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.
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 Work
30.00%
End of Module Formal Examination
70.00%
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