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%
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 : 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