Department of Mathematics at Columbia University

This is a sample syllabus. The schedule and topics covered for your section are likely to be different.

Meeting	Topics	Reading
1	Double integrals over rectangles	15.1, 15.2
2	Double integrals over general regions	15.3
3	Polar coordinates, applications of double integrals	15.4, 15.5
4	More applications, triple integrals	15.5, 15.6
5	Cylindrical coordinates, spherical coordinates	15.7, 15.8
6	Spherical coordinates, change of variables	15.8, 15.9
7	Change of variables	15.9
8	Review
9	1st Midterm
10	Vector fields	16.1
11	Line integrals	16.2
12	Fundamental theorem for line integrals	16.3
13	Green’s theorem	16.4
14	Curl and divergence	16.5
15	Parametric surfaces, surface area	16.6
16	Surface integrals	16.7
17	Stokes’ Theorem	16.8
18	Divergence Theorem	16.9
19	Review
20	2nd Midterm
21 & 22	Complex functions
23 & 24	Cauchy-Riemann equations
25 – 27	Contour integrals and Cauchy’s Theorem
28	Review

Programs