Course Title: Differential Equations and Matrixes
Part B: Course Detail
Teaching Period: Term1 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
Brian Hayes
Office: 51:7:5
ph: 9925 4535
Michael Nyblom
Office 8.9.31
ph 9925 3763
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: |
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Performance Criteria: |
National Competency Code And Title |
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 |
| 11 Feb | 1 | First order differential Equations – Type 1, Type 2 |
| 18 Feb | 2 | First order differential Equations - Separable Variable |
| 25 Feb | 3 | First order Linear Differential Equations |
| 3 Mar | 4 | First Order Homogenous Differential Equations |
| 10 Mar | 5 | Revision / First Written Assignment Due 24th March Worth 10% |
| 17 Mar | 6 | Test 1 worth 40% |
| 24 Mar | 7 | Second order Linear Homogeneous Differential Equations |
| 31 Mar | 8 | Second order linear non- Homogeneous Differential Equations |
| 7 Apr | Student Vacation | |
| 14 Apr | 9 | Particular Integral – f(x) is a polynomial |
| 21 Apr | 10 | Particular Integral – f(x) is an exponential |
| 28 Apr | 11 | Particular Integral – f(x) is a trigonometrical |
| 5 May | 12 | Matrices |
| 12 May | 13 | Solving System of Linear Equations using Matrices |
| 19 May | 14 | Calculating Inverse of Square Matrix |
| 26 May | 15 | Eigen Vector and Eigen Values of Square Matrix |
| 2 Jun | 16 | Revision/ Second Written Assignment Due 16th June Worth 10% |
| 9 Jun | 17 | Test 2 worth 40% |
Learning Resources
Prescribed Texts
RMIT Lecture Notes |
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: 40% of overall score
Assignment One
Due Date: 24th March
Worth : 10% of overall score
Final Semester Examination
Topics: Second Order Differential Equations – Homogeneous and Non - Homogeneous Differential Equations with constant co-efficients, Matrices, and Eigen Vector Problems
Duration: 2 hours
Due Date: The week beginning with 9th June
Worth: 40%
Assignment 2
Due Date: The week beginning 16th June.
Worth: 10%
Assessment Matrix
Course Overview: Access Course Overview