MATH07024 2016 Mathematics 3
Full Title
Mathematics 3
Transcript Title
Mathematics
Code
MATH07024
Attendance
N/A %
Subject Area
MATH - Mathematics
Department
MENG - Mech. and Electronic Eng.
Level
07 - NFQ Level 7
Credit
05 - 05 Credits
Duration
Stage
Fee
€
Start Term
2016 - Full Academic Year 2016-17
End Term
9999 - The End of Time
Author(s)
David Mulligan, Kevin Collins
Programme Membership
SG_ETRON_B07 201600 Bachelor of Engineering in Electronic Engineering
SG_EMECL_B07 201600 Bachelor of Engineering in Mechanical Engineering
SG_EMECH_B07 201700 Bachelor of Engineering in Engineering Mechatronics Systems Engineering
SG_EDATA_J07 201700 Bachelor of Engineering in Data Centre Facilities Engineering
SG_EELCO_B07 201700 Bachelor of Engineering in Electronic and Computer Engineering
SG_EELCO_B07 201800 Bachelor of Engineering in Electronic and Computer Engineering
SG_EDATA_J07 201900 Bachelor of Engineering in Engineering in Data Centre Facilities Engineering
SG_EMECH_H08 202400 Bachelor of Engineering (Honours) in Mechatronic Systems
Description
This module consists of topics from Integral and Differential Calculus, Linear Algebra and Complex Numbers. These topics include differential equations and applications, Laplace Transforms, De Moivre's Theorem, Fourier Transforms, Gaussian Elemination and z-transforms.
Learning Outcomes
On completion of this module the learner will/should be able to;
1.
Solve first order differential equations using separable variables technique and the integrating factor method
2.
Solve first and second order differential equations using Laplace transforms
3.
Solve second order differential equations using the complementary function and particular integral methods.
4.
Calculate powers of complex numbers using theorems of DeMoivre and Euler.
5.
Solve linear systems using Gaussian Elemination and apply this to engineering problems
6.
Be able to obtain the z-Transform of some standard functions and solve first order difference equations.
7.
Evaluate eigenvalues and eigenvetors and solve matrix transformation problems
Teaching and Learning Strategies
.
Module Assessment Strategies
.
Repeat Assessments
.
Indicative Syllabus
- First order differential equations: separation of the variables, exact and inexact forms. Solution of homogeneous differential equations (use of the substitution y= vx )Solution of linear differential equations using the Integrating Factor Method.
- Definition of Laplace transform and calculation of the Laplace transform and inverse Laplace transform of functions. First Shifting Theorem and Laplace transform of derivatives. Solution of first and second order differential equations using Laplace transforms.
- The homogeneous equation . Solution of the non-homogeneous equation using the complementary function and particular integral.
- DeMoivre's Theorem and Euler's Theorem for the polar form of a complex number. Argand diagrams and powers of complex numbers. Fourier transform of functions.
- Gaussian Elemination and applications.
- Eigenvalues and eigenvectors, matrix transformations.
Coursework & Assessment Breakdown
Coursework & Continuous Assessment
30 %
End of Semester / Year Formal Exam
70 %
Coursework Assessment
| Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
|---|---|---|---|---|---|---|
| 1 | CA 15% Semester 1, 15% Semester 2 | Coursework Assessment | Assessment | 30 % | OnGoing | 1,2,3,4,5,6,7 |
End of Semester / Year Assessment
| Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
|---|---|---|---|---|---|---|
| 1 | FE 35% Semester 2, 35% Semester 2 | Final Exam | Assessment | 70 % | End of Year | 1,2,3,4,5,6,7 |
Full Time Mode Workload
| Type | Location | Description | Hours | Frequency | Avg Workload |
|---|---|---|---|---|---|
| Lecture | Lecture Theatre | lecture | 2 | Weekly | 2.00 |
| Tutorial | Computer Laboratory | Tutorial | 1 | Weekly | 1.00 |
| Independent Learning | Not Specified | Independent Learning | 3 | Weekly | 3.00 |
Total Full Time Average Weekly Learner Contact Time 3.00 Hours
Part Time Mode Workload
| Type | Location | Description | Hours | Frequency | Avg Workload |
|---|---|---|---|---|---|
| Lecture | Not Specified | Independent Learning | 4 | Weekly | 4.00 |
Total Part Time Average Weekly Learner Contact Time 4.00 Hours
Online Learning Mode Workload
| Type | Location | Description | Hours | Frequency | Avg Workload |
|---|---|---|---|---|---|
| Lecture | Distance Learning Suite | Lecture | 2 | Weekly | 2.00 |
Total Online Learning Average Weekly Learner Contact Time 2.00 Hours
Module Resources
Non ISBN Literary Resources
|
Authors |
Title |
Publishers |
Year |
|
K.A.Stroud |
Engineering Mathematics |
Palgrave and Macmillan |
2007 |
Other Resources
None
Additional Information
None