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 ...
We introduce locally convex vector spaces. As an example we treat the space of test functions and the space of distributions. In the second part of the course, we discuss differential calculus in Banach spaces and some elements from nonlinear functional an ...
The aim of the course is to review mathematical concepts learned during the bachelor cycle and apply them to concrete problems commonly found in Engineering, and Materials Science in particular. ...
Today one is able to manipulate matter at the nanoscale were quantum behavior becomes important and possibly information processing will have to take into account laws of quantum physics. We introduce concepts developed in the last 25 years to take advanta ...
Ce cours est une introduction à la mécanique quantique. En partant de son développement historique, le cours traite les notions de complémentarité quantique et le principe d'incertitude, le processus de mesure, l'équation de Schrödinger, ainsi que des élém ...