Unit convenor and teaching staff |
Unit convenor and teaching staff
Lecturer
Elena Vynogradova
Contact via elena.vynogradova@mq.edu.au
E7A 204
Unit Convenor
Stuart Hawkins
Contact via stuart.hawkins@mq.edu.au
E7A 212
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Credit points |
Credit points
3
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Prerequisites |
Prerequisites
MATH133 or MATH136
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Corequisites |
Corequisites
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Co-badged status |
Co-badged status
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Unit description |
Unit description
This unit develops techniques and skills that are fundamental in the study and application of mathematics at an advanced level. In any successful application, two contrasting but complementary skills must be developed: the ability to formulate a given real-world problem in appropriate mathematical terms; and sufficient knowledge to obtain useful information and testable predictions from that model, by analytical and numerical means. The unit shows how differential equations arise as mathematical models of such real phenomena in science, engineering and the social sciences, and introduces some tools – Fourier series and numerical methods – for the study and eventual solution of these equations. Fourier series and transforms are particularly useful in those situations where the system response (and indeed many functions) can be seen as a complex sum of simpler vibrations or oscillations. When analytical methods fail, or provide only limited information about the model, numerical techniques are essential to quantify its behaviour precisely; some simple methods are introduced and the conditions under which reliable and accurate solutions may be obtained are described.
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Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates
On successful completion of this unit, you will be able to:
Name | Weighting | Due |
---|---|---|
Five assignments | 20% | Week 4, 6, 9, 11, 13 |
One Test | 20% | Week 7 |
Final examination | 60% | University Examination Period |
Due: Week 4, 6, 9, 11, 13
Weighting: 20%
Due: Week 7
Weighting: 20%
Due: University Examination Period
Weighting: 60%
Lectures: you should attend two hours of each lecture stream each week, making a total of four hours.
Tutorials: you should attend one tutorial each week.
The required text for MATH232 is available for download on
You should download and study these.
The online notes are intended primarily as a source of reference. These are not intended to be treated as the only source for learning.
The following texts provide useful references for various sections of the course:
Other similar texts are available in the Library.
Students are expected to have access to an internet enabled computer with a web browser and Adobe Reader software. Several areas of the university provide wireless access for portable computers. There are computers for student use in the Library and in the Numeracy Centre (C5A 255).
Difficulties with your home computer or internet connection do not constitute a reasonable excuse for lateness of, or failure to submit, assessment tasks.
WEEK |
A |
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TASK DUE |
1 |
Fourier series |
Introduction to modelling |
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2 |
Fourier series (ctd.). Bessel's inequality. |
Modelling with ordinary differential equations (ODEs) |
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3 |
Fourier series: convergence |
Models drawn from biology, physics and other fields |
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4 |
Fourier series: differentiation |
Assignment 1 |
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5 |
Fourier series: integration |
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6 |
Fourier series: application to ODEs and PDEs |
ODEs and phase plane |
Assignment 2 |
7 |
Fourier series: application to ODEs and PDEs (ctd.) |
Modelling with PDEs |
Test 1 |
MID-SEMESTER BREAK |
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8 |
Fourier transforms |
Heat and diffusion: PDE models |
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9 |
Fourier transforms (ctd.) |
Waves and potentials: PDE models |
Assignment 3 |
10 |
Fourier transforms: application to differential equations |
Modelling with maps |
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11 |
Laplace transforms, convolutions |
The logistic map: period doubling and chaos |
Assignment 4 |
12 |
Application to ODEs |
Brief introduction to numerical methods for ODEs |
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13 |
Revision |
Revision |
Assignment 5 |
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Academic Honesty Policy http://mq.edu.au/policy/docs/academic_honesty/policy.html
Assessment Policy http://mq.edu.au/policy/docs/assessment/policy.html
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In addition, a number of other policies can be found in the Learning and Teaching Category of Policy Central.
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This graduate capability is supported by:
Satisfactory performance on supervised assessment tasks, such as tests and the final exam, is necessary to pass this unit. If there is a significant difference between a student's marks on supervised assessment tasks and on unsupervised assessment tasks, the scaling of these tasks may be adjusted when determining the final grade, to reflect more appropriately that student's performance on supervised tasks.