Notes for Math 520 Complex Analysis Ko Honda

Overview & Synopsis

The contents of this
book include, Complex numbers, Polynomials and rational functions, Riemann
surfaces and holomorphic maps, Fractional linear transformations, Power series,
More Series, Exponential and trigonometric functions, Arcs, curves, etc, Inverse
functions and their derivatives, Line integrals, Cauchys theorem, The winding
number and Cauchys integral formula, Higher derivatives, including Liouvilles
theorem, Removable singularities, Taylors theorem, zeros and poles, Analysis of
isolated singularities, Local mapping properties, Maximum principle, Schwarz
lemma, and conformal mappings, Weierstrass theorem and Taylor series, Plane
topology, The general form of Cauchys theorem, Residues, Schwarz reflection
principle, Normal families, ArzelaAscoli, Riemann mapping theorem, Analytic
continuation, Universal covers and the little Picard theorem.