  This mini-course of 20 lectures aims at highlights of spectral theory for
self-adjoint partial differential operators, with a heavy emphasis on problems
with discrete spectrum. Part I: Discrete Spectrum (ODE preview, Laplacian -
computable spectra, Schroedinger - computable spectra, Discrete spectral
theorem via sesquilinear forms, Laplace eigenfunctions, Natural boundary
conditions, Magnetic Laplacian, Schroedinger in confining well, Variational
characterizations, Monotonicity of eigenvalues, Weyl's asymptotic, Polya's
conjecture, Reaction-diffusion stability, Thin fluid film stability) Part II:
Continuous Spectrum (Laplacian on whole space, Schroedinger with $-2sech^2$
potential, Selfadjoint operators, Spectra: discrete and continuous, Discrete
spectrum revisited)
