Analytic Functions of One Complex Variable 1000-134FAN

Functions of one complex variable, function series, power series. Complex derivative. Holomorphic functions. Contour integrals. Path-independence of the contour integral from the path vs existence of a primitive function. Cauchy Theorem. Cauchy integral formula. Holomorphic functions vs analytic functions. Morera Theorem. Entire functions and Liouville Theorem. Weierstrass Theorem. The identity principle. Laurent series. The
classification of isolated singular points. Casorati-Weierstrass Theorem. Residue Theorem and its applications. Meromorphic functions. The argument principle. Rouche Theorem. The Multiplicity Theorem and the Open Mapping Theorem. The maximum principle. Schwarz Lemma. Conformal mappings.