Complex Analysis
An introduction to functions of a single complex variable. Topics include analytic functions, contour integrals, Cauchy integral formula, harmonic functions, Liouville's theorem, Laurent series, analytic continuation, and conformal mapping. Additional topics may include theorems of Picard and Rouché, the Riemann mapping theorem, Riemann surfaces, and the fast Fourier transform.
Prerequisites: Graduate Student Status.
Outcomes: Students will be able to: analyze limits and continuity for complex functions; evaluate contour integrals (by the fundamental theorem, by Cauchy integral formula, and by the residue theorem); and represent functions as Laurent series, classifying singularities and poles.
Prerequisites: Graduate Student Status.
Outcomes: Students will be able to: analyze limits and continuity for complex functions; evaluate contour integrals (by the fundamental theorem, by Cauchy integral formula, and by the residue theorem); and represent functions as Laurent series, classifying singularities and poles.