This course aims to bridge the gap between theoretical physics and numerical experiments by treating the computer as a strict physics laboratory. Students will learn to confidently implement numerical methods to simulate complex physical systems, with a heavy emphasis on rigorously quantifying computational errors. The objectives according to Dublin Descriptors are:

• Knowledge and understanding: Understand the mathematical limits of discrete computation, including truncation versus round-off errors, the necessity of symplectic integrators, and the Nyquist-Shannon limits in spectral analysis.
• Applying knowledge and understanding: Translate physical laws (ordinary differential equations, partial differential equations, stochastic processes) into working numerical code to simulate multi-dimensional and non-linear physical systems.
• Making judgements: Develop the critical ability to distinguish between genuine physical phenomena and numerical artifacts (e.g., algorithmic energy generation, grid aliasing) through quantitative and qualitative error analysis.
• Communication skills: Communicate scientific results clearly by compiling Jupyter Notebooks that logically combine executable code, mathematical hypotheses, and graphical data representation.
• Learning skills: Develop autonomous debugging and algorithmic problem-solving skills, allowing students to independently assess the validity of computational models in future research setups.