MATH2800
10 units
2000 level
Course handbook
Description
Differential equations provide one of the most powerful mathematical tools for understanding the natural world. Since rates of change are commonly expressed using derivatives, single and systems of 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 (ODEs). This course introduces students to the world of ODEs. The main focus of the course will be to investigate analytical and numerical solution techniques, qualitative behaviour of solutions and mathematical modelling to explore a wide breadth of application areas. A large component of the analysis of systems of first order linear ODEs and of nonlinear systems near critical points involves applications of linear algebra techniques.
Availability2024 Course Timetables
Callaghan
- Semester 1 - 2024
Learning outcomes
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, interpret solutions 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 including applications of linear algebra to investigate properties of their solutions.
Content
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
Assumed knowledge
MATH1120
Assessment items
Written Assignment: Assignments
Formal Examination: Examination
Demonstrated competency: Tutorial assessment
Quiz: Online Quizzes
In Term Test: Mid Semester Test
Contact hours
Semester 1 - 2024 - Callaghan
Lecture-1
- Face to Face On Campus 3 hour(s) per week(s) for 13 week(s) starting in week 1
Tutorial-1
- Face to Face On Campus 1 hour(s) per week(s) for 13 week(s) starting in week 1
- The tutorial may be held in a computer lab when needed.
Course outline
- MATH2800 - Semester 1, 2024 (Callaghan) (PDF, 224.2 KB)
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