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.

Teaching periods
Location
Start and end dates
Last self-enrolment date
Census date
Last withdraw without fail date
Results released date

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
TOTAL150

Assessment

Type Task Weighting ULO's
ExaminationIndividual 40 - 50% 1,2,3,4 
Mid-Semester TestIndividual 10 - 15% 1,2,3 
Mid-Semester TestIndividual 10 - 15% 
Online QuizzesIndividual 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.