Faculty of ScienceComplex integration, Cauchy?s theorem and consequence. Laurent series. Calculus of residues. Inverses and implicit functions. Rouche?s theorem. Harmonic and subharmonic functions. The poison integral. The mean-value property. Positive harmonic functions. Dirichlet?s problem. The poisson- Jensen formula and related topics. Conformal mapping. Fractional linear transformations. Normal families. The Riemann mapping theorem. Continuity at the boundary. Confromal mapping of an annulus maximum ? modulus principle. Schwarz?s lemma. The Phagemen-Lindel ?of and Hadamord?s theorem. Entire functions with rational values. Converse of the maximum modulus theorem.
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