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

Many real world problems are not solvable analytically, meaning that it is necessary to develop computational methods that can be used to solve these problems. Additionally, to be able to apply these methods to large problems, they must be implemented as algorithms in a computer language such as MATLAB. This unit addresses both the theoretical development of computational methods and their implementation in MATLAB.

Aims

The aim of this unit is to provide you with the introductory concepts, computational techniques and programming skills that will allow you to solve many real world problems. It is also designed to prepare you for study in further units in computational mathematics.

Objectives

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

1. Demonstrate a sound understanding of the basic concepts, knowledge and skills underlying computational mathematics by applying the concepts, knowledge and skills to specific problem types.
2. Apply programming skills to implement algorithms in MATLAB.
3. Engage critical and analytical thinking skills and communicate in writing appropriate to context.

Content

Discussions of numerical error and floating point arithmetic.
Roots of nonlinear functions: bisection method, fixed point iteration, Newton's method, secant method.
Solution of linear systems: substitution, Gaussian elimination, factorisation methods, iterative methods.
Interpolation: Lagrange polynomials, divided differences, forward differences.
Differentiation and integration: first and second order difference quotients, trapezoidal rule, Simpson's rule.
Ordinary differential equations: Euler's method, modified Euler method, Taylor methods, Runge-Kutta methods.

Approaches to Teaching and Learning

You are expected to attend lectures (3 hours per week) in which the course content will be presented and the computational techniques will be demonstrated. You are also expected to attend a practical session (1 hour per week) where the MATLAB programming language will be introduced, and subsequently used to implement the techniques discussed in lectures.

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 student where numbers allow.

Assessment

The assessment is designed to allow you to demonstrate your ability in each of the content areas, and to give you continual feedback on your progress.Formative feedback will be provided for the in-semester assessment items by way of 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: There will be ten individual problem solving exercises, equally weighted. They will consist of problems similar to those demonstrated in lectures and practical.
Relates to objectives: 1, 2, 3
Weight: 40%
Internal or external: Internal
Group or individual: Individual
Due date: Throughout Semester

Assessment name: Examination
Description: There are two exams included in this unit. The mid semester exam is a progressive examination that will assess you on your knowledge and ability in the first three sections of lecture content. The end of semester examination will assess you on your knowledge and ability in all sections of lecture as well as your ability to apply this knowledge to solve new problems.
Relates to objectives: 1, 3
Weight: 60%
Internal or external: Internal
Group or individual: Individual
Due date: Mid & End 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

There is no set text for this unit.

Two useful references are:

Bradie (2006) A Friendly Introduction to Numerical Analysis

Moler (2004) Numerical Computing with MATLAB. Available online:
http://www.mathworks.com/moler/chapters.html

Risk assessment statement

There are no out of the ordinary risks associated with this unit as lectures and practicals are conducted in standard QUT classrooms or computer laboratories. Emergency exits and assembly locations for each classroom associated with this unit will be described during the first week of classes. You are referred to the university policy on health and safety 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: 03-May-2012