Module Details

Module Code: MATH7005
Title: Engineering Maths Methods
Long Title: Engineering Maths Methods
NFQ Level: Intermediate
Valid From: Semester 2 - 2019/20 ( January 2020 )
Duration: 1 Semester
Credits: 5
Field of Study: 4610 - Mathematics
Module Delivered in: 3 programme(s)
Module Description: This module treats: Laplace transforms and their application to solving differential equations; Z-transforms with applications to solution of difference equations; the eigenvalue approach to solving systems of differential equations; the Fourier Series representation of periodic signals.
 
Learning Outcomes
On successful completion of this module the learner will be able to:
# Learning Outcome Description
LO1 Use the method of Laplace transforms to solve differential equations involving periodic functions, the Heaviside unit step function and the Dirac delta function.
LO2 Calculate the eigenvalues and the eigenvectors of a matrix and use the eigensystem to solve systems of differential equations.
LO3 Use Z-transforms to solve difference equations.
LO4 Obtain the Fourier series representation of a periodic function.
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).
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
Further Laplace Transforms
Review of Laplace transforms. The convolution theorem. The Heaviside unit step function and the Dirac delta function. Periodic functions such as rectangular, sawtooth and triangular waves. Solution of differential equations involving periodic functions and step functions.
Fourier Series
Orthogonal functions and the derivation of Fourier series. Fourier series representation of periodic functions. Even and odd functions.
Linear Algebra
Eigenvalues and eigenvectors of a matrix. Solution of systems of differential equations using matrix methods with applications to systems of vibrating masses. Diagonalisation of a matrix. Orthogonal matrices to include matrices representing the rotation of axes.
Z-Transforms
Definition. Development of a short table of Z-transforms. The inverse Z-transform. Solution of difference equations using Z-Transforms.
Module Content & Assessment
Assessment Breakdown%
Coursework30.00%
End of Module Formal Examination70.00%

Assessments

Coursework
Assessment Type Other % of Total Mark 15
Timing Week 6 Learning Outcomes 1,2
Assessment Description
In class assessment
Assessment Type Other % of Total Mark 15
Timing Week 10 Learning Outcomes 3
Assessment Description
In class assessment
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 lecture Every Week 3.00 3
Tutorial Contact Based on exercise sheets Every Week 1.00 1
Independent & Directed Learning (Non-contact) Non Contact Review of lecture material, completion of exercise sheets Every Week 3.00 3
Total Hours 7.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
This module has no Part Time workload.
 
Module Resources
Recommended Book Resources
  • Erwin Kreyszig. (2011), Advanced Engineering Mathematics, 10th. John Wiley & Sons, [ISBN: 9780470913611].
Supplementary Book Resources
  • Dennis G. Zill & Michael R. Cullen. (2016), Advanced Engineering Mathematics, 6th. Jones & Barlett, [ISBN: 9781284105902].
This module does not have any article/paper resources
Other Resources
 
Module Delivered in
Programme Code Programme Semester Delivery
CR_EBIOM_8 Bachelor of Engineering (Honours) in Biomedical Engineering 4 Mandatory
CR_EMECH_8 Bachelor of Engineering (Honours) in Mechanical Engineering 4 Mandatory
CR_EMECE_9 Master of Engineering in Mechanical Engineering 4 Mandatory