Modeling and Simulation in Physics

This course unit covers a review and in-depth exploration of programming techniques, as well as an introduction to computational physics. We will begin with a review of procedural programming using Python 3. We will then take an in-depth look at numerical methods relevant to physics, studying a selection of classical algorithms from numerical analysis and applying them to physics problems.

Learn to program at an advanced level using Python and apply this knowledge to scientific computing. Understand the concepts of numerical error, numerical stability, and algorithmic complexity. Understand and be able to implement selected methods for the numerical computation of integrals, for solving ordinary and partial differential equations, and for Monte Carlo sampling.

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

Recommended Prerequisites

Proficiency in Python 3 and its modules, particularly NumPy. Courses in the bachelor’s degree program in programming and computational physics, specifically either “Programming for Physics” or “Simulation Tools” in the third year (L3) or equivalent.

Comprehensive Continuous Monitoring

Procedural Programming with Python 3 (Review and In-Depth Study)

Scientific Programming: The NumPy Library

Graphics with Matplotlib

Concepts of Numerical Error, Stability, and Algorithmic Complexity

Numerical integration methods: Newton-Cotes methods, adaptive methods, Gaussian integration

Ordinary Differential Equations: Runge-Kutta Methods, Implicit Methods, Adaptive Methods

Finite Difference Methods for Partial Differential Equations

Sampling and Monte Carlo Integration