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

Building upon the foundations established in MAB120 or Senior Maths C, this unit addresses the significant role of mathematical modelling using differential equations for the description and resolution of simple and complex problems relevant to real world situations. The formulation and solution of such problems is supported by appropriate advanced mathematical concepts used for function approximation, differentiation and integration.

Aims

Undertaking this unit will allow you to develop your problem solving skills, especially in the context of advanced mathematical techniques applied to ordinary differential equations used to model real world problems. You will also gain a deeper understanding of the concepts of the derivative and the integral, and how these may be used in applied contexts.

Objectives

Successful completion of this unit will enable you to:

1. Demonstrate competency in the use and interpretation of mathematical notation.
2. Recognise, construct and solve ordinary differential equations, in mathematical and real world contexts.
3. Construct integrals relating to real world problems and calculate or approximate related solutions.
4. Demonstrate your ability to reduce complex problems to smaller elements.

Content

Continuity and differentiability of functions of a single variable will be considered in greater depth than covered in prerequisite studies. Techniques for integrating such as by parts and trigonometric substitution will be covered as well as simple approximations for integrals based on the Riemann sum. Applications of using integrals may include the calculation of volumes of revolution and centres of mass.

Various classes of differential equations will be discussed and appropriate solution methods described. Differential equations that may be classified as 1st order linear or non-linear, and 2nd order linear with constant coefficients will be the principal focus here. The use of Taylor and Fourier series for approximating functions, as well as advanced techniques such as solution by Laplace Transforms may be introduced.

Where appropriate relevant mathematical software will be introduced to support and illustrate concepts covered in the content of this unit.

Approaches to Teaching and Learning

Lectures: 3 hr/wk
Workshops: 1 hr/wk
Maths Access Centre: Strongly recommended for students needing further practice with concepts and applied techniques.

You are expected to attend lectures in which the unit content will be introduced and the associated skills will be demonstrated and discussed. You should also attend and participate in workshop sessions, designed to reiterate key elements of content and to provide you with directed assistance to develop your competency in the techniques required.

Participation in the voluntary Mathematics Access Centre support sessions is recommended for those students needing additional specific learning support.

Lecture, workshop, homework and related resources are provided via Blackboard and you are strongly encouraged to make use of these.

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 items 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: Exposition of techniques, with an emphasis on short answers required.
Relates to objectives: 1, 2, 3 and 4.
Weight: 30%
Internal or external: Internal
Group or individual: Individual
Due date: Mid Semester

Assessment name: Examination
Description: Exposition of techniques and problem solving, with a distribution of short and long answers required.
Relates to objectives: 1, 2, 3 and 4.
Weight: 60%
Internal or external: Internal
Group or individual: Individual
Due date: Mid and End Semester

Assessment name: Quiz/Test
Description: Exposition of techniques, short answers only.
Relates to objectives: 1, 2 and 3.
Weight: 10%
Internal or external: Internal
Group or individual: Individual
Due date: Early 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

Additional Reference:

1. Anton, Bivens and Davis. Calculus early transendentals, 9th Edition. Wiley. or

2 Fulford GR and Mallet DG Calculus and Differential Equations. Pearson

Risk assessment statement

There are no out of the ordinary risks associated with this unit since lectures and workshops are held in ordinary lecture theatres or computer laboratories. Basic safety procedures in computer laboratories will be given to you when entering the computer laboratory for the first time. In addition, emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the university's health and safety website for further information.

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: 29-Aug-2012