Series and Transforms
Overview
This unit of study aims to provide students with mathematical knowledge and skills needed to support their concurrent and subsequent engineering and science studies. It also discusses important examples of applications of advance mathematical methods for science and engineering problems.
Requisites
AND ONE OF:
MTH10013 Linear Algebra and Applications
OR
MTH10003 Engineering Mathematics 2P *
OR
MTH10007 Engineering Mathematics 2 *
27-October-2024
Learning outcomes
Students who successfully complete this unit will be able to:
- Determine the convergence or divergence of infinite series, sequence of functions and series of functions (K2)
- Appreciate conceptual aspects of Fourier series expansions of periodic and periodically extended functions. Apply the technique in practice (K2, S1)
- Demonstrate a good understanding of the Laplace and Fourier transforms and their properties. Apply it for solving differential equations describing motion and forces (K2, S1)
Teaching methods
Hawthorn
| Type | Hours per week | Number of weeks | Total (number of hours) |
|---|---|---|---|
| On-campus Lecture | 4.00 | 12 weeks | 48 |
| On-campus Class | 1.00 | 12 weeks | 12 |
| Unspecified Activities Independent Learning | 7.50 | 12 weeks | 90 |
| TOTAL | 150 |
Assessment
| Type | Task | Weighting | ULO's |
|---|---|---|---|
| Examination | Individual | 50 - 60% | 1,2,3 |
| Online Quizzes | Individual | 5 - 15% | 1,2,3 |
| Test | Individual | 20 - 25% | 1,2 |
| Test | Individual | 20 - 25% | 2,3 |
Hurdle
As the minimum requirements of assessment to pass a unit and meet all ULOs to a minimum standard, an undergraduate student must have achieved:
(i) an aggregate mark of 50% or more, and(ii) at least 40% in the final exam.Students who do not successfully achieve hurdle requirement (ii) will receive a maximum of 45% as the total mark for the unit.
Content
- Infinite series: convergence, divergence and tests of convergence. Sequences of functions and series of functions: properties and applications.
- Fourier series: Fourier series expansion, functions defined over a finite interval, differentiation and integration of Fourier series, engineering and science applications
- Laplace and Fourier transforms: definitions, properties and usage, solution of differential equations, step functions, engineering and science applications.
Study resources
Reading materials
A list of reading materials and/or required textbooks will be available in the Unit Outline on Canvas.