Numerical analysis - KAIE7M06

  • Number of hours

    • Lectures 18.0
    • Projects -
    • Tutorials -
    • Internship -
    • Laboratory works 16.0
    • Written tests 2.0

    ECTS

    ECTS 0.4

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

RENDU, CC, EXAM

Calendar

The course exists in the following branches:

  • Curriculum - IESE - Semester 7

Additional Information

Course ID : KAIE7M06
Course language(s): FR

You can find this course among all other courses.

Bibliography

« Analyse numérique et équations différentielles », J.P. Demailly, Presses Universitaires de Grenoble, 1991
« Théorie et applications des équations différentielles », F. Ayres Jr., série Schaum, 1986.
« Matlab/Simulink. Application à l?automatique linéaire », S. Le Ballois, Ed. Ellipes Marketing, 2002.