Complex Analysis

Introduce the basic tools of complex analysis.

This EU will address the following points:

- Analytic functions: definition, zeros of an analytic function, analytic continuation, maximum principle

- Holomorphic functions: definition, examples (including exponential, logarithms), Cauchy-Riemann equations, existence of primitives.

- Cauchy's formula and its consequences: Index of a loop relative to a point, Cauchy's formula in a convex set, analyticity of holomorphic functions.

- Singularities and meromorphic functions: poles and essential singularities, meromorphic functions, Laurent series expansion, residue theorem

The L1, L2, and first semester of L3 analysis courses, in particular:

- HAX403X Analysis 4, Function sequences, entire series, Fourier

- HAX404X Topology of^Rn and functions of several variables

- HAX502X Differential Calculus and Differential Equations

Recommended prerequisites: first semester of L3

Hourly volumes:

            CM: 27

            TD: 27

            TP: -

            Land: -