Welcome

Syllabus

Homework

Project

Schedule

Week	Sec.	Topic	Materials	Resources
1	12.1	Three dimensional coordinate systems	Calculus I and II Review	A robust 3D grapher
	12.2	Vectors	Lengths of vectors	Seeing a vector in 3D
	12.3	The dot product	The dot and cross products	The dot product in 3D
	12.4	The cross product	Practice with vectors (optional)	Visualizing the cross product
2	12.5	Equations of lines and planes	Intersections of lines and planes	Parameterizing a line in 3D
	12.6	Cylinders and quadric surfaces	Understanding surfaces	Visualzing quadric surfaces
3	14.1	Functions of several variables	Contour plots and multi-variable domains	Bivariate functions in Desmos A robust 3D grapher
	14.3	Partial derivatives	Higher-order partials	Visualizing the partial derivative at a point
	14.4	Tangent planes and linear approximation	Tangent planes and linearization	Seeing an infinite collection of tangent lines. A "good" linear approximation. Examples used in class: #1 (.png) #2 (.png) #3 (.png)
	14.5	The chain rule	The chain rule
4	14.6	Directional derivatives and the gradient vector	The gradient and directional derivatives	Visualizing directional derivatives
	14.7	Local extrema of multi-variate functions	Classifying extrema	Visualizing absolute and local extrema A function with one local max, two local mins and three saddle points. A hard function to graph with a local minimum
	15.1	Double integrals over rectangles	Double integrals over rectangles	Visualizing a single and a double Riemann sum
5	15.2	Double integrals over general regions	Double integrals over general regions
	15.3	Double integrals in polar coordinates	Double integrals in polar coordinates
6		Review
		Exam 1: 7:30 - 8:30pm on 10/2 Covers sections 12.1 - 12.6, 14.1, 14.2, 14.3 - 14.7, 15.1 - 15.3	Practice Exam 1 (Solutions) Review Exercises
		Review of exam 1
	15.3	Double integrals in polar coordinates
	15.6	Triple integrals	Triple integrals
7	15.6	Triple integrals
	15.7	Triple integrals in cylindrical coordinates	Triple integrals in cylindrical coordinates	Visualizing cylindrical coordinates
8	15.7	Triple integrals in cylindrical coordinates
	15.8	Triple integrals in spherical coordinates	Triple integrals in spherical coordinates	Visualizing spherical coordinates Basic surfaces in spherical coordinates
				Triple integrals "cheatsheet"
	13.1	Vector functions and space curves		Interactive examples Space curves #1 and #2 A line segment A gallery of space curves
9	13.2	Calculus of vector-valued functions	Vector functions part 1
	13.3	Arc length	Vector functions part 2	Visualizing approximations of arc length A few practice problems
	16.2	Line integrals of scalar functions	Line integrals of scalar functions	The area calculated in a line integral and in one projection
10	16.2 (and 16.1)	Line integrals of vector fields	Line integrals of vector fields	Vector field examples #1 #2 and #3
	16.3	The fundamental theorem for line integrals	Fundamental theorem for line integrals
11	16.4	Green's theorem	Green's theorem
		Review
		Exam 2: 7:30 - 8:30pm on 11/8 Covers sections 15.4, 15.6 - 15.8, 13.1 - 13.3, 16.1 - 16.3	Practice Exam 2 (Solutions) Review Exercises
12	16.5	Curl and divergence	Curl and Divergence	Curl examples #1 #2 #3 #4 #5 Divergence examples
	16.6	Parametric surfaces and their areas	Parametric surfaces
	13		Fall Break	No class
14	16.7	Surface integrals of scalar functions
	16.7	Surface integrals of vector fields	16.7 Surface integrals	Motivating examples
15	16.9	The divergence theorem	Quiz 9 Quiz 9 Key
	16.8	Stokes' theorem	16.9 The divergence theorem and Stokes' theorem
16		Final Exam 6 - 8pm on Wednesday 12/13/17 in Monteith 111 Cumulative	Review questions Cheat sheet