Course - Complex Analysis MT23

Created: August 28, 2023
Updated: October 11, 2024

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Builds on the content taught in [[Course - Metric Spaces MT23]]^U and generalises the study of real analysis in Prelims ( [[Course - Analysis I 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, Integration and residue calculation]]^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 removable 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.
• Sheet 4
• Sheet 5
• Sheet 6
• Sheet 7
• Sheet 8

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Related posts

• [[About]]^B

  (incoming)
• [[Course - Analysis II HT23]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Dirichlet problem]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Cauchy's theorem]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Multifunctions and branch cuts]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Misc]]^U

  (incoming)
• [[About this website]]^B

  (incoming)
• [[Notes - Complex Analysis MT23, Riemann's removable singularity theorem]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Complex integration]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Logarithms]]^U

  (incoming)
• [[Courses MT23]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Power series]]^U

  (incoming)
• [[Course - Analysis I MT22]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Morera's theorem]]^U

  (incoming)
• [[University Notes]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Residue theorem]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Zeroes, singularities and poles]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Jordan's lemma]]^U

  (incoming)
• [[Course - Analysis III TT23]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Casorati-Weierstrass theorem]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Rouché's theorem]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Möbius maps]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Identity theorem]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Complex differentiability]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Laurent series]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Geometry]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Argument principle]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Conformal maps]]^U

  (incoming)
• [[Course - Metric Spaces MT23]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Integration and residue calculation]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Extended complex plane]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Domains]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Cauchy's integral formula]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Homotopies]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Analytic functions]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Winding numbers]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Liouville's theorem]]^U

  (incoming)
• [[Notes - Complex Analysis MT23, Open mapping theorem]]^U

  (incoming)
• [[Lecture - Complex Analysis MT23, IV]]^U

  (sim: 0.697)
• [[Lecture - Complex Analysis MT23, III]]^U

  (sim: 0.675)
• [[Lecture - Complex Analysis MT23, II]]^U

  (sim: 0.638)
• [[Lecture - Complex Analysis MT23, I]]^U

  (sim: 0.621)