Lecturer: Stef van Eijndhoven
The aim of this course is to provide an overview of techniques used in the analysis of the basic differential equations originating from mathematical physics. The Laplacian operator plays the leading role in diffusion equations, Laplace/Helmholtz equations and wave equations. The applied techniques are based on a spectral analysis of the Laplacian. Results from this analysis are the classical transformations (Fourier and Hankel) and the classical orthogonal decompositions (Fourier, Legendre and Hermite). Relevant links are made with the fundamentals from distribution theory. Further, the Laplace transformation and complex Fourier transformation are discussed. From a wider perspective, these transformations are related to spectral analysis also. Finally, though they are not the main topic of the course, functional analytic concepts are introduced.
The duration of the course is 14 weeks. Each week covers two hours of lectures and one hour of discussion of assignments. The course is based on lecture notes and is divided in the following chapters: