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Bilkent University

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Undergraduate and Graduate Programs 2020-2021

MATH 302 Complex Analysis II

Evaluation of sums by residues. Argument principle, Rouche theorem, open mapping theorem. Conformal mapping, mapping by elementary functions. Riemann sphere, linear fractional transformations. Schwarz lemma, automorphisms of the disc and the upper half plane. Schwarz-Christoffel transformations. Applications to fluid flow and electrostatics. Harmonic functions, Poisson integral formula. Infinite products, entire and meromorphic functions, gamma and zeta functions. Credit units: 3 ECTS Credit units: 5, Prerequisite: MATH 202.

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