# 18.112 Functions of a Complex Variable

**Catalog description:**

Studies the basic properties of analytic functions of one complex variable. Conformal mappings and the Poincare model of non-Euclidean geometry. Cauchy-Goursat theorem and Cauchy integral formula. Taylor and Laurent decompositions. Singularities, residues and computation of integrals. Harmonic functions and Dirichletâ€™s problem for the Laplace equation. The partial fractions decomposition. Infinite series and infinite product expansions. The Gamma function. The Riemann mapping theorem. Elliptic functions.

Also see the math departmentâ€™s subject overview for courses on analysis.

### Resources:

- Fall 2019 in-class scribe lecture notes
- Fall 2008 OCW (homework, solutions, exams, lecture notes)