Complex calculus

  1. The Cauchy Riemann Equations: what do they really mean?
  2. Contour Integration I: Cauchy and Morera's integral theorems
  3. Contour Integration II: Everything about singularities and the origin of Pi + Picard's theorem
  4. Conformal maps, preserving angles, etc. 
  5. Power series and disks of convergence
  6. Analytic continuation, monodromy theorem
  7. Random properties of holomorphic functions, Maximum modulus principle, FTA, etc.
  • Visual Complex Analysis (Needham)

Why "disk" of convergence? Why singularity at $i$ affects 1? Why do quaternion singularities not matter?

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