Differential Equations

Course code MATH2800Units 10Level 2000Faculty of Science and Information TechnologySchool of Mathematical and Physical Sciences

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.

MATH2800 cannot be counted for credit with MATH2470.

Available in 2015

Callaghan CampusSemester 2
Previously offered in 2014
ObjectivesOn successful completion of this course, students will:

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.
ContentTopics will include:
1. Differential equations and mathematical modelling (model building, simplification, limitations and validation)
2. First order differential equations
3. Higher order differential equations
4. Systems of first order differential equations
5. Numerical solution techniques
6. Partial differential equations (heat equation, wave equation and
Laplace's equation)
7. 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.
Replacing Course(s)n/a
Industrial Experience0
Assumed KnowledgeMATH2310
Modes of DeliveryInternal Mode
Teaching MethodsLecture
Computer Lab
Assessment Items
Essays / Written Assignments
Examination: Formal
Quiz - Class
Contact HoursTutorial: for 1 hour(s) per Week for Full Term
Lecture: for 3 hour(s) per Week for Full Term
Timetables2015 Course Timetables for MATH2800