Applied Mathematics

General targets: acquire basic knowledge of the physical and mathematical aspects of Fluid Mechanics and Kinetic Theory. Knowledge and understanding: knowledge of physical principles and modeling assumptions that lead to the equations of fluids and particle systems; knowledge of fluid and gas equations and their mathematical properties: weak formulations, existence and uniqueness of solutions, models for the evolution of singular data. Applying knowledge and understanding: the student will be able to modeling fluid and particle motions, also through the formulation of appropriate action functionals, discuss the evolution of singularity, use the mathematical tools for the treatment of fluids and gases in other contexts. To develop these aspects, in the course they are assigned and carried out appropriate exercises. Making judgements: ability to identify the most significant aspects of the theory, to know how to evaluate the limits and the advantages of simplifications operated (incompressibility, absence or presence of viscosity...), and the limits of mathematical results. Communication skills: ability to expose the development of the physical-mathematical theory for fluids and particle systems, highlighting the relationship between physical and mathematical aspects; ability to illustrate the demonstrations, summarizing the main ideas, and discussing the mathematical details. Communication skills: the acquired knowledge will allow a study, individual or given in an LM course, related to numerical aspects or modeling of fluid mechanics and kinetic theory.