Complex Analysis

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Author(s): I. Smith, ed. Dexter Chua
Series: Cambridge Mathematical Tripos Part IB Lecture Notes
Publisher: University of Cambridge
Year: 2016

Language: English
City: Cambridge
Tags: maths; mathematics; math; advanced; college; university; higher; further; pure; applied; complex variable; complex analysis; complex numbers

Introduction
Complex differentiation
Differentiation
Conformal mappings
Power series
Logarithm and branch cuts
Contour integration
Basic properties of complex integration
Cauchy's theorem
The Cauchy integral formula
Taylor's theorem
Zeroes
Singularities
Laurent series
Residue calculus
Winding numbers
Homotopy of closed curves
Cauchy's residue theorem
Overview
Applications of the residue theorem
Rouchés theorem