Math 405
Complex Analysis

Progression and homework

Presentation: written work should be done on one side only of 8.5''x11'' paper with smooth edges. Each problem should begin on a new page.

Deadlines: papers should be turned in outside of Jones 130. Extensions may be granted if requested at least twenty-four hours before the due date. Late homework will not be accepted.

	Date	Topic
1	8/31	Complex numbers
2	9/05	Labor Day
	9/07	Geometry of the complex plane
3	9/12	Series and power series
	9/14	More on power series
4	9/19	The complex exponential
	9/21	Polar form and arguments
5	9/26	Logarithms, branches
	9/28	Analytic and holomorphic functions
6	10/03	Analytic and holomorphic functions
	10/05	The Cauchy-Riemann equations
7	10/10	Curves in the complex plane
	10/12	Integrals along curves
8	10/17	Midterm 1
	10/19	The index
9	10/24	The Cauchy-Goursat theorem
	10/26	Cauchy's theorem in convex domains
10	10/31	Taylor expansions, Morera's theorem
	11/02	The reflection principle
11	11/07	Zeros of holomorphic functions
	11/09	Isolated singularities
12	11/14	Liouville's theorem, limits of holomorphic functions
	11/16	Midterm 2
13	11/21	Class rescheduled
	11/23	Thanksgiving Break
14	11/28	The Riemann sphere, meromorphy
	11/30	Local behavior of holomorphic functions
15	12/05	The Open Mapping and Maximum Modulus theorems
	12/07	Residues and applications
★	12/15	Final Examination