MTH3060 Advanced ordinary differential equations
Faculty of Science
MTH3060 Advanced ordinary differential equations is a level 3, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2027 in Semester 2 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2027
- Semester 2
- Clayton
- Assessment
- Exam 50%
- and 1 other task
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Requisites
Before MTH3060
No prerequisites or corequisites besides the enrolment rules below.
After MTH3060
No unit lists MTH3060 as a prerequisite in the 2027 handbook.
Enrolment rules
PREREQUISITE: You must have passed one unit from MTH2032 or MTH2040 or be enrolled in the Master of Financial Mathematics or the Master of Mathematics.
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 in 2027
| Teaching period | Campus | Mode |
|---|---|---|
| Second semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.
Learning outcomes
When you finish this unit, you should be able to:
- 1
Apply analytical and numerical methods to solve advanced ordinary differential equations, including Sturm–Liouville problems, series solutions, and Green’s functions;
- 2
Analyse the qualitative behaviour of dynamical systems by classifying critical points, studying stability, and applying perturbation methods for periodic and near-periodic motion;
- 3
Demonstrate how differential equations model real-world phenomena, integrating theory, computation, and interpretation in applied contexts;
- 4
Communicate reasoning and results in differential equations effectively, both orally and in writing, and collaborate in small groups to solve problems.
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.
Active learning will occur in lectures and applied classes.
Learning resources
Required resources
G. Birkhoff & G.‐C. Rota, Ordinary Differential Equations, 4th edition, Wiley, Hargrave-Andrew Library 514.5 B619.O4 1984.
E. Kreyszig, Advanced Engineering Mathematics, 10th edition, Wiley, Hargrave-Andrew Library 510.2462 K92A 2011.
C.H. Edwards & D.E. Penney, Differential Equations and Boundary Value Problems, 3rd edition, Pearson/Prentice‐Hall, Hargrave‐Andrew Library 514.5 E26D 2004.
Contacts
- Chief Examiners
- Dr Theodore Vo
- Unit Coordinators
- Dr Alina Donea
Common questions
What are the prerequisites for MTH3060?
MTH3060 has no prerequisites, but enrolment rules apply.
When is MTH3060 offered?
In 2027, MTH3060 runs in Semester 2 at Clayton.
Does MTH3060 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.