Short Title:Mathematics 6
Full Title:Mathematics 6
Module Code:MATH H3006
Credits: 5
NFQ Level:7
Field of Study:Mechanics and metal work
Module Delivered in 5 programme(s)
Module Description:The first aim of Mathematics 6 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 apply numerical implementations of transforms to sampled signals and data. 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 and interpret a real or complex Fourier series and be able to rewrite both in either form [POa, POb]
LO2 Calculate real Fourier coefficients in simple cases (including even and odd functions/extensions) and deduce the Fourier series for periodic functions occurring in engineering. [POa, POb, POd]
LO3 Construct piecewise defined functions in Matlab and Excel VBA using Case statements and recursion and calculate their Fourier Series. [POa, POb, POd]
LO4 Calculate amplitude and power spectra of engineering waves using Fourier transform techniques, including implementing the FFT in Matlab to calculate these numerically . [POa, POb, POd, POg]
LO5 Construct transfer functions of simple engineering systems using Fourier transform techniques.[POa, POb, POd, POg]
LO6 Calculate z-transforms and z transfer functions using a standard table, linearity, shift theorems and multiplication theorems. [POa, POb]
LO7 Solve first and second order linear difference equations using z-transforms. [POa, POb, POd]
Pre-requisite learning
Co-requisite Modules
No Co-requisite 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 and even and odd extensions. Fourier Series for functions of arbitrary period. Review of complex numbers, polar and exponential form. converting from real to omplex form of Fourier series. Parseval’s theorem and power spectra.
Introduction to Fourier Transforms
The Fourier transform. Amplitude and phase spectra. Transfer functions and filters for simple systems. Fast Fourier Transform in Matlab and sampling.
Review of sequences. Sampling and discrete time signals. Definition of the z-Transform. Simple examples and table of common z-Transforms. Linearity and shift theorems. Inverting z-Transforms. Use of the z-Transform to find transfer functions and to solve first and second-order, linear difference equations with constant coefficients.
Assessment Breakdown%
Course Work30.00%
End of Module Formal Examination70.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Other Calculate Fourier Series and their associated spectra 1,2,3,4 10.00 Week 7
Practical/Skills Evaluation High threshold Key Skills test in basic mathematical techniques used to support this module 2,4,5,7 10.00 Every Second Week
Laboratory Use Matlab to sample and edit a sound (.wav file) using a filter (Matlab function) 4,5 10.00 Week 10
End of Module Formal Examination
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Formal Exam End-of-Semester Final Examination   70.00 End-of-Semester
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 Resources

Required 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

Programme Code Programme Semester Delivery
TA_EBIOM_B B.Eng (Hons) in Biomedical Design 6 Mandatory
TA_EAMEC_B B.Eng(Hons) in Mechanical Engineering [Ab Initio] 6 Mandatory
TA_EBIOM_D Bachelor of Engineering in Biomedical Design 6 Mandatory
TA_EAMEC_D Bachelor of Engineering in Mechanical Engineering 6 Mandatory
TA_EAUTO_D Bachelor of Mechanical Engineering (Automation) 6 Mandatory