Lecture Notes

Antoine Cerfon
CIMS, NYU
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Notes for Complex Variables

The notes below follow fairly closely the textbook Complex Analysis (3rd edition) by Lars V. Ahlfors (McGraw-Hill). Some of the proofs and explanations were also inspired by great notes by Dan Romik (UC Davis).

  • Lecture 1: Complex numbers
  • Lecture 2: Analytic functions
  • Lecture 3: Usual complex functions
  • Lecture 4: Complex Integration
  • Lecture 5: Cauchy's Theorem
  • Lecture 6: Consequences of Cauchy's Theorem
  • Lecture 7: Local properties of analytic functions - Part 1
  • Lecture 8: Local properties of analytic functions - Part 2
  • Lecture 9: The general form of Cauchy's Theorem
  • Lecture 10: The calculus of residues
  • Lecture 11: Harmonic functions
  • Lecture 12: Series and product developments
  • Lecture 13: The Euler Gamma function and the Riemann Zeta function
  • Lecture 14: Conformal Mapping
  • Lecture 15: The Riemann Mapping Theorem
  • Lecture 16: Applications of Conformal Mapping
  • Lecture 17: Analytic Continuation



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