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

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. This unit requires the use of elementary calculus (particularly the ability to solve simple differential equations), and represents the beginning of a coherent stream in Mathematical Modelling.

Aims

In this unit you will develop skills in the formulation and interpretation of mathematical models of "real-world" problems drawn from the literature, the media and the lecturer's own research areas. You will also develop and extend your skills in the use of mathematical software to investigate solutions of some of these models. By emphasising the need to write clear mathematical arguments and to explain in logical and clear English the conclusions drawn from the mathematical models developed in the unit, you will also develop your written communication skills.

Objectives

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

1. Employ calculus techniques to solve and further interpret solutions of differential equations

2. Formulate real world problems as differential equations and be able to critically understand the underlying assumptions in existing mathematical models

3. Write short, professional, reports of your findings which communicate clearly the assumptions of a model, how the model was arrived at, and interpretation of the results; and to use current technology to visualise the results.

Content

You are expected to have knowledge of solution techniques for 1st-order separable differential equations and constant coefficient 2nd-order differential equations, as taught in MAB121. Students are advised to revise this material prior to the start of semester.

Mathematical models will be selected from a diverse range of areas which could include: modelling the spread of infectious disease through a population during an epidemic or occurring endemically; heating and cooling problems (e.g. how to best insulate); modelling the oxygen distribution and growth of an isolated tumour; modelling the way populations interact in ecology (e.g. predator-prey interactions).

Strategies for how to formulate problems as differential equations will be demonstrated and discussed.

Techniques for analysing the models will be taught. These include: numerical and analytic solutions of the differential equations; and qualitative techniques, such as finding equilibrium points and analysing their stability.

An opportunity to learn about a mathematical model in an area of your interest will be available through your participation in a group project.

Case studies of some mathematical models used in the real world from research will be presented along with a critical analysis of whether these models have been used to influence policy.

Since this unit involves answering questions which involve the formulation of differential equations you should be aware that a good command of the English language is necessary to be able to accurately extract the key information needed to answer these questions.

Approaches to Teaching and Learning

During lectures, the textbook material will be augmented with a variety of related models designed to illustrate the development of the modelling skills and to give you precedents to help with your own working of problems and exercises. In addition there will also be a weekly practical session in a computer laboratory where you will learn to use appropriate computer software to numerically solve models involving differential equations and to visualise the behaviour of the solutions. These practical sessions also provide you with an opportunity to practise working problems with a demonstrator close at hand, and to request personal help with specific problems or types of problems.

Assessment

A range of activities will be assessed that will determine your competence in setting up and analysing and interpreting mathematical models as well as the ability to clearly communicate these in a technical written document. Your level of competency will be determined by measuring against given criteria.You are strongly encouraged to also use practical sessions as formative assessment by attempting a range of exercises and problems beforehand and seeking the demonstrator's advice on any difficulties or errors. These problems will form the basis of the final exam. Feedback will include the provision of answers and some fully worked solutions in the practical sessions and comments on submitted work.

Assessment name: Examination (Theory)
Description: You will sit a formal examination held during the examination period at the end of semester which will assess your understanding of the models presented in the lectures and practicals and the techniques used to analyse the models.
Relates to objectives: 1 and 2.
Weight: 60%
Internal or external: Internal
Group or individual: Individual
Due date: End of Semester

Assessment name: Problem Solving Task
Description: An assignment will be given early in the semester to provide you with some limited feedback of your understanding of some of the early concepts of mathematical modelling.
Relates to objectives: 1-3
Weight: 10%
Internal or external: Internal
Group or individual: Individual
Due date: Before end Semester

Assessment name: Report
Description: You will work to solve, analyse and possibly extend an existing model from a provided set of models from books and research papers. You will prepare a professional report based on of your investigations. The report will be due shortly after the middle of the semester. There will be an opportunity to work as a group to produce a comprehensive report.
Relates to objectives: 1-3
Weight: 30%
Internal or external: Internal
Group or individual: Individual
Due date: Late in 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

Texts:
Barnes B & Fulford GR (2008). Mathematical Modelling with Case Studies: A Differential Equation Approach using Maple and MATLAB, 2nd Edn, CRC Press. Further references: will be provided online on QUT Blackboard.

Software:
Software will be provided in QUT computer labs. Also some alternative freeware software will be given, so it is not mandatory to purchase software for this unit.

Risk assessment statement

There are no unusual risks associated with undertaking this unit. You will be made aware of fire exits in all classrooms, computer labs and lecture theatres. More information about health and safety can be found on the university's web site http://www.hrd.qut.edu.au/healthsafety/healthsafe/index.jsp.

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: 08-May-2012