# Course Title: Differential Equations and Matrixes

## Part B: Course Detail

Teaching Period: Term2 2009

Course Code: BUSM6021L

Course Title: Differential Equations and Matrixes

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

Dr. Ejanul Haque
Building 51 Level 6 Room 21
Ph: 9925 4530
ejanul.haque@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 and Vectors

Course Description

Students will develop fundamental mathematical skills necessary to support articulation into tertiary studies in engineering. It involves mathematical objects such as differential equations, matrices and series, which are needed by electronic engineer.

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. Analyse and subsequently model physical situations described by differential equations

2. Interpret the solutions to first order linear and separable differential equations in terms of the physical problem

3 Interpret solutions to second order linear differential equations having constant coefficients which correspond to damping and resonance

4. Apply the concept of convergence of a series and investigate the behaviour of positive term and alternating series

5. Determine power series expansions for functions to manipulate standard power series

6. Perform basic operations on matrices

7. Use row-echelon forms to solve systems of linear equations and to determine the inverse of a matrix/

8. Interpret 3 X3 matrices geometrically, especially rotation matrices

9. Determine eigenvalues and eigenvectors of a matrix

10. Determine partial derivatives of a function of several variables and understand their physical/geometric significance

11. Use space curves to specify motion of a body through space and determine the body’s velocity

12. Determine the directional derivative and gradient of a scalar function

13. Understand the geometric significance of for a surface defined by

14. Apply functions of several variables to problems involving errors and maxima/minima

15. Evaluate simple double integrals and interpret as volume of region under a given surface

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 06 Jul 1 First order Differential Equations – Type 1, Type 2 13 Jul 2 First order Differential Equations - Variable Separable 20 Jul 3 First order Linear Differential Equations (Integrating Factor) 27 Jul 4 First Order Homogenous Differential Equations 03 Aug 5 Application of First order Differential Equations 10 Aug 6 Second order Linear Homogeneous Differential Equations 17 Aug 7 Second order linear non- Homogeneous Differential Equations 24 Aug 8 Mid semester test 31 Aug 8 Mid semester break (31 Aug-06 Sep) 07 Sep 9 Particular Integral – f(x) is a polynomial 14 Sep 10 Particular Integral – f(x) is an exponential 21 Sep 11 Particular Integral – f(x) is a trigonometrical 28 Sep 12 Matrices 05 Oct 13 Solving System of Linear Equations using Matrices 12 Oct 14 Calculating Inverse of Square Matrix (Written Assignment Due) 19 Oct 15 Eigen Vector and Eigen Values of Square Matrix 26 Oct 16 Eigen Vector and Eigen Values of Square Matrix 02 Nov/09 Nov 17/18 End semester test

Learning Resources

Prescribed Texts

 RMIT Lecture Notes Mathematical Methods for engineers and Scientists, Fourth Edition, G.F. Fitz-Gerald and I.A. Peckham

References

 Advanced Engineering Mathematics, Fourth Edition, K.A. Stroud

Other Resources

Students will be expected to bring a scientific or graphic calculator to each class.

Overview of Assessment

Test 1 worth 50%
Test 2 worth 50%

The assessment consists of Mid semester test worth 40%, an Assignment worth 10%, and End semester test worth 50% of total assessment.

The examinations will be closed book and consist of a series of short answer and application questions.

The assignment will be on application of defferential equations and student should complete it outside the class time.

Assessment Matrix

Assessment                              Topics Covered                            % of Total Assessment

Mid semester test                  Studied during week 1-7                                 40
Assignment                            Studied during week 1-11                              10
End semester test                 Studied during week 6-16                               50

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