Advanced ordinary differential equations

This unit examines two particular classes of ordinary differential equations: dynamical systems and boundary-value problems. The investigation of boundary-value problems considers Sturm-Liouville eigenvalues problems and orthogonal polynomials, shooting and direct matrix methods for the numerical investigation of boundary-value problems and iterative matrix methods. The second topic of dynamical systems considers analytical and numerical methods for planar autonomous systems, classification of critical points using eigenvalues and eigenvectors and perturbation methods for periodic and nearly periodic motion. Programming skills are developed in the context of the analytic and numerical investigation of advanced ordinary differential equations using MATLAB.