ECTS
6 credits
Component
Faculty of Science
Description
Introduce the basic tools of complex analysis.
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
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
Further information
Hourly volumes :
CM: 27
TD : 27
TP: -
Land: -