# MATH08008 2013 Mathematics 4

### General Details

Full Title
Mathematics 4
Transcript Title
Mathematics
Code
MATH08008
Attendance
N/A %
Subject Area
MATH - Mathematics
Department
MENG - Mech. and Electronic Eng.
Level
08 - NFQ Level 8
Credit
05 - 05 Credits
Duration
Stage
Fee
Start Term
2013 - Full Academic Year 2013-14
End Term
9999 - The End of Time
Author(s)
Leo Creedon, Grace Corcoran
Programme Membership
SG_ETRON_K08 201300 Bachelor of Engineering (Honours) in Electronic Engineering SG_EMECH_K08 201300 Bachelor of Engineering (Honours) in Engineering in Mechatronics SG_EMECH_K08 201300 Bachelor of Engineering (Honours) in Engineering in Mechatronics SG_EELEC_N08 201300 Level 8 Certificate in Engineering in Electronic Engineering
Description

Maths for 4th year classes in M & E department

### Learning Outcomes

On completion of this module the learner will/should be able to;

1.

Use first and second order differential equations to model and solve engineering problems

2.

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

3.

Use Gaussian elimination to solve systems of m equations in n unknowns and apply this to networks (including electrical networks using Kirchoff's Laws)

4.

Calculate Fourier transforms and inverse Fourier transforms

5.

Solve first and second order difference equations using z-transforms

### Indicative Syllabus

1. Review of the solution of first and second order differential equations.  Application to model and solve engineering applications

2. 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

3. Gaussian elimination, solution of systems of m equations in n unknowns and applications to networks (including electrical networks using Kirchoff's Laws)

4. Calculate Fourier transforms and inverse Fourier transforms of functions using the theory of even and odd functions and complex numbers.  Calculate the magnitude spectra and phase spectra of a Fourier transform

5. 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

### 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

### 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

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
Other Resources

None