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MTH-203.4 Complex Analysis

Complex numbers, complex differentiation, Cauchy-Riemann equations, complex integration, homotopy version of Cauchy theorem, fundamental theorem of algebra, power series expansion.

Maximum modulus and residue theorems, singularities and meromorphic functions,

Laurent series, Rouché theorem, Hurwitz theorem, Weierstrass and Mittag-Leffler theorem.

Conformal maps, Schwarz theorem, Montel's theorem, Schwarz-Christoffel formula.

Riemann mapping theorem.