APM_41012_EP - Introduction à l'Analyse Numérique : des fondements mathématiques à l’expérimentation avec Jupyter (2024-2025)

When you want to design and simulate a real issue (be a question of population dynamism in ecology, tumor growth in biomedical engineering, combustion dynamics in new-generation rocket engines - for example at SpaceX, prediction of solar storms and magnetic reconnection phenomena in solar physics, simulation of turbulence and turbulent combustion in fluid mechanics) the engineer or the researcher in applied mathematics or in "computational science" has to use a range of digital methods and must be able to analyze it mathematically, assess in terms of quality and computational efficacity, and finally, implement.

This course offers an introduction to numerical analysis, starting with the mathematical foundations on which numerical methods are based through to the implementation and the use of these methods on Jupyter notebooks (an active field at the Ecole Polytechnique), including their stability in relation to mathematical conditioning of the problems posed. The link is made with applications to understand the extent to which this type of method can be used from a practical point of view. Implementations of these methods in existing digital libraries are also documented.

Every class sessions include an analysis of the mathematical foundations on which a numerical method class is built, a description and analysis of the digital method (with a historical perspective). Those two aspects are covered during the course. The PC offers a review and an in-depth look at some concepts of the course, use of the method in the context of Jupyter notebooks and a description of how students can implement the method in a notebook to be handed in for the next class session.