# MATH08013 2019 Mathematics 4

### General Details

Full Title
Mathematics 4
Transcript Title
Mathematics 4
Code
MATH08013
Attendance
N/A %
Subject Area
MATH - Mathematics
Department
MECT - Mechatronics
Level
08 - NFQ 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 Electronics 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 202000 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
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 Continuous 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

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

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