UE Holomorphic functions

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Degrees incorporating this pedagocial element :

Description

  1. Holomorphic and analytical functions, in particular the equivalence between the two notions, exponential function and logarithm, principle of analytic continuation, principle of isolated zeros, Cauchy formula for the disc
  2. Elemental properties of holomorphic functions (Cauchy inequalities, sequences and series of holomorphic functions, property of the mean, and principle of the maximum)
  3. Cauchy theory (existence of primitives, Cauchy theorems)
  4. Meromorphic functions (classification of isolated singularities, meromorphic functions, residue theorem, Laurent series)
  5. Riemann conformal representation theorem