### Announcements

• 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 the following:
• 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
• 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.
Prerequisites: A score of 68% or higher in MATH 226.

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), 8th ed. Pearson, 2013, ISBN 978-0-321-87741-3.

Course topics:
• 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).
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.

Examinations: 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.