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 or physical processes, behaviours of solids or liquids, ecological or mechanical systems, differential equations provide essential insights. If only one independent variable is involved, which is often time, these equations are called ordinary differential equations.
This course introduces students to the world of ordinary differential equations. The main focus of the course will be to investigate analytical and numerical solution techniques, qualitative behaviour of the solutions and mathematical modelling to explore a wide breadth of application areas.
Availability2020 Course Timetables
- Semester 2 - 2020
On successful completion of the course students will be able to:
1. Formulate differential equation models arising from the mathematical modelling of real-life problems and assess their implications for answering questions of practical importance.
2. Solve important classes of differential equations analytically and numerically.
3. Analyse important classes of numerical methods to approximate solutions of differential equations.
4. Use qualitative analysis of important classes of differential equations to investigate properties of their solutions.
Topics will include:
- Differential equations and mathematical modelling
- Analytical solution techniques of ordinary differential equations including systems
- Numerical solution techniques: Taylor series and Runge-Kutta methods, error analysis, step-size control and stability
- Existence, uniqueness and continuous dependence on the data
- Stability of solutions
- Lyapunov techniques
- The phase plane
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.