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 … For more content click the Read More button below.

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.

Offerings

S2-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Dr Theodore Vo

Unit Coordinator(s)

Dr Theodore Vo

Notes

This Level 4 unit and its Level 3 counterpart MTH3060 share the same core content and learning activities such as seminars and applied classes. However, studies at Level 4 are distinguished from those at Level 3 by a deeper understanding of mathematical theories and their applications, more challenging assessment tasks, higher levels of critical thinking, and greater autonomy in learning.

Learning outcomes

On successful completion of this unit, you should be able to:

Demonstrate a deep understanding of the significance and applications of differential equations in advanced mathematical modelling.

Analyse and solve complex Sturm-Liouville eigenvalue problems, utilising orthogonal polynomials to find exact solutions of boundary-value problems.

Employ advanced series methods and Green’s functions to resolve complex linear ordinary differential equations.

Integrate advanced analytical and numerical techniques for the efficient resolution of planar autonomous systems.

Evaluate and classify critical points through a rigorous analysis using eigenvalues and eigenvectors in higher-dimensional systems.

Apply sophisticated perturbation techniques to analyse and predict the behaviour of periodic and nearly periodic dynamical system

Teaching approach

Active learning

Assessment

1 - Continuous assessment

2 - Final assessment - Exam (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Seminars

Workload requirements

Workload

Learning resources

Required resources

Other unit costs

Costs are indicative and subject to change.

Miscellaneous items required (Unit course reader, Printing, Stationery) - $120.

Availability in areas of study

Applied mathematics
Financial and insurance mathematics
Mathematical statistics
Mathematics