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MATH7005 - Engineering Maths Methods

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Title:Engineering Maths Methods
Long Title:Engineering Maths Methods
Module Code:MATH7005
 
Duration:1 Semester
Credits: 5
NFQ Level:Intermediate
Field of Study: Mathematics
Valid From: Semester 2 - 2019/20 ( January 2020 )
Module Delivered in 2 programme(s)
Module Coordinator: David Goulding
Module Author: Maryna Lishchynska
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:
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.
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 CIT 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
 

Module Content & Assessment

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.
Assessment Breakdown%
Course Work30.00%
End of Module Formal Examination70.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Other In class assessment 1,2 15.0 Week 6
Other In class assessment 3 15.0 Week 10
End of Module Formal Examination
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Formal Exam End-of-Semester Final Examination 1,2,3,4 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 lecture 3.0 Every Week 3.00
Tutorial Based on exercise sheets 1.0 Every Week 1.00
Independent & Directed Learning (Non-contact) Review of lecture material, completion of exercise sheets 3.0 Every Week 3.00
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 Ed., John Wiley & Sons [ISBN: 9780470913611]
Supplementary Book Resources
  • Dennis G. Zill & Michael R. Cullen 2016, Advanced Engineering Mathematics, 6th Ed., 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

Cork Institute of Technology
Rossa Avenue, Bishopstown, Cork

Tel: 021-4326100     Fax: 021-4545343
Email: help@cit.edu.ie