### Complex calculus

1. The Cauchy Riemann Equations: what do they really mean?
2. Integrating complex functions: FTC, Cauchy Int Thm
3. Cauchy integral formula, holomorphic implies analytic
4. Power series and disks of convergence
5. Singularities, poles, residue theorem, Laurent series https://math.stackexchange.com/questions/60330/intuition-about-the-values-of-cauchy-integrals-on-the-unit-circle
6. Analytic continuation, monodromy theorem
7. Random properties of holomorphic functions, Maximum modulus principle, FTA, etc.
8. Conformal maps, preserving angles, etc.
Resources
• Visual Complex Analysis (Needham)