Complex Analysis I

3 credits · Undergraduate credit

Review analysis in R2 including metric spaces, differentiable maps, Jacobians; analytic functions. Cauchy-Riemann equations, conformal mappings, linear fractional transformations; Cauchy's theorem, integral formula; power series and Laurent expansions, residue theorem and applications, maximum modulus theorem, argument principle; harmonic functions; analytic functions' global properties; analytic continuation; normal families, Riemann mapping theorem.