# 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 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%

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