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 Dirichlet’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 department’s subject overview for courses on analysis.

Resources:

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