Complex Analysis

Algebra of complex numbers, topology of the complex plane. Analytic functions, Cauchy-Riemann equations, power series. Complex line integrals, Cauchy theorem, Cauchy integral formula, Taylor series. Mean value property, Liouville theorem, isolated zeros, uniqueness theorem, maximum modulus principle. Isolated singularities, singularities at infinity, Laurent series. Residues, evaluation of improper integrals.