This course will be an introduction to multivariable calculus, following Apostol's Calculus, Volume II.

Announcements

• (05/07) Office hours this week will be Thursday afternoon from 4pm-5pm.
• (04/25) The midterm will be available for pickup from the Math Office next Monday, April 30. It will be due on Monday, May 7 at 10am. There will be a review session next Thursday or Friday evening.
• (04/08) Office hours this week will be Thursday night from 9pm-10pm.
• (04/04) Please fill out and return the questionnaire to me during office hours.

Lecture Notes

• Lecture 1 (04/05): Open sets, limits, continuity. Appendix: the open set definition of continuity is equivalent to the epsilon-delta definition. ("Sets are not doors!")
• Lecture 2 (04/12): Directional derivatives, partial derivatives, total derivatives. Common pitfalls. The gradient. When is a function differentiable?
• Lecture 3 (04/19): The chain rule for partials, general derivatives and the Jacobian, the general chain rule, critical/stationary points and the Hessian.
• Lecture 4 (04/26): Lagrange multipliers, integration in multiple variables, measure zero, content zero.
• Lecture 5 (05/03): Midterm review examples.
• Lecture 6 (05/10): Line integrals, line integrals with respect to arc length, path-connected sets, line integrals and gradients.
• Lecture 7 (05/17): Green's theorem, divergence and curl.
• Lecture 8 (05/24): Change of variables in multivariable calculus.
• Lecture 9 (05/31): Integration on surfaces, 2-manifolds, Stokes' theorem.
• Lecture 10 (06/07): Final review examples.

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