MXB322 Partial Differential Equations
To view more information for this unit, select Unit Outline from the list below. Please note the teaching period for which the Unit Outline is relevant.
| Unit code: | MXB322 |
|---|---|
| Prerequisite(s): | (MXB201 and MXB202) or MXB225 or MXB221 or MAB413 |
| Equivalent(s): | MAB613 |
| Assumed Knowledge: | MXB202 is assumed knowledge. |
| Credit points: | 12 |
| Timetable | Details in HiQ, if available |
| Availabilities |
|
| CSP student contribution | $555 |
| Domestic tuition unit fee | $3,324 |
| International unit fee | $4,296 |
Unit Outline: Semester 1 2024, Gardens Point, Internal
| Unit code: | MXB322 |
|---|---|
| Credit points: | 12 |
| Pre-requisite: | (MXB201 and MXB202) or MXB225 or MXB221 or MAB413 |
| Equivalent: | MAB613 |
| Assumed Knowledge: | MXB202 is assumed knowledge. |
| Coordinator: | Michael Dallaston | michael.dallaston@qut.edu.au |
Overview
Partial differential equations are the foundation of mathematical models that describe evolving processes exhibiting spatial and temporal variation. In this unit you will learn how the study of such equations synthesises and extends many of the concepts you have learned previously in linear algebra and calculus. The powerful frameworks of Fourier analysis and integral transforms that underpin partial differential equations provide a means for obtaining solutions to a number of equations of unparalleled physical importance, and for understanding the behaviour of mathematical models more generally.
Learning Outcomes
On successful completion of this unit you will be able to:
- Demonstrate knowledge of the principles of functional analysis and its relevance to analysing the solutions of partial differential equations.
- Employ a number of standard solution methods to solve partial differential equation problems in both applied and purely mathematical contexts.
- Critically apply the theory and techniques that underpin solution methods for partial differential equations to problems of an unfamiliar form or nature.
- Communicate in writing the assumptions, outcomes and interpretation of results of modelling real phenomena with partial differential equations.
Content
Linear PDEs of applied mathematics: heat equation, Laplace equation, wave equation. Classification and taxonomy of linear PDEs. Methods of solution including separation of variables, Fourier series, Fourier transforms, complex variable methods. Supporting mathematical theory and concepts for analysis of linear PDEs. Topics from functional analysis including function spaces, norms, inner products, orthonormal bases. Integral transforms and Fourier analysis.
Learning Approaches
Feedback on Learning and Assessment
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 Canvas.
Assessment
Overview
The assessment items in this unit are designed to determine your level of competency in meeting the unit 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
This task will provide you with an opportunity to exhibit newly acquired skills in the early material covered in the unit. This will also give you experience with the style of examination question used in your final exam.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Case Study
This assessment will provide you with the opportunity to apply your skills and knowledge to solve real-world problems using analytical solution techniques.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
Exposition of techniques and problem solving, with a distribution of short and long answers required.
The examination will require attendance on QUT campus.
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
There are many reference texts for this unit, many of which can be located in the library. There are also many online resources such as lecture notes and some e-books that can be found online. Example reference texts are:
1. Trim, Applied Partial Differential Equations, Prindle, Weber and Schmidt
2. Snider, Partial Differential Equations, Prentice Hall
3. Zill DG & Cullen MR (2013) Differential Equations with Boundary-Value Problems, 8th revised edition, Cengage.
Risk Assessment Statement
There are no out of the ordinary risks associated with this unit.