250062 VO Applied analysis (2016W)

We present some aspects of modern asymptotic analysis and harmonic analysis.

Starting with the "scaling" of model equations we introduce regular and singular perturbation

theory as a tool for asymptotic expansions in the context of model hierarchies like the transition from Burgers to Hopf equation or Boltzmann to Navier-Stokes to Euler equation.

In a second part we present basic aspects of harmonic analysis and sampling theory and applications in imaging.

We also present the basics of harmonic analysis and sampling theory and applications in imaging.

Methods: Dimensionless variables, scaling, perturbations; continuum mechanics;

multi-scale problems; Fourier transform; Radon transform; mathematical foundations of imaging.

Part of the course consists of examples that the students work out and present on the blackboard.