Modeling and Simulation in Physics

This UE includes a refresher and a deepening of programming techniques as well as an introduction to numerical physics. We'll start with a review of procedural programming with the Python 3 language. Then we'll take an in-depth look at numerical methods relevant to physics, studying a selection of classical numerical analysis algorithms and applying them to physical problems.

Learn to program at an advanced level with Python and apply your knowledge of scientific programming. Understand the concepts of numerical error, numerical stability and algorithmic complexity. Know and know how to implement selected methods for the numerical calculation of integrals, for the solution of ordinary and partial differential equations and for Monte Carlo sampling.

Basic programming skills. Knowledge of computer science, physics and mathematics at bachelor's level in physics.

Recommended prerequisites

Good knowledge of Python 3 and its modules, especially NumPy. Bachelor's degree courses in programming and digital physics, in particular either "Programming for physics" or "Simulation tools" in L3 or equivalent.

Full continuous assessment

Procedural programming with Python 3 (review and refresh)

Scientific programming, the NumPy library

Graphics with Matplotlib

Notions of numerical error, stability and algorithmic complexity

Numerical quadrature methods: Newton-Cotes methods, adaptive methods, Gauss quadrature

Ordinary differential equations: Runge-Kutta methods, implicit methods, adaptive methods

Finite-difference methods for partial differential equations

Monte Carlo sampling and integration