Units

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Sample subject outline - Semester 1 2013

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

Rationale

One of the most exciting and rewarding areas in mathematics is that of mathematical modelling, which involves the application of mathematical ideas to the investigation of "real-world" problems. Mathematics is being increasingly applied to areas such as economics, finance, biology, medicine and industrial situations and as such, an understanding of the role and potential of mathematical modelling is an important component in the education of any scientist or mathematician.

Aims

The aim of this unit is to develop concepts, skills and an understanding of Mathematical Modelling by providing examples and outlining the steps required in the development, analysis and interpretation of a model using 'real-world' problems and associated mathematical software to solve these problems.

Objectives

1. Improved communication skills by emphasising the need to write mathematical arguments and the conclusions drawn from the mathematical models developed, in logical and clear English.
2. Enhanced critical and analytical thinking skills by formulating ordinary and partial differential equations as models of "real-world" problems.
3. Competency in the use of software packages used to obtain numerical solutions of ordinary differential equations and diffusion-like partial differential equations.
4. An ability to draw on a range of knowledge and thinking skills to develop mathematical models, choose between different modelling techniques on the basis of their suitability to the problem being investigated and the form of the solutions obtained, and to write reports on your findings.

Content

The mathematical models will focus on those that arise from fluid mechanics. Key topics covered include: Formulation of Navier-Stokes equation (Cartesian tensors, continuity equation, the stress tensor, Navier-Stokes equations for a viscous fluid, scaling and the Reynolds number); Unidirectional flows (exact solutions of the Navier-Stokes equations, shear flow, Poiseuille flow (flow in a tube) , oscillating flows). Other topics: A selection from: Thin-film flows, Low Reynolds number flows, similarity solutions, boundary layers, computational fluid dynamics, flow in porous media, visco-elastic fluids, water wave theory.

Approaches to Teaching and Learning

An overview lecture will be given each week. However you will be expected to do additional reading outside of class time. Reading material and selected exercises will be provided and should be studied prior to each class. You will have opportunities to apply your knowledge in problem-solving exercises with guidance from the lecturer (either in class or in informal consultation outside of class times).

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 increasing 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: (Formative/Summative) - A number of assignments that extend the unit material will be given. The assignments will be returned to you with comments and marks. These assignments may involve the use of appropriate computer software to visualise results and to present the results as a professional report.
Relates to objectives: 1, 2, 3, 4
Weight: 40%
Internal or external: Internal
Group or individual: Group
Due date: Progressive

Assessment name: Examination (written)
Description: (Summative) - The final examination will allow you to demonstrate the level of newly acquired knowledge in the material of the unit.
Relates to objectives: 2, 4
Weight: 60%
Internal or external: Internal
Group or individual: Individual
Due date: Exam Period

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

Texts:
There is no single nominated text for this unit. Some printed notes will be provided on Blackboard.

References:
Appropriately detailed, fully referenced reading material will be issued throughout the semester, as appropriate.

Risk assessment statement

There are no out of the ordinary risks associated with this unit. Emergency exits, evacuation procedures and assembly areas will be described in the first few lectures. More information can be found on the university's Health and Safety web site at 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: 21-Feb-2013