units

MTH3060

Faculty of Science

This unit entry is for students who completed this unit in 2015 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study. print version

## 6 points, SCA Band 2, 0.125 EFTSL

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

 Level Undergraduate Faculty Faculty of Science Organisational Unit School of Mathematical Sciences Offered Clayton Second semester 2015 (Day) Coordinator(s) Professor Paul Cally and Dr Simon Clarke

### Synopsis

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.

### Outcomes

On completion of this unit students will be able to:

1. Understand the importance of differential equations in modelling;

1. Understand and solve Sturm-Liouville eigenvalue problems and use orthogonal polynomials to find exact solutions of boundary-value problems;

1. Solve linear ordinary differential equations using series methods and Green's functions;

1. Apply both analytical and numerical methods for the solution of planar autonomous systems;

1. Classify critical points using eigenvalues and eigenvectors;

1. Use perturbation methods for periodic and nearly periodic motion.

### Assessment

Final examination (3 hours): 70%
Assignments and tests: 30% 