MTH3060 - Advanced ordinary differential equations - 2017

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.

On completion of this unit students will be able to:

1. Understand the importance of differential equations in modelling;
2. Understand and solve Sturm-Liouville eigenvalue problems and use orthogonal polynomials to find exact solutions of boundary-value problems;
3. Solve linear ordinary differential equations using series methods and Green's functions;
4. Apply both analytical and numerical methods for the solution of planar autonomous systems;
5. Classify critical points using eigenvalues and eigenvectors;
6. Use perturbation methods for periodic and nearly periodic motion.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

Three 1-hour lectures and one 2-hour combined tutorial and computer laboratory class per week

See also Unit timetable information

Professor Paul Cally

Applied mathematics

Financial and insurance mathematics

Mathematical statistics

Mathematics

Students must be enrolled in the Master of Financial Mathematics or have passed one of the following units: MTH2032 or MTH2040