Overview

Introduction to PDEs; first-order PDEs and characteristics, the advection equation, nonlinear equations. Classes of second-order PDEs; boundary and/or initial conditions for well-posed problems. The wave equation: exact solutions on infinite and finite spatial domains, other hyperbolic PDEs, reflection of waves. The heat equation: exact solutions on infinite domain, separation of … For more content click the Read More button below.

Offerings

S1-01-CLAYTON-ON-CAMPUS

Rules

Enrolment Rule

Contacts

Chief Examiner(s)

Dr Kengo Deguchi

Unit Coordinator(s)

Dr Kengo Deguchi

Learning outcomes

On successful completion of this unit, you should be able to:
1.

Understand the role of partial differential equations in the mathematical modelling of physical processes;

2.

Solve a range of first-order partial differential equations including using the 'method of characteristics';

3.

Appreciate the properties of the three basic types of linear second-order partial differential equations, including suitable initial and/or boundary conditions;

4.

Understand the mathematical properties of the diffusion equation, wave equation and Laplace's equation and solve them exactly under some simple conditions;

5.

Analyse and interpret simple applications modelled by the advection equation, diffusion equation and Laplace's equation;

6.

Understand the principles of finite-difference approximation of ordinary and partial differential equations and appreciate the advantages and disadvantages of a range of useful numerical techniques, including their stability;

7.

Evaluate numerical solutions of some partial differential equations using computers, and display those results graphically.

Assessment

1 - Continuous assessment
2 - Examination (3 hours and 10 minutes)

Scheduled and non-scheduled teaching activities

Applied sessions
Lectures

Workload requirements

Workload

Learning resources

Required resources

Other unit costs

Costs are indicative and subject to change.
Miscellaneous items required (unit course reader, printing, stationery) - $120.

Availability in areas of study

Applied mathematics
Financial and insurance mathematics
Mathematical statistics
Mathematics
Pure mathematics