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Lecture notes on several complex variables

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Math 650, Fall 2011. Texas A&M University Lecture notes on several complex variables Harold P. Boas Draft of November 30, 2011. Contents 1 Introduction 1. Power series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Integral representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Partial differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. 2 Power series 4. Domain of convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Characterization of domains of convergence . . . . . . . . . . . . . . . . . . . . 5. Elementary properties of holomorphic functions.

The domain of convergence of a power series means the interior of the set of points at which the series converges absolutely. 1 For example, the set where the two-variable power series P

  Lecture, Notes, Variable, Complex, Convergence, Several, Lecture notes on several complex variables

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