.4: Higher order partial derivatives
- Section 12.5: Chain Rule (You can skip "Homogeneous functions" and Euler's Theorem, pp. 700-701.)
- Section 12.6: Differentiability and linear approximation (You can skip "Differentials in Applications" and "Differentials and Legendre Transformations", pp. 712-714. These sections provide information about applications of differentials in physics, for those interested, but they will not be required on tests or homework.)
- Section 12.7: Gradients and directional derivatives. ("Rates Perceived by a Moving Observer", pp. 722-723, will not be required, but it provides a nice interpretation of directional derivatives.)
- Section 12.8: Implicit differentiation. This material will be covered before the midterm. We will only focus on two important special cases: functions of two variables defined by an equation F(x,y,z)=0 (Example 1), and coordinate transformations (Examples 3, 8). We will also need the concept of the Jacobian (Definition 8). We will not try to cover the general theory for arbitrary systems of equations (as in Theorem 8).

- Practice Midterm 2 is available here.
- Solutions to the sample midterm are available here.
- Solutions to Midterm 1 are available here.
- Midterm 1 was on Wednesday, October 5, in class.
- The exam is strictly closed-book: no books, notes, calculators, or electronic communication devices are permitted.
- The midterm will cover Sections 10.1-10.6: points, sets and vectors in n-space, dot and cross product (with applications to finding angles, areas and volumes), lines, planes, quadric surfaces, cylindrical and spherical coordinates.
- We have skipped "Hanging cables and chains," pp. 574-576. and some of the examples with distances, pp. 592-593. You are not required to memorize the names of all possible quadric surfaces (Section 10.5), but you have to be able to sketch basic surfaces such as those discussed in the textbook (possibly with the x,y,z coordinates interchanged), and to find and sketch cross-sections in planes parallel to coordinate planes.
- Cylindrical and spherical coordinates (Section 10.6) will be covered n Friday, Sept. 30. We will also start Chapter 12 (functions of several variables, partial differentiation) before the midterm, but this will not be included on the test.
- A sample midterm is available here.
- Solutions to the sample midterm are available here.
- A list of recommended practice problems fron the textbook is available here. The textbook has answers to all odd-numbered questions, and solutions to even-numbered questiosn are available in the Student Solutions Manual.

- Math Bldg 200, (604) 822 4457, ilaba@math.ubc.ca
- Office hours: Mon 1-2, Wed 10-11, Fri 12-1, 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.

**Vectors in 3-space (Chapter 10)**: vectors, dot and cross product, planes and lines, quadric surfaces, cylindrical and spherical coordinates.**Functions of several variables (Chapter 12):**graphs, limits, continuity, derivatives and differentiability, gradients and directional derivatives, implicit functio ns.**Applications of partial derivatives (Chapter 13):**extreme values of functions, minimization and maximization problems.**Multiple integration (Chapter 14):**double and triple integrals, changing variables, applications.

Additional links and resources:

- Please read the UBC policy on Student Conduct and Discipline.
- Mathematics Learning Centre: The Math Learning Centre (or MLC for short) is a space for undergraduate students to study math together, with support from tutors, who are graduate and undergraduate students in the math department. Please note that while students are encouraged to seek help with homework, the MLC is not a place to check answers or receive solutions, rather, our aim is to aid students in becoming better learners and to develop critical thinking in a mathematical setting. The MLC is located in Rooms 301 and 302 in the Leonard S. Klinck (LSK) Building, and is open Monday through Friday, 11:00am to 6:00pm. Check the website above for any changes to hours and announcements.
- 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]