# Course Title: Differential Equations and Matrixes

## Part B: Course Detail

Teaching Period: Term2 2008

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

Course Contact                     Dr. Michael Nyblom

Course Contact Phone       +61 3 9925  2189

Course Contact Email          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 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 textbooks.

Teaching Schedule

Note: Dates and activities may alter. students will be advisied in advance.

 Week starting Week No. Content 7 July 1 Review of Integration First Order Differential Equations- Type1, Type 2 14 July 2 First Order Differential Equations- Separable 21 July 3 First Order Linear Differential Equations 28 July 4 First Order Homogeneous Equations 4 August 5 Review 11 August 6 Test 1 Worth 50% 18 August 7 Second Order Linear Homogeneous Differential Equations 25 August 8 Second Order Linear Non-Homogeneous Differential Equations 1 September Week Vacation 8 September 9 Particular Integral- f(x) is polynomial type 15 September 10 Particular Integral- f(x) is exponential type 22 September 11 Particular Integral - f(x) is trigonometric type 29 September 12 Matrices Overview Algebra of Matrices 6 October 13 Solving Systems of Linear Equations 13 October 14 Eigen Vector and Eigen Value of Square Marices 20 October 15 Application of Eigenvalue and Eigen Vector of Matrices 27 October 16 Review 3 November 17 Test 2 Worth 50%

Learning Resources

Prescribed Texts

 RMIT Lecture Notes : Differential Equations. RMIT Lecture Notes : Matrices

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%

Mid Semester Test

Topics: First Order Differential Equations- Type 1 and Type 2. Differential Equations, Separable Variables, Linear Differential Equations and

Homogeneous Differential Equations.

Duration : 2 hours.

Date : Week beginninig with 11 August.

Worth : 50% of overall score.

Final Semester Exam

Topics : Second Order Differentail Equations - Homogeneous and Non-Homogeneous Differential Equations with constant co-efficients, Matrices, System of Linear Equations and

Eigen Vector and Eigen Value Problems for Matrices.

Duration : 2 hours.

Date : The week beginning with 3rd November.

Assessment Matrix

Course Overview: Access Course Overview