This is a joint seminar with Analysis. Please note special day, time and location. We aim at obtaining equations of fluid dynamics from Newton's laws governing the motion of the particles of fluid, in the limit when the number of particles goes to infinity and their diameter simultaneously goes to zero under the Boltzmann-Grad scaling. As suggested by Hilbert in his sixth problem, it is useful to use Boltzman's equation as an intermediate level of description. In this talk we shall report on some progress on this question in the linear case, when one derives the heat and the Stokes equations. This is a joint work with Thierry Bodineau and Laure Saint-Raymond.