# 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%