Videos and slides for the course Complex Functions
Main reference: Serge Lange's Analysis in one complex variable
Course content
- Introduction
- The complex derivative
- Analytic functions
- Integration
- Integration I: path integrals: video and slides
- Integration Ib: clarification on dz and |dz|: video and slides
- Integration II: primitives: video and slides
- Integration II: existence of primitives, step 1: video and slides
- Integration II: existence of primitives, step 2: video and slides
- Cauchy Integral Formula
- Cauchy Integral Formula I -- Statement and proof: video and slides
- Cauchy Integral Formula I -- Consequences: video and slides
- Global Cauchy Integral Formula
- The logarithm
- Sequences and series of holomorphic functions
- Singularities
- The Riemann Sphere
- Calculus of residues
- Calculus of residues: Tricks
- Moebius transformations
- Geodesics
- Harmonic functions
- Solution to the Mock exam