Numerical analysis - KAEL8M17

Informations générales

  • Number of hours

    • Lectures 14.0
    • Projects -
    • Tutorials 18.0
    • Internship -
    • Laboratory works -
    • Written tests -

    ECTS

    ECTS 0.35

Goal(s)

To understand the basics of scientific and numerical calculus and analysis.

Content(s)

1. Polynomial interpolation
1.1 Piecewise polynomial interpolation (linear, quadratic, spline)
1.2 Interpolation by a single polynomial (Van der Monde, Lagrange, Newton)
1.3 Interpolation error (improvement by Tchebycheff)

2. Numerical function integration
2.1 Elementary formula
2.2 Composed formula
2.3 Integration error
2.4 Convergence improvement by Romberg

3. Numerical integration of ordinary differential equations
3.1 Differential equation of first order, and one step methods (Euler, Runge-Kutta)
3.2 Differential equation of nth order, systems of first order equations

4. Basics of numerical optimization
4.1 Definitions, problem, local minima
4.2 Direct optimisation methods
4.3 Gradient and Newton methods

Prerequisites

Polynomials, functions, Taylor development, ordinary differential equations

Test

Calendar

The course exists in the following branches:

  • Curriculum - E2I - Semester 8

Additional Information

Course ID : KAEL8M17
Course language(s): FR

You can find this course among all other courses.

Bibliography

Analyse Numérique pour ingénieurs, André Fortin Editions de l?école polytechnique de Montréal

Introduction à l'analyse numérique Applications sous Matlab, Jérôme Bastien et Jean-Noël Martin, Editions Dunod