Short Title:  Mathematics 6 

Full Title:  Mathematics 6 

Field of Study:  Mechanics and metal work 

Reviewed By:  FIONA CRANLEY 

Module Author:  PAUL ROBINSON 

Module Description:  The first aim of Mathematics 5 is provide the student with further transform based techniques so as to have completed a broad range of methods for the solution of engineering problems. A second aim of the module is to develop the students power of judgement in the selection of appropriate techniques for problem solving and the evaluation of results. Finally the module aims to complete the process of putting in place a firm mathematical foundation for future development of the student. 

Learning Outcomes 
On successful completion of this module the learner will be able to: 
LO1 
Recognise a Fourier series and explain its interpretation. [POa, POb] 
LO2 
Calculate Fourier coefficients in simple cases and deduce the Fourier series for periodic functions occurring in engineering. [POa, POb, POd] 
LO3 
Calculate Fourier series for even or odd engineering functions.[POa, POb, POd] 
LO4 
Calculate amplitude and phase spectra of engineering waves using Fourier transform techniques. [POa, POb, POd, POg] 
LO5 
Construct transfer functions of simple engineering systems using Fourier transform techniques.[POa, POb, POd, POg] 
LO6 
Calculate ztransforms using a standard table, linearity, shift theorems and multiplication theorems. [POa, POb] 
LO7 
Solve first and second order linear difference equations using ztransforms. [POa, POb, POd] 
Prerequisite learning 

Corequisite Modules
 No Corequisite modules listed 
Module Content & Assessment
Content (The percentage workload breakdown is inidcative and subject to change) 
% 
Fourier Series Classification of signals. Piecewise linear signals. Periodic signals. Even and odd signals.
Fourier synthesis – superposition of sinusoidal waves. Fourier’s Theorem and Fourier coefficients. Fourier series for piecewise constant and piecewise linear signals. Fourier Series for even and odd functions. Fourier Series for functions of arbitrary period. Review of complex numbers, polar and exponential form. Complex form of Fourier series. Parseval’s theorem and power spectra.

50.00% 
Introduction to Fourier Transforms The Fourier transform. Amplitude and phase spectra. Transfer functions and filters for simple systems.

20.00% 
zTransforms Review of sequences. Sampling and discrete time signals. Definition of the zTransform. Simple examples and table of common zTransforms. Linearity and shift theorems. Inverting zTransforms. Use of the zTransform to solve first and secondorder, linear difference equations with constant coefficients.

30.00% 
Assessment Breakdown  % 
Course Work  30.00% 
End of Module Formal Examination  70.00% 
Course Work 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Other 
High threshold test on Fourier series and transforms. 

15.00 
Week 7 
Practical/Skills Evaluation 
High threshold Key Skills test in basic mathematical techniques used to support this module 

15.00 
Every Second Week 
End of Module Formal Examination 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Formal Exam 
EndofSemester Final Examination 

70.00 
EndofSemester 
Reassessment Requirement 

Repeat examination Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element. 
IT Tallaght reserves the right to alter the nature and timings of assessment Module Workload
Workload: Full Time 
Workload Type 
Workload Description 
Hours 
Frequency 
Average Weekly Learner Workload 
Lecture 
No Description 
3.00 
Every Week 
3.00 
Lab 
No Description 
1.00 
Every Week 
1.00 
Independent Learning Time 
No Description 
3.00 
Every Week 
3.00 
Total Weekly Learner Workload 
7.00 
Total Weekly Contact Hours 
4.00 
This module has no Part Time workload. 

Module ResourcesRequired Book Resources 

 Glyn James... [et al.], Modern engineering mathematics [ISBN: ISBN: 0130183199]
 Recommended Book Resources 

 KA Stroud with additions by Dexter J Booth 2003, Advanced Engineering Mathematics, Palgrave Macmillan
 K.A. Stroud, Dexter J. Booth,, Advanced Engineering Mathematics
 Glyn James... [et al.] 1999, Advanced modern engineering mathematics, Prentice Hall Harlow [ISBN: ISBN: 0201596210]
 Erwin Kreyszig 1999, Advanced Engineering Mathematics, John Wiley and Sons (WIE)
 Anthony Croft, Robert Davison, Martin Hargreaves, Engineering mathematics [ISBN: ISBN 0130268585]
 This module does not have any article/paper resources 

This module does not have any other resources 

Module Delivered in
