Overview

To provide students with knowledge of ordinary differential equations required for practising scientist and engineer.

Requisites

Prerequisites
MTH30002 Differential Equations

Rule

Concurrent Pre-requisite
MTH20011 Mathematics 4A
OR
MTH20012 Series and Transforms
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

Teaching Periods
Location
Start and end dates
Last self-enrolment date
Census date
Last withdraw without fail date
Results released date
Semester 1
Location
Hawthorn
Start and end dates
26-February-2024
26-May-2024
Last self-enrolment date
10-March-2024
Census date
31-March-2024
Last withdraw without fail date
12-April-2024
Results released date
02-July-2024

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
TOTAL150

Assessment

Type Task Weighting ULO's
ExaminationIndividual 55% 1,2,3,4,5 
Weekly ExercisesIndividual 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.