- 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:
- Midterm 2 solutions are posted here
- Midterm 1 was on Wednesday, Feb. 5, and covered
- Midterm 1 solutions are posted here
Mathematics 227 (Advanced Calculus II), Winter/Spring 2014
Section 201: MWF 12:00-12:50, MATH 103
Lecturer: Prof. I. Laba
A score of 68% or higher in MATH 226.
- Math Bldg 200, (604) 822 4457, email@example.com
- 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.
Course web page: http://www.math.ubc.ca/~ilaba/teaching/math227_S2014
Homework assignments will be posted here.
Textbook: Robert A. Adams and Christopher Essex, Calculus: Several Variables (or Calculus: A Complete Course),
Pearson, 2013, ISBN 978-0-321-87741-3.
Your course mark will be based on homework (10%),
two midterm exams (20% each), and the final exam (50%). The grades may be slightly
scaled at the end of the course.
- 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).
There will be two in-class 50-minute midterms, scheduled on Wednesdays, February 5
and March 12,
and a 2.5 hour final exam in April.
The date of the final examination will be announced by the Registar later
in the term.
Attendance at the final examination is required, so be careful about
making other committments (such as travel) before this date is confirmed.
All examinations will be strictly closed-book:
no formula sheets, calculators, or other aids will be allowed.
Homeworks: There will be 5 homework assigmnents, due tentatively on
Wednesdays, January 15, January 29, February 26, March 19, and Monday, March 31.
Each homework will be announced and posted here at least a week in advance.
The homeworks are to be handed in at the beginning of class.
If you cannot come to class, you may drop off your homework at your instructor's office prior to the start of class.
Late assignments will not be accepted.
Solutions will be posted on the course webpage immediately after the lecture.
To allow for minor illnesses and other emergencies, the lowest homework score will be dropped.
Academic concession: Missing a midterm, or handing in a homework
after the deadline, will result in a mark of 0.
Exceptions may be granted in two cases: prior consent of the
instructor, or a documented medical reason.
Your course mark will then be based on your remaining coursework.
Additional course related resources:
- Here are some videos on non-orientable surfaces:
- 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.
[University of British Columbia]