Course Title: Differential Equations and Matrixes

Part B: Course Detail

Teaching Period: Term1 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

Donna Baker

Office 8.9.71 ph 9925 3763

donna.baker@rmit.edu.au

Michael Nyblom

Office 8.9.71 ph 9925 3763

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:

-


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 NumberContent
11 Feb1First order differential Equations – Type 1, Type 2
18 Feb2First order differential Equations - Separable Variable
25 Feb3First order Linear Differential Equations
3 Mar4First Order Homogenous Differential Equations
10 Mar5Revision
17 Mar6Test 1 worth 50%
24 Mar7Second order Linear Homogeneous Differential Equations
31 Mar8Second order linear non- Homogeneous Differential Equations
7 Apr Student Vacation
14 Apr9Particular Integral – f(x) is a polynomial
21 Apr10Particular Integral – f(x) is an exponential
28 Apr11Particular Integral – f(x) is a trigonometrical
5 May12Matrices
12 May13Solving System of Linear Equations using Matrices
19 May14Taylor polynomials and infinite series
26 May15Power series
2 Jun16Partial Differentiation of a function of several variables
9 Jun17Test 2 worth 50%


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%


Assessment Tasks

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: The week beginning with 17th March

Worth: 50% of overall score

Final Semester Examination

Topics: Second Order Differential Equations – Homogeneous and Non - Homogeneous Differential Equations with constant co-efficients, Matrices and Power Series

Duration: 2 hours

Date: The week beginning with 9th June


Assessment Matrix

Course Overview: Access Course Overview