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

An essential skill for practicing applied mathematicians and engineers is the derivation and implementation of computational models for solving the equations that govern many of the physical processes encountered in research and industry. Through the investigation of specific case studies, the derivation of numerical techniques, the implementation of efficient algorithms and the visualisation of the simulation results, you will develop an understanding of the value of computational mathematics.

Aims

This unit provides you with the opportunity to employ a number of the skills that you have developed in the discipline of computational mathematics, combining them in a coherent manner for solving topical and relevant real world problems. You will become familiar with the methodologies for developing numerical algorithms that can be employed for problems that would otherwise be unsolvable, and with the skills of communicating the results of your numerical studies to a diverse audience.

Objectives

On satisfactory completion of this unit, you should be able to:

1. Identify and develop skills associated with the formulation of mathematical models for problems where there is dependence in both time and space.
2. Develop numerical algorithms for solving linear and nonlinear partial differential equations in one and two spatial dimensions on regular structured grids.
3. Develop numerical algorithms for solving nonlinear systems of algebraic equations.
4. Use MATLAB to implement the algorithms discussed throughout the unit and apply them to solve real world problems.
5. Engage critical, analytical and communication skills though a combination of report writing, group collaboration, individual problem solving and computer programming.

Content

Content will be based on the following topics:

1. Introduction and the Diffusion Equation: A discussion of the conservation equations that describe fluid motion. A brief look at the types of problems analysed in this unit, including the generalised diffusion equation. Discussion of boundary and initial conditions.
2. Introduction to Finite Volume Methods: Basic concepts and rules of the finite volume method. Application to the generalised diffusion equation. Cell-centred and vertex-centred schemes. Treatment of diffusion coefficients at control volume boundaries. Incorporating boundary condition information into the model and the treatment of initial conditions. Extension to two spatial dimensions.
3. Solution of nonlinear systems: Newton's method, inexact Newton methods, globally convergent methods.

Approaches to Teaching and Learning

Essential theoretical material as outlined above will be delivered to you by way of lecture presentations and reinforced by way of practical demonstration using MATLAB.

You will be exposed to a variety of numerical techniques for solving partial differential equations and nonlinear systems of equations. You will develop and implement the underlying algorithms in MATLAB. In addition, there will be real-world problem solving by formulating and solving various case study models.

There will be four contact hours per week, of which two hours will be located in the computer laboratory.

Assessment

All assessment contributes to your grade.Feedback will be available on your progress.

Assessment name: Problem Solving
Description: There will be two problem solving exercises, which will be undertaken in small groups. These exercises will test your ability to solve real-world problems using the techniques outlined above, as well as your ability to present your results and communicate your findings both orally and as a written report.
Relates to objectives: 1 to 5.
Weight: 50%
Internal or external: Internal
Group or individual: Individual
Due date: Mid & End Semester

Assessment name: Examination
Description: End of semester examination.
Relates to objectives: 1 to 5.
Weight: 50%
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

Text:

There are no set texts for this unit.

References:

1. Atkinson KE (1998) An Introduction to Numerical Analysis, Wiley

2. Bradie B (2006) A Friendly Introduction to Numerical Analysis, Pearson

3. Burden RL & Faires JD (2002) Numerical Analysis, 7th edition, PWS-KENT Publishing Company

4. Kelley CT (1995) Iterative Methods for Linear and Nonlinear Equations, SIAM

5. Morton KW (1996) Numerical Solution of Convection-Diffusion Problems, Chapman & Hall

6. Patankar SV (1980) Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing, McGraw Hill

7. Schilling RJ & Harris SL (2000) Applied Numerical Methods for Engineers using Matlab and C, Brooks/Cole

8. Saad Y (1996) Iterative Methods for Sparse Linear Systems, Boston: PWS Publishing Co

9. Versteeg HK & Malalasekera W (1995) An introduction to Computational Fluid Dynamics: the finite volume method, Pearson.

Many other good references pertaining to the topic are available in the Library.

Risk assessment statement

There are no out of the ordinary risks associated with this unit, as all classes will be held in ordinary lecture theatres or computer laboratories. Rules pertaining to health and safety in computer labs will be provided. Emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the University policy on health and safety.

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: 19-Oct-2012