|Course code MATH2800||Units 10||Level 2000||Faculty 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
|Objectives||On 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.
|Content||Topics 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
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.
|Modes of Delivery||Internal Mode|
|Contact Hours||Tutorial: for 1 hour(s) per Week for Full Term|
Lecture: for 3 hour(s) per Week for Full Term
|Timetables||2015 Course Timetables for MATH2800|