Found 7 relevant results in 0.72s where lecturer="Mikaela Iacobelli"
This course aims to give an introductory description of the classical approaches to the problem of the mean-field limit in mathematical analysis. In particular, the intent is to learn essential tools and techniques for studying Partial Differential Equations while applying them to Vlasov equations.
In this lecture we treat problems in applied analysis. The focus lies on the solution of quasilinear first order PDEs with the method of characteristics, and on the study of three fundamental types of partial differential equations of second order: the Laplace equation, the heat equation, and the wave equation.
Measure and integration theory, including: Caratheodory's theorem, Lebesgue measure, Radon measure, Hausdorff measure, convergence theorems, L^p spaces, Radon-Nikodym theorem, product measure and Fubini's theorem
This class covers the basic theory of Hilbert spaces, Fourier series and Fourier Transform, and its application to the study of classical linear PDEs.
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