Syllabus

The table below indicates which topics we will cover in each class. Before each class, you should read the lecture notes up to and including the place indicated below.

Lec Date Notes Topics
1 Sep 8 1.1, 1.2 Open sets, boundaries, limits
2 Sep 10 1.3, 1.4, 1.5 Affine approximations, the derivative
3 Sep 15 1.6, 1.7 Differentiation rules; paths, curves, and surfaces
4 Sep 17 1.8, 1.9, 1.10 Directional derivatives, higher order derivatives, Taylor's theorem
5 Sep 22 1.11, 1.12 The implicit function theorem, the inverse function theorem
6 Sep 24 2.1, 2.2, 2.3 Extrema, the second derivative test
7 Sep 29 2.4, 2.5 Lagrange multipliers, multiple constraints
8 Oct 1 2.6, 3.1 Global extrema, double integrals by vertical slices
9 Oct 6 3.2, 3.3, 3.4 Double integrals by horizontal slices, Fubini's theorem
10 Oct 8 3.5, 3.6 Double integrals over general regions, examples and applications
11 Oct 13 3.7 Triple integrals
12 Oct 15 4.1, 4.2, 4.3 Change of variables, polar coordinates
13 Oct 20 4.4, 4.5, 5.1 Cylindrical and spherical coordinates, vector fields
14 Oct 22 5.2, 5.3 Conservative vector fields, curl
Oct 25–29 Reading week
15 Nov 3 1.1–5.3 Midterm exam
16 Nov 5 6.1, 6.2, 6.3 Path and line integrals, reparameterization
17 Nov 10 6.4, 6.5 Line integrals of conservative vector fields, path independence
18 Nov 12 7.1, 7.2, 7.3 Parameterized surfaces, tangent planes, surface area
19 Nov 17 7.4, 7.5 (DGD), 7.6 Surface integrals
20 Nov 19 7.7, 8.1 Reparameterization and orientation; gradient, divergence, and curl
21 Nov 24 8.2 Divergence theorem
22 Nov 26 8.3 Green's theorem
23 Dec 1 8.4 Stokes' theorem
24 Dec 3 Review