MATH 3006 Mathematical Modelling

Credit Points 10

Legacy Code 200022

Coordinator Stephen Weissenhofer Opens in new window

Description Mathematical Modelling is about solving real world problems. The real world is a complicated place which we often need or want to understand better. One way to do this is to set up a mathematical model which we hope can provide insights, predictions and a greater understanding of a complex system. Selected real-world problems are approximated by mathematical models that are amenable to being written in terms of linear and non-linear equations or differential equations. Once equations are solved emphasis is placed on interpreting solutions, modifying models as required and using models for prediction.

School Computer, Data & Math Sciences

Student Contribution Band HECS Band 1 10cp

Check your HECS Band contribution amount via the Fees page.

Level Undergraduate Level 3 subject

Pre-requisite(s) MATH 2003

Assumed Knowledge

Matrix algebra and how to find eigenvalues and eigenvectors.

Learning Outcomes

On successful completion of this subject, students should be able to:
  1. formulate equations (both differential and non-differential) which describe selected common physical situations,
  2. solve such equations analytically, where appropriate
  3. apply computer packages to solve such equations
  4. interpret the effects of altering parameters involved in a modelling situation
  5. identify limitations of mathematical models proposed
  6. evaluate the effectiveness of a model.

Subject Content

1. The modelling process
2. Modelling using proportionality and geometric similarity
3. Modelling discrete dynamical systems:
- modelling change with difference equations
- approximating change with difference equations
- solving difference equations
4. Modelling continuous dynamical systems:
- first and second order ordinary differential equations
- higher order linear ordinary differential equations
- systems of ordinary differential equations - nonlinear ordinary differential equations
5. Applications will be drawn from areas of biology, chemistry, physics, social sciences and economics.

Assessment

The following table summarises the standard assessment tasks for this subject. Please note this is a guide only. Assessment tasks are regularly updated, where there is a difference your Learning Guide takes precedence.

Item Length Percent Threshold Individual/Group Task
Class Test 1: Covers weeks 1 to 6 of lecture material on the modelling process, modelling with difference equations, geometric similarity, and fitting models to data. Interpreting solutions and identifying limitations, suggesting improvements. 50 minutes 20 N Individual
Class Test 2: Covers weeks 7 – 13 of the lecture material on modelling with differential equations, applied to arms race, population growth, managing prescription drug dosages, predator-prey models or other situations. 50 minutes 20 N Individual
Final exam 3 hours 60 N Individual

Prescribed Texts

  • Giordano, F. R., Fox, W. P., & Horton, S. (2014). A first course in mathematical modeling (5th ed.). Boston, MA Brooks/Cole Thomson Learning.

Teaching Periods

2022 Semester 2

Campbelltown

Day

Subject Contact Stephen Weissenhofer Opens in new window

Attendance Requirements 80% attendance rate is imposed in all core subjects’ due to the nature of class activities that are aligned with subject assessments.

View timetable Opens in new window

Parramatta - Victoria Rd

Day

Subject Contact Stephen Weissenhofer Opens in new window

Attendance Requirements 80% attendance rate is imposed in all core subjects’ due to the nature of class activities that are aligned with subject assessments.

View timetable Opens in new window