Course Title: Modelling with Differential Equations

Part A: Course Overview

Course Title: Modelling with Differential Equations

Credit Points: 12.00


Course Code

Campus

Career

School

Learning Mode

Teaching Period(s)

MATH2138

City Campus

Undergraduate

145H Mathematical & Geospatial Sciences

Face-to-Face

Sem 2 2006,
Sem 2 2007,
Sem 2 2008,
Sem 2 2009,
Sem 2 2010,
Sem 2 2011,
Sem 2 2012,
Sem 2 2013,
Sem 2 2014,
Sem 2 2015

Course Coordinator: Prof. Lewi Stone

Course Coordinator Phone: +61 3 9925 1728

Course Coordinator Email: lewi.stone@rmit.edu.au


Pre-requisite Courses and Assumed Knowledge and Capabilities

MATH1144, Calculus and Analysis 2


Course Description

This course introduces modern mathematical modelling approaches using dynamical systems (largely differential equation approaches) that are relevant in many different applications and in particular for biological and ecological systems. In recent years, mathematical modelling has indeed become one of the most important research tools in biological research.

We will introduce the basic concepts and methods for analysing these models. There will be an emphasis on studying nonlinear dynamical systems taking advantage of applied bifurcation and chaos theory.

These tools will be used in particular to explore complex biological systems ranging from genetics and evolution to the periodic processes driving the heart and brain or for studying ecological processes such as species persistence and biodiversity.

The assessment of this course will include implementing the techniques encountered in the lectures in a programming environment such as Matlab.


Objectives/Learning Outcomes/Capability Development

This course contributes to the following Program Learning Outcomes for BP083 - Bachelor of Science, BP245 - Bachelor of Science (Statistics) and BH119 - Bachelor of Analytics (Honours):

Knowledge and Technical Competence:

  • use the appropriate and relevant, fundamental and applied mathematical and statistical knowledge, methodologies and modern computational tools.

Problem-solving:

  • synthesise and flexibly apply knowledge to characterise, analyse and solve a wide range of problems
  • balance the complexity / accuracy of the mathematical / statistical models used and the timeliness of the delivery of the solution.

Communication

  • the ability to effectively communicate both technical and non-technical material in a range of forms (written, electronic, graphic, oral) and to tailor the style and means of communication to different audiences. Of particular interest is the ability to explain technical material, without unnecessary jargon, to lay persons such as the general public or line managers.


On completion of this course you should be able to:

  1. Analyse nonlinear dynamical systems and use them for modelling real problems, in particular in biology;
  2. Identify and apply key concepts of stability and bifurcation theory;
  3. Analyse and simulate some of the key mathematical models that have become famous in the biological sciences;
  4. Identify and apply key concepts of modelling oscillatory systems and biological synchrony;
  5. Run biological models through an implementation with a programming environment such as Matlab.
  6. Collaborate with peers to analyse and solve mathematical problems using communication strategies that optimise both team and individual performance


Overview of Learning Activities

This course is taught through a mix of classroom instruction, computer laboratory exercises and assignments. Key concepts will be explained in detail in lectures. A weekly lab tutorial will be devoted to programming models using a programming environment like Matlab. There are individual homework assignments (2) and an individual or group assignment which also involves an oral presentation. 


Overview of Learning Resources

You will have access to computer laboratories.

You will have access to extensive course materials made available through myRMIT, including lecture notes, a detailed study program, external internet links and access to RMIT Library online and hardcopy resources. Journal articles will be provided in lectures and via email.

http://rmit.libguides.com/mathstats


Overview of Assessment

Assessment Tasks:

Assessment Task 1: Homework Assignments

Two individual homework assignments addressing a given problem worth 15% each that assess all the learning outcomes as well as general problem solving skills.

Weighting 25%

This assessment task supports CLOs 1, 2, 3, 4, 5, 6

Assessment Task 2: Individual or in-group Assignment

One individual or in-group homework assignment with an oral presentation component.

Weighting 10%

This assessment task supports CLOs 1, 2, 3, 4, 6

Assessment Task 3:  Mid-semester exam

An mid-semester exam assesses the acquisition of key mathematical concepts and the ability to use them in the frame of models

Weighting 15%

This assessment task supports CLOs 1, 2, 3, 4

Assessment Task 4: Final Exam  

An end of semester 2-hour exam that assesses the acquisition of the main mathematical concepts and the ability to use them in the frame of models

Weighting 50% 

This assessment supports CLOs 1, 2, 3, 4