ECTS
8 credits
Component
Faculty of Science
Description
This course will cover the concepts of sequences and series of functions and the various convergences. The integer and Fourier series will also be developed.
Objectives
Sequence of functions Simple convergence and uniform convergence of a sequence of functions
- Definitions and link between simple and uniform convergence of a sequence of functions
- Uniform Cauchy criterion
- Dini's theorems
- Stone Weierstrass theorem by Bernstein polynomials
- Stability of continuity (resp. derivability, integration) by uniform convergence
Series of functions
- Simple and uniform convergence
- Normal convergence
- Continuity, differentiability, integrability of a series of functions
Whole series.
Definitions, radius of convergence, Hadamard's formula, d'Alembert's rule.
Properties of the sum of the whole series: continuity, differentiability, integrability.
Integer developable functions.
Applications to the solution of differential equations: resolution by integer and exponential series of matrices.
Fourier series.
- Why Fourier series (problematic and definitions)?
- Convergence (root mean square, simple, normal) of Fourier series
- Applications to the calculation of certain series and differential equations
Necessary pre-requisites
HAX201X - Analysis II Sequences, series, limited developments
HAX302X: Analysis III integration and elementary differential equations
Recommended prerequisites: L1 math
Additional information
Hourly volumes:
CM : 39h
TD : 39h
TP:
Terrain: