84039 - Complex Analysis (2018/2019)

General information

84039 - Complex Analysis (AC, 7 CFU), first semester, years: 3° LT.

Course content

Power series: formal power series; convergent power series; analytic functions. Complex differentiation: holomorphic functions; Cauchy-Riemann equations; conformal transformations; elementary functions. Complex integration: integration along paths; primitives; Cauchy's theorem. Consequences of Cauchy's theorem: Cauchy's integral formula; holomorphic functions are analytic; further consequences (theorems by Morera and Liouville, mean value, maximum modulus, Weierstrass' convergence theorems). Singularities and residues: Laurent series; behavior near singularities; residue theorem and applications. Miscellanea: zeros and poles of meromorphic functions; Euler's Gamma function; analytic continuation.

Language

Italian

Teacher

Alberto Perelli

Teaching style

In presence

Attendance

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