Final exam problems and solutions are available here.

Mathematics 226 (Advanced Calculus I), Fall 2005

MWF 12:00-12:50, MATH 203. Functions of several variables: limits, continuity, differentiability; implicit functions; Taylor's theorem; extrema; Lagrange multipliers; multiple integration, Fubini's theorem; improper integrals.

Homeworks and solutions are available here.

Study topics and recommended problems.

Tentative schedule:

Textbook sectionsTopicsHours (approx.)
1.1-1.7 Vectors: points and vectors, dot product, cross product, lines, planes, hyperplanes, coordinate systems, polar, cylindrical, and spherical coordinates 6
2.1-2.6 Differentiation in several variables: functions and their graphs, limits, derivatives, linearization and differentiability, tangent planes, higher-order derivatives, the chain rule, the gradient and its interpretations, directional derivatives. (Skip Newton's Method, Sec. 2.4) 10
4.1-4.3 Maxima and Minima in Several Variables: differentials and Taylor's theorem, critical points and extrema, Lagrange multipliers 9
5.1-5.4 Multiple Integration: double and triple integrals, changing the order of integration, applications to areas and volumes 9

Instructor: Dr. I. Laba. Office: Math Bldg 239. Phone: 822 2450. E-mail:
Office hours: Mon 3-4, Tue 11-12, Fri 10-11.
Textbook: S.J. Colley, Vector Calculus, 3rd ed., Prentice Hall 2005.
Course web page:

Prerequisites: A score of at least 68% in Math 121, or permission of department head.
Corequisites: One of Math 221, 223.

Your course mark will be based on the homeworks (20%), two midterms (15% each), and the final exam (50%). Grades may be scaled due to the challenging nature of the course material. Both midterms and the final exam will be strictly closed-book: no formula sheets, calculators, or other aids will be allowed. Academic concession. Missing a midterm, or handing in a homework after the due date, will normally result in a mark of 0. Exceptions may be granted in two cases: prior consent of the instructor, or a medical emergency. Supporting documentation (e.g. a doctor's note) will be required. If your request for academic concession is approved, your course mark will be based on your remaining coursework (homework: 20%, midterms and final exam: total of 80%).

Useful links:
[Mathematics Department] [University of British Columbia]