Units

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Sample subject outline - Semester 2 2013

Note: Subject outlines often change before the semester begins. Below is a sample outline.

Rationale

Partial differential equations are the classical foundation of mathematical models used to unambiguously describe processes exhibiting spatial and temporal variation. There exist numerous modern important examples of such so called continuum models and so it is essential that any practicing mathematician be conversant with both the background, formulation and solution of such equations.

Aims

This unit aims to develop your understanding of the construction, analysis, solution and interpretation of partial differentil equation models of real-world processes.

Objectives

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

1. Characterize a broad class of mathematical models built upon various forms of partial differential equations and their associated boundary and initial conditions.
2. Demonstrate the execution of a number of standard solution methods for partial differential equations.
3. Demonstrate a sound understanding of the fundamental theory and concepts that underpin the solution methods for partial differential equations.
4. Draw on a range of knowledge and engage in analytical thinking skills to solve problems modelled using partial differential equations.
5. Communicate your understanding of the mathematical concepts and techniques developed in this unit, in both verbal and written forms.

Content

The motivation for, and the construction of partial differential equation models with particular reference to the classical models known as `The heat equation', `the wave equation' and `Laplace's equation'. Characterisation and classification of various partial differential equation models with particular reference to their associated boundary and initial conditions. Fundamental and background theory associated with the solution of partial differential equations such as the definitiion and application of orthogonal functions and Sturm-Liouville systems. The Solution of partial differential equations by method of separation of variables, and eigenfunction expansions. The Solution of partial differential equations by the Fourier and Laplace trnasformation methods, and by the method of Green's functions.

Approaches to Teaching and Learning

The material presented in this unit will be context based utilising a wide variety of both classical and modern examples. The emphasis will be on learning through experience, learning in groups and as individuals, written and oral communication, and developing skills and attitudes to promote life-long learning. Whole-of-class lectures as well as traditional small group workshops requiring the active solution of real-world problems will form part of the learning and teaching strategy for this unit. A combination of discussion, working on small real world problems and presenting solutions will promote creativity in problem solving, critical assessment skills and intellectual debate.

Note that this unit is being taught concurrently with an undergraduate offering of the same subject. University policy permits that postgraduate and undergraduate students attend the same lectures. Separate workshop/discussion groups will be provided for postgraduate students where numbers allow. As a postgraduate student you will be required to complete separate or additional assessment.

Assessment

The assessment items in this unit are designed to determine your level of competency, measured against criteria, in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.Formative feedback will be provided for the in-semester assessment tasks by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required.

Summative feedback will be provided throughout the semester with progressive posting of results via Blackboard.

Assessment name: Problem Solving Task
Description: This assessment will involve a number of individual tasks generally consisting of traditional pen-and-paper exercises. Formative and summative.
Relates to objectives: 1 to 5
Weight: 40%
Internal or external: Internal
Group or individual: Individual
Due date: Progressive

Assessment name: Examination (Theory)
Description: Exposition of techniques and problem solving, with a distribution of short and long answers required.
Relates to objectives: 1 to 5
Weight: 60%
Internal or external: Internal
Group or individual: Individual
Due date: End of Semester

Academic Honesty

QUT is committed to maintaining high academic standards to protect the value of its qualifications. To assist you in assuring the academic integrity of your assessment you are encouraged to make use of the support materials and services available to help you consider and check your assessment items. Important information about the university's approach to academic integrity of assessment is on your unit Blackboard site.

A breach of academic integrity is regarded as Student Misconduct and can lead to the imposition of penalties.

Resource materials

References:

The library contains a comprehensive selection of suitable books on Partial Differential Equations. Some suggestions are:

1. Trim, Applied Partial Differential Equations, Prindle, Weber and Schmidt
2. Snider, Partial Differential Equations, Prentice Hall
3. Zill DG & Cullen MR (2009) Differential Equations with Boundary-Value Problems, 7th edition, Thomson

Risk assessment statement

There are no out of the ordinary risks associated with this unit as lectures and workshop are conducted in standard QUT classrooms. Emergency exits and assembly locations for each classroom associated with this unit will be described during the first week of classes. Information regarding health and safety can be found at the following web-site http://www.hrd.qut.edu.au/healthsafety/.

Disclaimer - Offer of some units is subject to viability, and information in these Unit Outlines is subject to change prior to commencement of semester.

Last modified: 23-May-2012