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
2. Determine the appropriate method of solving physical problems using Laplace
3. Solve first order differential equations using Laplace
4. Solve second order differential equations using Laplace
5. Solve simultaneous differential equations using Laplace
6. Identify the odd and even functions
7. Determine the Fourier Series for periodic functions
8. Determine the half range Fourier Series
9. Determine the Directional Derivatives and Tangent planes


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 NumberContent
 6 Jul1Basic results of Laplace Transforms
 13 Jul2Theorems of Laplace Transforms
 20 Jul3Inverse Laplace Transforms
 27 Jul4Solving Linear Differential Equations using Laplace
 3Aug5Solving Second order Differential Equations using Laplace
 10 Aug6Revision
 17 Aug7Test 1 worth 35%
 24 Aug8Periodic functions
 31 Aug Student Vacation
 7 Sep9Even & odd functions
 14 Sep10Fourier coefficients
 21 Sep 11Fourier series of periodic functions
 28 Sep12Half range Fourier sine and cosine series - Project (worth 10%)
 5 Oct13Partial Differential Equations
 12 Oct14Normal Vectors, Tangent Plane and Directional derivatives
 19 Oct15Boundary Value Problems
 26 Oct16Revision
 2 Nov17Test 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