MATH08013 2019 Mathematics 4
Full Title
Mathematics 4
Transcript Title
Mathematics 4
Code
MATH08013
Attendance
N/A %
Subject Area
MATH - 0541 Mathematics
Department
MECT - Mechatronics
Level
08 - Level 8
Credit
05 - 05 Credits
Duration
Stage
Fee
€
Start Term
2019 - Full Academic Year 2019-20
End Term
9999 - The End of Time
Author(s)
Leo Creedon
Programme Membership
SG_ETRON_K08 201900 Bachelor of Engineering (Honours) in Electronic and Computer Engineering
SG_EMECL_K08 201900 Bachelor of Engineering (Honours) in Mechanical Engineering
SG_EMTRN_K08 201900 Bachelor of Engineering (Honours) in Mechatronic Engineering
SG_EMTOL_K08 202400 Bachelor of Engineering (Honours) in Mechatronic Engineering
SG_EROBO_H08 202000 Bachelor of Engineering (Honours) in Robotics and Automation
SG_EELEC_H08 202000 Bachelor of Engineering (Honours) in Electronics and Self Driving Technologies
SG_EELCO_K08 202000 Bachelor of Engineering (Honours) in Electronic and Computer Engineering
SG_EMECS_H08 202400 Bachelor of Engineering (Honours) in Mechatronic Systems
SG_EMECH_K08 202200 Bachelor of Engineering (Honours) in Mechatronic Engineering
SG_EMECI_K08 202300 Bachelor of Engineering (Honours) in Mechatronic Engineering
SG_EROBO_H08 202400 Bachelor of Engineering (Honours) in Robotics and Automation
SG_EROBO_H08 202500 Bachelor of Engineering (Honours) in Robotics and Automation
Description
Level 8 Mathematics for 4th year classes in Mechatronics, Mechanical and Electronic Engineering.
Learning Outcomes
On completion of this module the learner will/should be able to;
1.
Use Taylor's series to approximate transcendental functions
2.
Use Fourier series to approximate periodic functions
3.
Calculate Discrete Fourier Transforms and inverse Discrete Fourier transforms of signals
4.
Solve first and second order difference equations using z-transforms
5.
Demonstrate an understanding of the concepts of vector space, dimension, rank, linear independence and spanning sets
6.
Solve geometrical problems using the i, j, k orthogonal triad system, and compute dot products and cross products. Compute projections and angles between vectors and interpret results geometrically
7.
Use first and second order differential and difference equations and linear algebra to model and solve engineering problems
Teaching and Learning Strategies
Lectures and tutorials
Module Assessment Strategies
CA and final examination
Repeat Assessments
Repeat final examination
Indicative Syllabus
1. Taylor's series and Taylor polynomials. Approximating transcendental functions in a neighbourhood of a point.
2. Even and odd functions, real Fourier series and complex Fourier series.
3. Complex roots of unity, Discrete Fourier Transforms and Inverse Discrete Fourier Transforms as symmetric linear transformations.
4. Sequences, sampling of functions, first and second order difference equations. Definition and properties of the z-transform. Inverse z-transform and left shift theorems. Solution of first and second order difference equations using z-transforms.
5. Introduction to abstract vectors as matrices. Linear independence (using Gaussian elimination), spanning sets, vector spaces, dimension and rank.
6. Vector geometry of 2, 3 and higher dimensions. The i, j, k orthogonal triad system, computation of dot products and cross products. Computation of projections and angles between vectors and interpretation of results geometrically.
7. Application of difference equations and linear algebra to model and solve engineering applications.
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 | Continuous Assessment Continious Assesment | Coursework Assessment | UNKNOWN | 30 % | OnGoing | 1,2,3,4,5,6,7 |
End of Semester / Year Assessment
| Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
|---|---|---|---|---|---|---|
| 1 | Final Exam | Final Exam | Closed Book Exam | 70 % | End of Term | 1,2,3,4,5,6,7 |
Full Time Mode Workload
| Type | Location | Description | Hours | Frequency | Avg Workload |
|---|---|---|---|---|---|
| Tutorial | Flat Classroom | Tutorial | 1 | Weekly | 1.00 |
| Lecture | Tiered Classroom | Theory | 2 | Weekly | 2.00 |
| Independent Learning | Not Specified | Independent Learning | 4 | Weekly | 4.00 |
Total Full Time Average Weekly Learner Contact Time 3.00 Hours
Part Time Mode Workload
| Type | Location | Description | Hours | Frequency | Avg Workload |
|---|---|---|---|---|---|
| Lecture | Distance Learning Suite | Lecture | 2 | Weekly | 2.00 |
| Tutorial | Distance Learning Suite | Tutorial | 1 | Weekly | 1.00 |
| Independent Learning | Not Specified | Independent Learning | 4 | Weekly | 4.00 |
Total Part Time Average Weekly Learner Contact Time 3.00 Hours
Module Resources
Non ISBN Literary Resources
|
Authors |
Title |
Publishers |
Year |
|
K.A.Stroud |
Engineering Mathematics |
Palgrave and Macmillan |
2007 |
Journal Resources
None
URL Resources
None
Other Resources
Khan Academy
Additional Information
None