Mathematics 226, Section 101

Advanced Calculus I

Department of Mathematics,  Undergraduate Math courses,  University of British Columbia

Prerequisite: Either (a) a score of 68% or higher in MATH 121 or (b) a score of 80% or higher in one of MATH 101, MATH 103, MATH 105, SCIE 001.

Corequisite: One of MATH 152, MATH 221, MATH 223.

Instructor

Joel Feldman

Text

I will post all handouts, problem sets, etc. on the web here.

Topics

1. Brief Introduction to Vectors (§ 10.1-10.4): vectors in R² and R³, inner product, cross product, lines and planes.
2. Differentiation (§ 12.1-12.3, § 12.5-12.8, § 12.4, § 12.9): limits, partial derivatives, tangent planes, chain rule, gradient, directional derivatives, implicit functions, higher order derivatives, equality of mixed partials, Taylor's theorem.
3. Maxima and Minima (§ 13.1-13.3): local and absolute extrema, classification of critical points, Lagrange multipliers.
4. Integration (§ 14.1-14.6): double integrals, iteration, improper integrals, polar coordinates, triple integrals, cylindrical and spherical coordinates.

Grading

• There will be two midterms (tentatively scheduled for Wednesday, October 5 and Wednesday, November 2) accounting for about 40% of the final mark.
• There will be weekly problem sets accounting for about 10% of the final mark.
• The final exam will account for about 50% of the final mark.
• Grades will probably be scaled.