Differential equations provide one of the most powerful mathematical tools for understanding the natural world. Since rates of change are commonly expressed using derivatives, differential equations arise whenever some continuously varying quantities and their rates of change in space or time are known or postulated. Whether seeking to understand biological processes, behaviours of solids or liquids, ecological systems, or mechanical systems, differential equations provide essential insights. The modelling range of differential equations extends well into the world of human endeavour, for example, they are important for understanding financial markets, or even traffic flows.
This course introduces students to fundamental problems in differential equations. It will introduce students to mathematical modelling, exploring a wide breadth of application areas, and will investigate solution techniques, including methods for numerical computation of solutions.
- Semester 2 - 2016
On successful completion of the course students will be able to:
1. Have the skills to build effective differential equations models and appreciate their implications for answering questions across the natural and human worlds.
2. Be able to classify the different classes of differential equation models, how they arise and what characterises them.
3. Be aware of solution and analytic approaches to important classes of differential equations arising from the mathematical modelling of physical, chemical and biological systems.
4. Be equipped to solve important classes of differential equations analytically and numerically.
Topics will include:
- Differential equations and mathematical modelling (model building, simplification, limitations and validation)
- First order differential equations
- Higher order differential equations
- Systems of first order differential equations
- Numerical solution techniques
- Partial differential equations (heat equation, wave equation and Laplace's equation)
- Fourier series and separation of variables methods for initial and boundary value problems
All topics will be taught in the context of applications drawn from real life examples.
Written Assignment: Assignment 1
Formal Examination: Examination
Quiz: In-class quiz 1
Written Assignment: Assignment 2
Quiz: In-class quiz 2
Face to Face On Campus 3 hour(s) per Week for Full Term
Face to Face On Campus 1 hour(s) per Week for Full Term
The tutorial may be held in a computer lab when needed.