Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
5 credits
30.0 h + 30.0 h
Q2
Teacher(s)
Legat Vincent; SOMEBODY;
Language
French
Main themes
This course is intended as an introduction to techniques for carrying out numerical computation on computers.
The course serves three main goals:
The course serves three main goals:
- the understanding of basic numerical techniques with the underlying mathematical notions,
- the hability to interpret the reliability of numerical results,
- the programming skills to implement simple numerical algorithms with Python.
Content
This course presents a broad overview of numerical methods, using calculus, algebra and computing science. The student must become aware of the relevant issues in selecting appropriate method and software and using them wisely, in terms of computational cost, numerical accuracy, complexity and stability. To make the presentation concrete and appealing, the programming environment PYTHON is adopted as a faithful companion.
Topics include:
Topics include:
- Error analysis: modelling error, truncation error, convergence and approximation order, floating point number representation (IEEE754).
- Approximation and interpolation: Lagrange polynomials, spline functions, NURBS, orthogonal polynomials, error estimators.
- Numerical integration and differentiation: backward and centered finite difference, midpoint, trapezoidal and Simpson formula, adaptive techniques.
- Ordinary Differential Equations (ODE): Taylor and Runge Kutta methods, predictor-corrector methods, stability on unbounded intervals and perturbation analysis.
- Linear equations: factorization methods and iterative techniques, complexity, computation of eigenvalues.
- Nonlinear equations: bisection and Newton methods, optimisation applications.
- Partial Differential Equations (PDE): boundary value problems (Laplace, heat equation, waves equation), approximation by finite differences.
Teaching methods
Lectures in auditorium, supervised exercise and problem sessions, and unsupervised assignments.
Real-life examples using numerical methods
Use of Python software
Real-life examples using numerical methods
Use of Python software
Evaluation methods
Written examination about the theory, exercises and problems inspired from the course (90% of the final grade) - Homeworks (10%)
Online resources
Faculty or entity
BTCI
