Modelling Nature’s Non-Linearity
Overview
Mathematical modelling of physical and biological systems and processes is a growing field that uses multiple mathematical techniques, many of which rely on nonlinear systems approaches. This unit will cover a range of these techniques, using examples from different areas of the natural world.
Requisites
01-June-2025
Learning outcomes
Students who successfully complete this unit will be able to:
- Model nonlinear physical and biological systems with mathematics
- Utilise coupled nonlinear differential equations to describe nonlinear systems
- Analyse coupled systems via phase plots, bifurcation diagrams and dynamical systems theory
- Describe and model nonlinear systems such as virus dynamics, immunity response, predator-prey dynamics, chemical reactions and cancer
Teaching methods
Hawthorn
| Type | Hours per week | Number of weeks | Total (number of hours) |
|---|---|---|---|
| On-campus Lecture | 3.00 | 12 weeks | 36 |
| On-campus Class | 1.00 | 12 weeks | 12 |
| Online Learning activities | 2.00 | 12 weeks | 24 |
| Unspecified Activities Independent Learning | 6.50 | 12 weeks | 78 |
| TOTAL | 150 |
Assessment
| Type | Task | Weighting | ULO's |
|---|---|---|---|
| Examination | Individual | 40 - 50% | 1,2,3,4 |
| Mid-Semester Test | Individual | 10 - 15% | 1,2,3 |
| Mid-Semester Test | Individual | 10 - 15% | 4 |
| Online Quizzes | Individual | 25 - 30% | 1,2,3,4 |
Hurdle
As the minimum requirements of assessment to pass a unit and meet all ULOs to a minimum standard, an undergraduate student must have achieved:
(i) an aggregate mark of 50% or more, and(ii) at least 40% in the final exam.Students who do not successfully achieve hurdle requirement (ii) will receive a maximum of 45% as the total mark for the unit.
Content
- Modelling using Difference Equations
- Fixed Points and Periodic Points of Maps
- Modelling with Differential Equations
- Geometric Approach to Differential Equations and Bifurcation Theory
Study resources
Reading materials
A list of reading materials and/or required textbooks will be available in the Unit Outline on Canvas.