Module Details

Module Code: MATH8012
Title: Maths for EPS4
Long Title: Maths for EPS4
NFQ Level: Advanced
Valid From: Semester 1 - 2023/24 ( September 2023 )
Duration: 1 Semester
Credits: 5
Field of Study: 4610 - Mathematics
Module Delivered in: 1 programme(s)
Module Description: Further theory of Laplace transforms with relevant applications. Z-transforms and their application to the solution of difference equations. Introduction to statistical inference and hypothesis testing. The Exponential and Weibull probability distributions and their application to reliability modelling.
 
Learning Outcomes
On successful completion of this module the learner will be able to:
# Learning Outcome Description
LO1 Apply the theory of Laplace transforms to the analysis of first- and second-order linear systems subject to impulsive and delayed inputs.
LO2 Use Z-transforms to solve first- and second-order difference equations relevant to electrical power systems.
LO3 Use sampling theory to determine confidence interval estimates of population means and carry out hypothesis testing.
LO4 Define the basic reliability functions, derive relationships between such functions and compute the reliabilities of series and parallel systems.
Dependencies
Module Recommendations

This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named MTU module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s).
14757 MATH7031 Transform Methods for E.Eng
Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list.
No incompatible modules listed
Co-requisite Modules
No Co-requisite modules listed
Requirements

This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section.
No requirements listed
 
Indicative Content
Laplace Transforms
Definition of the unit-impulse function, unit area property, sifting property and Laplace transform. Review of the Second Shift theorem with application to a variety of signals and waveforms relevant to electrical engineering. Solution of differential equations with step inputs, impulsive inputs and inputs containing delayed terms.
Z-transforms
Sequences, discrete functions, sampling. Examples of first- and second-order linear difference equations. Z-transform - definition and notation. Discussion of the properties of the Z-transform to include the first- and second-shifting properties. Z-transform of a sequence of sampled values of a continuous function. Determination of the inverse transform using table look-up and partial fractions. Solution of first- and second-order linear difference equations subject to specified initial conditions.
Statistical Inference
Review of prerequisites from probability theory including the Normal distribution. Discussion of the distribution of the sample mean via the Central Limit theorem. Confidence intervals for population means. Hypothesis tests – null hypothesis, alternative hypothesis. One-tailed and two-tailed tests.
Reliability
Probability distribution function, cumulative distribution function, reliability function. Failure rate function. Mean life. Exponential life distributions - constant failure rate, memoryless property. Weibull life distributions. The bathtub curve. Determination of the reliability of a system with exponential and Weibull components.
Module Content & Assessment
Assessment Breakdown%
Coursework30.00%
End of Module Formal Examination70.00%

Assessments

Coursework
Assessment Type Short Answer Questions % of Total Mark 15
Timing Week 5 Learning Outcomes 1
Assessment Description
Test 1 - Laplace Transforms
Assessment Type Short Answer Questions % of Total Mark 15
Timing Week 10 Learning Outcomes 2,3
Assessment Description
Test 2 - Z-Transforms/Sampling Theory
End of Module Formal Examination
Assessment Type Formal Exam % of Total Mark 70
Timing End-of-Semester Learning Outcomes 1,2,3,4
Assessment Description
End-of-Semester Final Examination
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.

The University reserves the right to alter the nature and timings of assessment

 

Module Workload

Workload: Full Time
Workload Type Contact Type Workload Description Frequency Average Weekly Learner Workload Hours
Lecture Contact Formal delivery of module content Every Week 3.00 3
Tutorial Contact Review of lecture material, assistance with exercise sheets, further questions Every Week 1.00 1
Independent & Directed Learning (Non-contact) Non Contact Independent study, completion of exercise sheets, preparation for assessments Every Week 3.00 3
Total Hours 7.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
Workload: Part Time
Workload Type Contact Type Workload Description Frequency Average Weekly Learner Workload Hours
Lecture Contact Formal delivery of module content Every Week 2.00 2
Tutorial Contact Review of lecture material, assistance with exercise sheets, further questions Every Week 1.00 1
Independent & Directed Learning (Non-contact) Non Contact Independent study, completion of exercise sheets, preparation for assessments Every Week 4.00 4
Total Hours 7.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 3.00
 
Module Resources
Recommended Book Resources
  • G. James and P. Dyke. (2018), Advanced Modern Engineering Mathematics, 5th Edition. Pearson Education, London, [ISBN: 129217434X].
  • A.Croft, R.Davison, M.Hargreaves and J. Flint. (2012), Engineering Mathematics: A Foundation for Electronic, Electrical, Communications and Systems Engineers, 4th Edition. Pearson, London, [ISBN: 0273719777].
Supplementary Book Resources
  • A. C. Grove. (1991), An introduction to the Laplace transform and the Z transform, Prentice Hall, New York, [ISBN: 0134889339].
  • D.C. Montgomery and G.C. Runger. (2013), Applied Statistics and Probability for Engineers, 6th edition. Wiley, New Jersey, [ISBN: 1118539710].
  • K. Singh. (2011), Engineering mathematics through applications, 2nd Edition. Palgrave Macmillan, London, [ISBN: 023027479X].
This module does not have any article/paper resources
Other Resources
 
Module Delivered in
Programme Code Programme Semester Delivery
CR_EEPSY_8 Bachelor of Engineering (Honours) in Electrical Engineering 7 Mandatory