# MATH206: Complex Analysis (Fall 2019)

## Topics Covered

Topics Covered

Complex differentiability; differentiability properties of elementary functions and harmonic functions; the reflection principle; integration along contours; the Cauchy-Goursat theorem; simple and multiple connectedness of domains; the Cauchy integral formula; the maximum modulus principle; Taylor and Laurent series; analytic continuation; absolute and uniform series convergence; classification of isolated singularities; branch cuts; zeroes and poles; residues; the Cauchy residue theorem and Jordan's lemma; principal values; computation of definite and improper integrals involving polynomials and trigonometric functions; contour deformation around branch points and branch cuts; Rouché's theorem.

## Course Information

Course Information

**Instructor:**Indrani Rao (indrani.rao@flame.edu.in), Karpur Shukla (karpur.shukla@flame.edu.in or kshukla@alumni.cmu.edu)**Course Times:**10:30 AM – 1:30 PM Wednesdays**Office Hours:**by appointment

## Course Texts:

Course Texts:

*Complex Variables and Applications (9th Edition)*

## Grading Structure

Grading Structure

## Assignments

Assignments

- Homework Assignment 1
- Homework Assignment 2
- Homework Assignment 3
- Homework Assignment 4
- Homework Assignment 5
- Homework Assignment 6
- Take-Home Exam