Schedule

A week-by-week breakdown of the material.

Week 1 (01/11-1/15)

Day 1: Introduction
Day 2: Complex Numbers, algebra
Day 3: Geometry of the Complex Plane

Week 2 (01/18-01/22)

Day 1: Sequences and Series in the Complex Plane
Day 2: Cauchy sequences
Day 3: Cauchy sequences

Week 3 (01/25-01/29)

Day 1: Series results from Calc 3
Day 2: Series results from Calc 3
Day 3: Series results from Calc 3

Week 4 (02/01-02/05)

Day 1

Series results from Calc 3

Assignment 1 due Friday, February 12

Day 2

Topology of the Complex Plane: Open and Closed sets

Day 3

Open and Closed sets (cont)

Week 5 (02/08-02/12)

Day 1: Continuous functions and relation to topology
Day 2: Catching up
Day 3: Sick day

Week 6 (02/15-02/19)

Day 1: Compact Sets, Heine-Borel theorem
Day 2: Midterm 1 (study guide)
Day 3: Compact Sets, Heine-Borel theorem

Week 7 (02/22-02/26)

Day 1: Sick day
Day 2: Analytic Polynomials
Day 3: Analytic Polynomials, cont

Week 8 (03/07-03/11)

Day 1: Power Series
Day 2: Power Series, cont
Day 3: Cauchy-Riemann Equations, Analytic functions

Week 9 (03/14-03/18)

Day 1: Extensions of standard functions
Day 2: Line Integrals and antiderivatives
Day 3: Line Integrals and antiderivatives, cont

Week 10 (03/21-03/25)

Day 1: Line Integrals and antiderivatives, cont
Day 2: Midterm 2 (study guide)
Day 3: Closed Curve Theorem

Week 11 (03/28-04/01)

Day 1

Closed Curve Theorem, cont

Day 2

Cauchy Integral Formula

Assignment 2 due Friday, April 15

Day 3

Power Series for analytic functions on a disc

Week 12 (04/04-04/08)

Day 1: Louisville Theorem, Fundamental Theorem of Algebra
Day 2: Uniqueness Theorem, Mean Value Theorem
Day 3: Maximum Modulus Theorem and Minimum Modulus Theorem

Week 13 (04/11-04/15)

Day 1: Schwartz’s Lemma
Day 2: Morera’s Theorem
Day 3: TBA