Course - Complex Analysis MT23

Builds on the content taught in Course - Metric Spaces MT23^U and generalises the study of real analysis in Prelims (Course - Analysis MT22^U, Course - Analysis II HT23^U and Course - Analysis III TT23^U) to the complex numbers, which turns out to be simpler than real analysis (sort of).
Proves some remarkable theorems related to functions which are complex differentiable:

• Notes - Complex Analysis MT23, Cauchy’s integral formula^U
• Notes - Complex Analysis MT23, Casorati-Weierstrass theorem^U
• Notes - Complex Analysis MT23, Liouville’s theorem^U
• Notes - Complex Analysis MT23, Residue theorem^U

• Course Webpage
• Lecture Notes
• Panopto for 2020
• Sister course: Course - Metric Spaces MT23^U
• Other courses this term: Courses MT23^U

Notes

• Notes - Complex Analysis MT23, Analytic functions^U
• Notes - Complex Analysis MT23, Argument principle^U
• Notes - Complex Analysis MT23, Casorati-Weierstrass theorem^U
• Notes - Complex Analysis MT23, Cauchy’s integral formula^U
• Notes - Complex Analysis MT23, Cauchy’s theorem^U
• Notes - Complex Analysis MT23, Complex differentiability^U
• Notes - Complex Analysis MT23, Complex integration^U
• Notes - Complex Analysis MT23, Conformal maps^U
• Notes - Complex Analysis MT23, Dirichlet problem^U
• Notes - Complex Analysis MT23, Domains^U
• Notes - Complex Analysis MT23, Extended complex plane^U
• Notes - Complex Analysis MT23, Geometry^U
• Notes - Complex Analysis MT23, Homotopies^U
• Notes - Complex Analysis MT23, Identity theorem^U
• Notes - Complex Analysis MT23, Integral examples^U
• Notes - Complex Analysis MT23, Jordan’s lemma^U
• Notes - Complex Analysis MT23, Laurent series^U
• Notes - Complex Analysis MT23, Liouville’s theorem^U
• Notes - Complex Analysis MT23, Logarithms^U
• Notes - Complex Analysis MT23, Misc^U
• Notes - Complex Analysis MT23, Möbius maps^U
• Notes - Complex Analysis MT23, Morera’s theorem^U
• Notes - Complex Analysis MT23, Multifunctions and branch cuts^U
• Notes - Complex Analysis MT23, Open mapping theorem^U
• Notes - Complex Analysis MT23, Paths and curves^U
• Notes - Complex Analysis MT23, Power series^U
• Notes - Complex Analysis MT23, Residue theorem^U
• Notes - Complex Analysis MT23, Riemann’s removeable singularity theorem^U
• Notes - Complex Analysis MT23, Rouché’s theorem^U
• Notes - Complex Analysis MT23, Winding numbers^U
• Notes - Complex Analysis MT23, Zeroes, singularities and poles^U

Lectures

• Lecture - Complex Analysis MT23, I^U
• Lecture - Complex Analysis MT23, II^U
• Lecture - Complex Analysis MT23, III^U
• Lecture - Complex Analysis MT23, IV^U
• Lecture - Complex Analysis MT23, V^U
• …started watching lecture videos, which may or may not have been a mistake…

Problem Sheets

• …continuing on from Course - Metric Spaces MT23^U.
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• Sheet 8