Transcription of MATH20101 Complex Analysis - …
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MATH20101 Complex AnalysisCharles WalkdenSchool of MathematicsThe University of Manchester11thOctober, 2018 MATH20101 Complex AnalysisContentsContents0 Preliminaries21 Introduction52 Limits and differentiation in the Complex plane and the Cauchy-Riemannequations113 Power series and elementary analytic functions224 Complex integration and Cauchy s Theorem375 Cauchy s Integral Formula and Taylor s Theorem586 Laurent series and singularities667 Cauchy s Residue Theorem758 Solutions to Part 1999 Solutions to Part 210310 Solutions to Part 311111 Solutions to Part 412012 Solutions to Part 512713 Solutions to Part 613014 Solutions to Part 7135c University of Manchester 20181 MATH20101
MATH20101 Complex Analysis 1. Introduction y x z = x+iy Figure 1.2.1: The Argand diagram or the complex plane. Here z = x+iy. We say that z ∈ Cis real if Im(z) = 0 and we say that z ∈ Cis imaginary if Re(z) = 0.
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