Course Title: Mathematical Transforms
Part B: Course Detail
Teaching Period: Term2 2009
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
Name: Ms. Aleksandra Labovic
Contact Phone: (03)9925 3763
Contact email: aleksandra.labovic@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: |
1. Identify appropriate method of finding Laplace of different types of functions |
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 in order to complete the learning outcomes, tasks and assessment outcomes using the provided and recommended materials, references and the textbook.
Teaching Schedule
Note: Dates and activities may alter. Students will be advised in advance.
Week Starting |
Week Number | Content |
| 6 Jul | 1 | Basic results of Laplace Transforms |
| 13 Jul | 2 | Theorems of Laplace Transforms |
| 20 Jul | 3 | Inverse Laplace Transforms |
| 27 Jul | 4 | Solving Linear Differential Equations using Laplace |
| 3Aug | 5 | Solving Second order Differential Equations using Laplace |
| 10 Aug | 6 | Revision |
| 17 Aug | 7 | Test 1 worth 35% |
| 24 Aug | 8 | Periodic functions |
| 31 Aug | Student Vacation | |
| 7 Sep | 9 | Even & odd functions |
| 14 Sep | 10 | Fourier coefficients |
| 21 Sep | 11 | Fourier series of periodic functions |
| 28 Sep | 12 | Half range Fourier sine and cosine series - Project (worth 10%) |
| 5 Oct | 13 | Partial Differential Equations |
| 12 Oct | 14 | Normal Vectors, Tangent Plane and Directional derivatives |
| 19 Oct | 15 | Boundary Value Problems |
| 26 Oct | 16 | Revision |
| 2 Nov | 17 | Test 2 worth 55% |
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
Mid Semester Test
Topics: Laplace Transforms – Theorems on Laplace Transforms, Inverse Laplace Transforms, and Solving First order & Second order Differential Equations using Laplace. (Week1 - Week6)
Duration: 2 hours
Date: The week beginning 18th August
Worth: 35% of overall score
Assignment
Duration: Two Weeks
Topics: topics covered from Week 1 to Week12
Final Semester Examination
Topics: Fourier Series - Periodic functions, Even and odd functions, Half range Fourier Series, Partial Differential Equations, tangent Plane, Normal vectors Directional Derivatives and Boundary Value Problems
Duration: 2 hours
Date: The week beginning 3rd Nov
Worth: 55% of overall score
Note: This course outline is subject to change. Students should check with their lecturer
Assessment Matrix
Course Overview: Access Course Overview