Multivariable Calculus

Calendar

LEC #	TOPICS	KEY DATES
I. Vectors and matrices
0	Vectors
1	Dot product
2	Determinants; cross product
3	Matrices; inverse matrices
4	Square systems; equations of planes	Problem set 1 due
5	Parametric equations for lines and curves
6	Velocity, acceleration Kepler’s second law
7	Review	Problem set 2 due
	Exam 1 (covering lectures 1-7)
II. Partial derivatives
8	Level curves; partial derivatives; tangent plane approximation
9	Max-min problems; least squares	Problem set 3 due
10	Second derivative test; boundaries and infinity
11	Differentials; chain rule
12	Gradient; directional derivative; tangent plane	Problem set 4 due
13	Lagrange multipliers
14	Non-independent variables
15	Partial differential equations; review	Problem set 5 due
	Exam 2 (covering lectures 8-15)
III. Double integrals and line integrals in the plane
16	Double integrals	Problem set 6 due
17	Double integrals in polar coordinates; applications
18	Change of variables
19	Vector fields and line integrals in the plane	Problem set 7 due
20	Path independence and conservative fields
21	Gradient fields and potential functions
22	Green’s theorem	Problem set 8 due
23	Flux; normal form of Green’s theorem
24	Simply connected regions; review
	Exam 3 (covering lectures 16-24)	Problem set 9 due
IV. Triple integrals and surface integrals in 3-space
25	Triple integrals in rectangular and cylindrical coordinates
26	Spherical coordinates; surface area
27	Vector fields in 3D; surface integrals and flux	Problem set 10 due
28	Divergence theorem
29	Divergence theorem (cont.): applications and proof
30	Line integrals in space, curl, exactness and potentials
31	Stokes’ theorem	Problem set 11 due
32	Stokes’ theorem (cont.); review
	Exam 4 (covering lectures 25-32)
33	Topological considerations Maxwell’s equations	Problem set 12 due
34	Final review
35	Final review (cont.)
36	Final exam