Lecture Notes
Antoine Cerfon
CIMS, NYU
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Notes for Complex Variables 1
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: Consequences of the Cauchy-Goursat Theorem
Lecture 6: Taylor series and Taylor formula
Lecture 7: Laurent series
Lecture 8: The calculus of residues
Lecture 9: Evaluation of Improper Integrals
Lecture 10: Conformal Mapping
Lecture 11: Harmonic functions
Lecture 12: Applications of Conformal Mapping
Lecture 13: Important Special Functions