The goal of this course is to give an introduction to the theory of distributions and cover the fundamental results of Sobolev spaces including fractional spaces that appear in the interpolation theory. Those notions are central to the study of partial dif ...
We develop, analyze and implement numerical algorithms to solve optimization problems of the form min f(x) where x is a point on a smooth manifold. To this end, we first study differential and Riemannian geometry (with a focus dictated by computational con ...
Le projet de transformation considère les sites existants comme des ressources pour réinventer nos manières d'habiter. À Renens, les étudiants exploreront la rénovation pour concevoir de nouvelles formes de vie, créant des typologies domestiques issues des ...
We discuss a set of topics that are important for the understanding of modern data science but that are typically not taught in an introductory ML course. In particular we discuss fundamental ideas and techniques that come from probability, information the ...
A theoretical and practical reflection on the possibilities, positions and methodologies of a minor approach to architectural research will reveal key concepts and tools to establish a critical position, build a situated architectural investigation and pro ...
Quantum mechanics is one of the most successful physical theories. This course presents the mathematical formalism (functional analysis and spectral theory) that underlies quantum mechanics. It is simultaneously an introduction to mathematical physics and ...
The goal of this course is to present an overview on the solvability and the regularity of relevant models of physical, technological and economical systems, which may be formulated as minimization problems of suitable integral functionals. ...