MTH3060 - Advanced ordinary differential equations

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Overview

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.

Offerings

S2-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Professor Paul Cally

Unit Coordinator(s)

Dr Theodore Vo

Notes

IMPORTANT NOTICE:
Scheduled teaching activities and/or workload information are subject to change in response to COVID-19, please check your Unit timetable and Unit Moodle site for more details.

Learning outcomes

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

Understand the importance of differential equations in modelling;

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

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

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

Classify critical points using eigenvalues and eigenvectors;

Use perturbation methods for periodic and nearly periodic motion.

Teaching approach

Active learning

Assessment

1 - In-semester assessment

2 - Examination (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions

Lectures

Workload requirements

Workload

Learning resources

Required resources

E. Kreyszig, Advanced Engineering Mathematics, 10th edition, Wiley, Hargrave-Andrew Library 510.2462 K92A 2011.

G. Birkhoff & G.‐C. Rota, Ordinary Differential Equations, 4th edition, Wiley, Hargrave-Andrew Library 514.5 B619.O4 1984.

C.H. Edwards & D.E. Penney, Differential Equations and Boundary Value Problems, 3rd edition, Pearson/Prentice‐Hall, Hargrave‐Andrew Library 514.5 E26D 2004.

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