Advanced analysis I

Additional Info

  • ECTS credits: 6
  • Semester: 3
  • University: University of L'Aquila
  • Objectives:

     

    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).
  • Topics:

     

    • 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.
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