MTH4060 Advanced ordinary differential equations
Faculty of Science
MTH4060 Advanced ordinary differential equations is a level 4, 6-credit-point, undergraduate and postgraduate unit from the Faculty of Science, offered in 2025 in Semester 2 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2025
- Semester 2
- Clayton
- Assessment
- Exam 50%
- and 1 other task
This is the 2025 handbook entry. See the 2027 entry.
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Requisites
Before MTH4060
No prerequisites or corequisites besides the enrolment rules below.
After MTH4060
No unit lists MTH4060 as a prerequisite in the 2025 handbook.
Enrolment rules
COREQUISITE: You must be enrolled in the Graduate Certificate in Mathematics or the Master of Mathematics.
PROHIBITION: MTH3060
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.
Offerings in 2025
| Teaching period | Campus | Mode |
|---|---|---|
| Second semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Learning outcomes
When you finish this unit, you should be able to:
- 1
Demonstrate a deep understanding of the significance and applications of differential equations in advanced mathematical modelling.
- 2
Analyse and solve complex Sturm-Liouville eigenvalue problems, utilising orthogonal polynomials to find exact solutions of boundary-value problems.
- 3
Employ advanced series methods and Green’s functions to resolve complex linear ordinary differential equations.
- 4
Integrate advanced analytical and numerical techniques for the efficient resolution of planar autonomous systems.
- 5
Evaluate and classify critical points through a rigorous analysis using eigenvalues and eigenvectors in higher-dimensional systems.
- 6
Apply sophisticated perturbation techniques to analyse and predict the behaviour of periodic and nearly periodic dynamical system
Workload and teaching
- Applied sessions22 hours
- Seminars36 hours
- Teaching approachActive learning
- Three 1-hour seminars;
- One 2-hour applied class (in weeks 2-12) and
- 7 hours of independent study per week.
Learning resources
Required resources
C.H. Edwards & D.E. Penney, Differential Equations and Boundary Value Problems, 3rd edition, Pearson/Prentice Hall, Hargrave Andrew Library 514.5 E26D 2004.;
E. Kreyszig, Advanced Engineering Mathematics, 10th edition, Wiley, Hargrave-Andrew Library 510.2462 K92A 2011.
Contacts
- Chief Examiners
- Dr Theodore Vo
- Unit Coordinators
- Dr Theodore Vo
Common questions
What are the prerequisites for MTH4060?
MTH4060 has no prerequisites, but enrolment rules apply.
When is MTH4060 offered?
In 2025, MTH4060 runs in Semester 2 at Clayton.
Does MTH4060 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.