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)

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