Assess students' ability to apply the spectral theorem for compact self-adjoint operators on Hilbert spaces to regular Sturm–Liouville boundary value problems: show compactness and self-adjointness of the relevant operator (or its inverse), deduce a real discrete spectrum and an orthonormal eigenbasis in L^2, compute normalized eigenfunctions and expansion coefficients for given data, state modes of convergence (L^2, uniform where applicable), and use the eigenfunction expansion to solve a prescribed inhomogeneous BVP.