Theory of Functions of a Complex Variable I

Algebra and geometry of complex numbers, analytic functions, Taylor and Laurent Series, Abel's Limit Theorem, meromorphic functions, residue calculus, Cauchy integral theorem and applications, classification of functions by singularities, analytic continuation, linear transformations, the cross ratio, conformal mapping, the Riemann Sphere.
Note. A course in Advanced Calculus is required and must be completed before taking this course.