MTH4060 · Advanced ordinary differential equations

Overview

This unit examines two particular classes of ordinary differential equations: dynamical systems and boundary-value problems. The investigation of boundary-value problems considers series methods, Green’s functions, Sturm-Liouville eigenvalues problems and orthogonal polynomials. 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.

Areas of study: Applied mathematics Financial and insurance mathematics Mathematical statistics Mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Apply analytical and numerical methods to solve advanced ordinary differential equations, including Sturm–Liouville problems, series solutions, and Green’s functions;
2. Analyse the qualitative behaviour of dynamical systems by classifying critical points, studying stability, and applying perturbation methods for periodic and near-periodic motion;
3. Demonstrate how differential equations model real-world phenomena, integrating theory, computation, and interpretation in applied contexts;
4. Communicate reasoning and results in differential equations effectively, both orally and in writing, and collaborate in small groups to solve problems;
5. Develop a deeper understanding of advanced ordinary differential equations through rigorous synthesis, independent analysis, and application to complex or novel systems.

Workload

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12) and • 7 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.