Course Title: Mathematical Transforms
Part B: Course Detail
Teaching Period: Term1 2010
Course Code: BUSM6020L
Course Title: Mathematical Transforms
School: 155T Life & Physical Sciences
Campus: City Campus
Program: C6050 - Advanced Diploma of Electrical Engineering
Course Contact : Selva Venkatesan
Course Contact Phone: +61 3 9925 4964
Course Contact Email:selva.venkatesan@rmit.edu.au
Name and Contact Details of All Other Relevant Staff
Teacher: Michael Nyblom
Office: 8:9:31
Telephone 9925 2189
E-Mail : michael.nyblom@rmit.edu.au
Nominal Hours: 60
Regardless of the mode of delivery, represent a guide to the relative teaching time and student effort required to successfully achieve a particular competency/module. This may include not only scheduled classes or workplace visits but also the amount of effort required to undertake, evaluate and complete all assessment requirements, including any non-classroom activities.
Pre-requisites and Co-requisites
Satisfactory completion of Calculus & Vectors and Differential Equations
Course Description
Students will develop fundamental mathematical skills necessary to support articulation into tertiary studies in engineering. It provides students with basic techniques for differential equations which occur in engineering environment and the application of Fourier series and Laplace Transformations properties.
National Codes, Titles, Elements and Performance Criteria
National Element Code & Title: |
UTENES008A Provide technical leadership in the workplace |
Element: |
- |
Performance Criteria: |
UTENES008A Provide technical leadership in the workplace. |
Learning Outcomes
1. Determine Laplace Transformations with the aid of tables.
2. Apply the method of Laplace transformations to find solutions of initial value problems.
3. Determine the Fourier Series of periodic functions.
4 Determine half range Fourier sine and cosine series
5. Apply the method of separation of variables to solve the heat equation with prescribed boundary conditions and initial conditions
6. Apply the method of separation of variables to solve the wave equation with prescribed boundary conditions and initial conditions
Details of Learning Activities
Students will be provided with classroom tutorial instruction in each of the units to complete the learning outcomes, tasks and assessment outcomes using the
provided and recommended materials, references and the textbook.
Teaching Schedule
| Dates | Week Number | Content |
| 11 Feb | 1 | Basic results of Laplace Transforms |
| 18 Feb | 2 | Theorems of Laplace Transforms |
| 26 Feb | 3 | Inverse Transforms |
| 4 Mar | 4 | Solving Linear Differential Equations |
| 11 Mar | 5 | Solving Second order Differential Equations |
| 18 Mar | 6 | Review |
| 25 Mar | 7 | Test 1 worth 40% |
| 1 Apri | 8 | Periodic functions |
| 8 Apri | 9 | Even and Odd functions |
| 15 Apri | 10 | Fourier Coefficients |
| 22 Apri | 11 | Fourier Series of Periodic Functions |
| 29 Apri | 12 | Half Range Fourier Series |
| 6 May | 13 | Partial Differential Equations |
| 13 May | 14 | Normal Vectors, Tangent Planes and Directional Derivative |
| 20 May | 15 | Bounday Value Problems |
| 27 May | 16 | Revision |
| 3 June | 17 | Test 2 worth 40% |
Learning Resources
Prescribed Texts
RMIT Lecture Notes |
References
Advanced Engineering Mathematics, Fourth Edition, K. A. Stroud |
Other Resources
Overview of Assessment
Test 1 worth 50%
Test 2 worth 50%
Assessment Tasks
Students will be provided with exercises to practice the use of Laplace Transforms in solving Differential Equations with
various right-hand sides use in circuit theory. In addition students will be given exercises in the calculation of Fourier
Series and elementary vector calculus.
Assessment Matrix
Course Overview: Access Course Overview