MATH 8339 Complex Theory
This course is an introduction to the fundamentals of complex analysis. Topics include: The Riemann sphere and stereographic projection, elementary functions, analytic functions, the theory of complex integration; power series; the theory of residues, the Cauchy-Riemann equations, Conformal mappings: fractional linear transformations; the geometric nature of the power, exponential, and logarithmic maps; Riemann Mapping Theorem, Weierstrass products, the Mittag-Leffler theorem, Schwarz lemma and hyperbolic geometry, harmonic functions: Laplacian; relation to analytic functions; conjugate harmonic functions; Dirichlet problem; Schwarz reflection principle; applications.
Prerequisite
Departmental approval
Offered
As scheduled