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MATH7031 - Transform Methods for E.Eng

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Title:Transform Methods for E.Eng
Long Title:Transform Methods for Elect. Eng.
Module Code:MATH7031
 
Duration:1 Semester
Credits: 5
NFQ Level:Intermediate
Field of Study: Mathematics
Valid From: Semester 1 - 2020/21 ( September 2020 )
Module Delivered in 4 programme(s)
Module Coordinator: David Goulding
Module Author: VIOLETA MORARI
Module Description: no description provided
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1 Find the Laplace transform of those functions which arise in electrical and electronic engineering.
LO2 Use Laplace transform theory to analyse first- and second-order linear systems.
LO3 Find trigonometric and complex forms of the Fourier series representation of periodic waveforms and sketch their related frequency spectra.
LO4 Use the mathematical software as a computational and illustrative aid in work associated with the learning outcomes specified above.
Pre-requisite learning
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).

14749 MATH6041 Technological Mathematics 220
14752 MATH6043 Technological Mathematics 221
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
 

Module Content & Assessment

Indicative Content
Laplace Transforms and Differential Equations
Definition and elementary properties of the Laplace transform. Determination of Laplace transform using look-up tables. First shift theorem. Inverse Laplace transform using table look-up, partial fractions and completing the square. Laplace transform of derivatives and solution of first and second order differential equations. Discussion of steady-state response, transient-response and transfer functions. Pole-zero analysis and stability. Definition and transform of the unit-step function. Second shift theorem.
Fourier Series
Odd and Even functions. Trigonometric form of the Fourier series representation of periodic functions and Dirichlet conditions. Parseval's Theorem with application to average power content. Derivation of the complex form of the Fourier representation of a periodic waveform via the Euler identities. Fourier amplitude and phase spectra.
Maple
Basic commands. Algebraic expressions, factorisation, expansions, partial fractions. Functions - definition, plotting, differentiation, integration. Laplace transform, inverse transform. Differential Equations.
Assessment Breakdown%
Course Work30.00%
End of Module Formal Examination70.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Short Answer Questions In class assessment: Laplace Transforms 1,2 10.0 Week 5
Short Answer Questions In class assessment: Fourier Series 3 10.0 Week 10
Practical/Skills Evaluation Maple - Laboratory Examination 4 10.0 Week 12
End of Module Formal Examination
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Formal Exam End-of-Semester Final Examination 1,2,3 70.0 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.

The institute 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 Formal delivery of module content 3.0 Every Week 3.00
Lab Maple lab 1.0 Every Second Week 0.50
Tutorial Problem solving 1.0 Every Second Week 0.50
Independent & Directed Learning (Non-contact) Class notes & exercise sheets 3.0 Every Week 3.00
Total Hours 8.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
Workload: Part Time
Workload Type Workload Description Hours Frequency Average Weekly Learner Workload
Lecture Formal delivery of module content 2.0 Every Week 2.00
Lab Maple Lab 1.0 Every Second Week 0.50
Tutorial Problem solving 1.0 Every Second Week 0.50
Independent & Directed Learning (Non-contact) Class notes & exercise sheets 4.0 Every Week 4.00
Total Hours 8.00
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 Ed., Pearson Education London [ISBN: 129217434X]
Supplementary Book Resources
  • A. C. Grove 1991, An introduction to the Laplace transform and the Z transform, Prentice Hall New York [ISBN: 0134889339]
  • A.Croft, R.Davison, M.Hargreaves and J. Flint 2012, Engineering Mathematics: A Foundation for Electronic, Electrical, Communications and Systems Engineers, 4th Edition Ed., Pearson London [ISBN: 0273719777]
  • K. Singh 2011, Engineering mathematics through applications, 2nd Edition Ed., Palgrave Macmillan London [ISBN: 023027479X]
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
CR_EEPSY_8 Bachelor of Engineering (Honours) in Electrical Engineering 5 Mandatory
CR_EELES_8 Bachelor of Engineering (Honours) in Electronic Engineering Sept 2021 5 Mandatory
CR_EELEC_7 Bachelor of Engineering in Electrical Engineering 5 Mandatory
CR_EELXE_7 Bachelor of Engineering in Electronic Engineering 5 Mandatory

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