• ECTS

    6 credits

  • Component

    Faculty of Science

Description

Introduce the basic tools of complex analysis.

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Objectives

This UE will cover the following points:

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

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

- Cauchy's formula and its consequences: Index of a yaw with respect to a point, Cauchy's formula in a convex, analyticity of holomorphic functions.

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

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Necessary prerequisites

Analysis courses in L1, L2 and the first semester of L3, in particular :

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

- HAX404X Topology of Rn and functions of several variables

- HAX502X Differential calculus and differential equations

 

Recommended prerequisites: first semester of L3

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Further information

Hourly volumes :

            CM: 27

            TD : 27

            TP: -

            Land: -

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