The main objectives of the course are as follows: to provide knowledge of mathematical methods that are widely used by researchers in the area of Applied Mathematics; to apply this knowledge to a variety of topics, including the basic equations of mathematical physics and some current research topics about nonlinear equations (traffic flow, gas dynamics, fluid dynamics).
Measure and integration theory. Functions of bounded variation. Distributions theory. Fourier transform. Sobolev spaces. Application to the study of partial differential equations: elliptic equations of second order, parabolic equations of second order, hyperbolic systems of first-order equations, nonlinear conservation laws. An outline of semigroup theory.