Lecture	Topics	Some Standard Examples/Concepts
Day 1	Review of algebra and geometry in Euclidean space (1.1-1.5)	Vector notation, dot and cross products, lines, planes
Day 2	Matrices; polar and cylindrical coordinates (1.6 -1.7)	Basic matrix operations, determinant and area, cartesian and polar coordiantes
Day 3	Functions in several variables (2.1 - 2.3)	Graphing surfaces, review of limits, continuity and partial derivatives
Day 4	Derivatives (2.3-2.5)	properties of partial derivatives, the chain rule
Day 5	Directional derivatives and the gradient (2.6)
Day 6	Parametrized curves (3.1)
Day 7	Arclength (no curvature) (3.2)
Day 8	Vector fields (3.2)
Day 9	Gradient, divergence, curl, and the Del operator (3.4)
Day 10	Double integrals (5.1)
Day 11	Double integrals (5.2)
Day 12	Changing the order of integration (5.3)
Day 13	Triple integrals (5.4)
Day 14	Change of variables (5.5)	linear transformations, the Jacobian
Day 15	Applications of Integration (5.6)	average value, center of mass
Day 16	Scalar and vector line integrals (6.1)
Day 17	Scalar and vector line integrals (6.1)
Day 18	Green's Theorem (6.2)
Day 19	Conservative vector fields (6.3)	path independence, potential functions, "partial integration"
Day 20	Parametrized surfaces (7.1)
Day 21	Areas of surfaces (7.1)
Day 22	Surface integrals (7.2)
Day 23	Surface integrasl (7.2)
Day 24	Stokes's theorem (7.3)
Day 25	Stokes's theorem (7.3)
Day 26	Gauss's Theorem (7.3)
Day 27	Gauss' theorem (7.3)
Day 28	Path Independence and the Fundamental Theorem of Calculus

Last Updated March 15, 2010 by R. Orellana