Differential Equations
Overview
To provide students with knowledge of ordinary differential equations required for practising scientist and engineer.
Requisites
Rule
Concurrent Pre-requisite
MTH20011 Mathematics 4A
OR
MTH20005 Engineering Mathematics 3B *
OR
MTH20004 Engineering Mathematics 3A
OR
MTH20007 Engineering Mathematics 3A *
OR
TNE30003 Communications Principles
OR
Pre-requisite
EEE20002 Circuits and Systems
OR
MEE20008 Vibration and Signal Analysis
OR
MTH20012 Series and Transforms
01-June-2025
Learning outcomes
Students who successfully complete this unit will be able to:
- Systematically classify ordinary differential equations as linear or nonlinear, homogeneous or non-homogeneous, determine their order and degree and identify and solve Logistic, Bernoulli's and Riccati's equations
- Analyse and solve second order ODEs with non-constant coefficients including Legendre equation using power series method
- Apply Frobenius methods for solving equations with singular coefficients and Bessel functions
- Generate orthogonal solutions to second order differential equations and use them as the basis for orthogonal eigenfunction expansion
- Identify basic linear second order PDEs with constant coefficients: Laplace's, Poisson's, heat and wave equations, and solve them by separation of variables
- Discuss physical examples requiring formulation of second order linear PDEs in simple rectangular and circular geometries: oscillating membranes; propagating waves, heat propagation
Teaching methods
Hawthorn
| Type | Hours per week | Number of weeks | Total (number of hours) |
|---|---|---|---|
| On-campus Lecture | 4.00 | 12 weeks | 48 |
| On-campus Class | 1.00 | 12 weeks | 12 |
| Online Learning activities | 2.00 | 12 weeks | 24 |
| Unspecified Activities Independent Learning | 5.50 | 12 weeks | 66 |
| TOTAL | 150 |
Assessment
| Type | Task | Weighting | ULO's |
|---|---|---|---|
| Examination | Individual | 55% | 1,2,3,4,5 |
| Weekly Exercises | Individual | 45% | 1,2,3,4,5,6 |
Hurdle
As the minimum requirements of assessment to pass a unit and meet all ULOs to a minimum standard, an undergraduate student must have achieved:
(i) an aggregate mark of 50% or more, and(ii) at least 40% in the final exam.Students who do not successfully achieve hurdle requirement (ii) will receive a maximum of 45% as the total mark for the unit.
Content
- Review of simple ODEs: terminology, types of ODEs and review of methods of their solution studied previously
- Special first order ODEs: Verhulst (logistic) equation with applications, Bernoulli equation, Riccati equation.
- Second order ODEs with non-constant coefficients: variation of parameters, power series method, Legendre’s equation and Legendre polynomials, Frobenius method, Bessel equation and its solutions, Sturm-Liouville problems and orthogonal functions, orthogonal eigenfunction expansions.
- Linear second order partial differential equations: wave, heat and Laplace’s equations and their physical origins.
- Linear second order PDEs in multiple spatial dimensions: waves on a rectangular and circular membranes with applications, Laplacian in cylindrical and spherical co-ordinates, applications in complex geometries.
Study resources
Reading materials
A list of reading materials and/or required textbooks will be available in the Unit Outline on Canvas.