Assess students' ability to formulate and solve second‑order linear boundary value problems using Sturm‑Liouville theory: identify self‑adjoint form and weight function, compute eigenvalues and orthogonal eigenfunctions for specified boundary conditions, expand prescribed functions in eigenfunction series, construct series solutions to homogeneous and nonhomogeneous BVPs (including via Green's functions or eigenexpansions), and justify convergence and orthogonality properties.