MXB226 Computational Methods 1

Unit Outline: Semester 2 2024, Gardens Point, Internal

Overview

This is a foundational unit for Computational Mathematics. It introduces the design and implementation of mathematical models that can then be solved using techniques in Computational Mathematics. These techniques will be analysed for important properties such as efficiency, stability, convergence and error. The main topics that will be covered include: finite difference methods for models of heat diffusion in two dimensions; direct and iterative methods for linear systems; efficient storage of data; approximation; numerical integration; numerical methods for ordinary differential equations.

Learning Outcomes

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

1. Demonstrate knowledge of mathematical principles underpinning the discretisation of continuous problems into discrete approximations.
2. Implement computational algorithms using MATLAB and synthesise individual components into high-level computational tools.
3. Critically select and apply appropriate computational algorithms, including the use of specialised data structures, to solve practical problems.
4. Engage communication skills through a combination of report writing, code documentation, group collaboration and individual problem-solving.

Content

Learning Approaches

This unit is strongly practical-based, with much of your learning taking place in the form of practical activities conducted in the computer lab. Here, you will have the opportunity to put in practice the theoretical knowledge you have gained from the weekly lectures. By implementing, experimenting with and profiling the relevant algorithms in MATLAB, you will gain an appreciation for the art and science of algorithm selection and design.
The material presented will be context-based utilising examples from a range of real-world applications and purely mathematical scenarios. The emphasis will be on learning by doing, learning in groups and as individuals, written and oral communication, and developing skills and attitudes to promote life-long learning. You will work with experts and peers to develop effective methods/approaches for communicating, retrieving, evaluating and presenting information.

Feedback on Learning and Assessment

Formative feedback will be provided for the in-semester assessment items by way of written comments, student perusal of marked assessment pieces and informal interview as required.

Summative feedback will be provided throughout the semester with progressive posting of results via Canvas.

Assessment

Overview

The assessment items in this unit are designed to determine your level of competency in meeting the unit learning outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.

Unit Grading Scheme

7- point scale

Assessment Tasks

Assessment: Problem Solving Task

The problem solving task is comprised of 9 components (each worth 5 marks) where you will implement the techniques discussed in lectures using MATLAB and conduct theoretical proofs.

This is an assignment for the purposes of an extension.

Assessment: Case Study

The case study will consider a real-world application where spatial discretisation leads to a large, sparse, structured linear system of equations. You will derive this system, investigate and compare different methods for its solution, and present your findings in a report.

This is an assignment for the purposes of an extension.

Assessment: Presentation

Each group will give a presentation of the outcomes of the case study.

This is an assignment for the purposes of an extension.

Academic Integrity

Students are expected to engage in learning and assessment at QUT with honesty, transparency and fairness. Maintaining academic integrity means upholding these principles and demonstrating valuable professional capabilities based on ethical foundations.

Failure to maintain academic integrity can take many forms. It includes cheating in examinations, plagiarism, self-plagiarism, collusion, and submitting an assessment item completed by another person (e.g. contract cheating). It can also include providing your assessment to another entity, such as to a person or website.

You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.

Further details of QUT’s approach to academic integrity are outlined in the Academic integrity policy and the Student Code of Conduct. Breaching QUT’s Academic integrity policy is regarded as student misconduct and can lead to the imposition of penalties ranging from a grade reduction to exclusion from QUT.

Resources

Risk Assessment Statement

There are no out of ordinary risks associated with this unit.