640:403 Spring 2018 Section 02 Syllabus

Date Topic
1Jan 16 1.1. Complex numbers and the complex plane
2Jan 18 1.2. Some geometry
3Jan 23 1.3. Subsets of the plane
4Jan 25 1.4. Functions and limits
5Jan 30 1.5. The exponential, logarithm and trigonometric functions
6Feb 1 1.6. Line integrals and Green's theorem
7Feb 6 2.1. Analytic and harmonic functions; the Cauchy-Riemann equations
8Feb 8 2.2. Power series
9Feb 13 2.3. Cauchy's theorem and Cauchy's formula
10Feb 15 Review and catch up
11Feb 20 Midterm 1
12Feb 22 2.4. Consequences of Cauchy's formula
13Feb 27 2.4. Continued
14Mar 1 2.5. Isolated singularities
15Mar 6 2.5. Laurent series
16Mar 8 2.6. The residue theorem.
17Mar 20 2.6. Applications of the residue theorem
18Mar 22 3.1. The zeros of an analytic function
19Mar 27 3.2. Maximum modulus and mean value
20Mar 29 Review and catch up.
21Apr 3 Midterm 2
22Apr 5 3.3. Linear fractional transformations
23Apr 10 3.4. Conformal mapping
24Apr 12 3.5. The Riemann Mapping Theorem and Schwarz-Christoffel Transformations
25Apr 17 4.1. Harmonic functions
26Apr 19 The Gamma function
27Apr 24 The Riemann zeta function
28Apr 26 Review and catch up.
May 4 Final Exam 8-11 AM