Module Details

Module Code: MATH7029
Title: Transforms and Fourier Series
Long Title: Transforms and Fourier Series
NFQ Level: Intermediate
Valid From: Semester 1 - 2019/20 ( September 2019 )
Duration: 1 Semester
Credits: 5
Field of Study: 4610 - Mathematics
Module Delivered in: 1 programme(s)
Module Description: This module develops the theory of advanced Laplace transforms including the study of unit step, Dirac and periodic functions. It introduces the learner to Z-transforms, with applications to difference equations. Fourier series makes up the remainder of the module.
 
Learning Outcomes
On successful completion of this module the learner will be able to:
# Learning Outcome Description
LO1 Use the Laplace transform method to solve first-order and second-order linear differential equations subject to unit step, impulsive and periodic inputs.
LO2 Compute the trigonometric form of the Fourier series of functions including odd and even functions.
LO3 Solve first and second order difference equations using method of Z-transforms.
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).
13585 MATH7030 Calculus & Laplace Transforms
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
Advanced Laplace Transforms
Review of Laplace transform theory. Definition of step function and unit impulse. Proof of second shift theorem. Transfer functions. Periodic inputs including square, triangular and sawtooth waves. Solving differential equations subject to step, impulsive and periodic inputs. Use of table look-up and partial fraction expansions.
Fourier Series
Odd and Even functions. Development of Euler formulae. Determining Fourier coefficients. Find half range expansions. Parseval's Theorem. Average power in a periodic signal.
Z-Transforms and Difference Equations
Sequences, discrete functions - direct formula, recursive formula. Z-transform - definition and notation. Discussion of properties of the Z-transform to include linearity, first- and second-shift properties. Z-transform of sampled signals. Determination of the inverse transform using table look-up and partial fractions. Use of the Z-transform to solve first- and second-order difference equations with constant coefficients.
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
In class assessment on Advanced Laplace
Assessment Type Short Answer Questions % of Total Mark 15
Timing Week 10 Learning Outcomes 1,2
Assessment Description
In class assessment on Advanced Laplace and Fourier Series
End of Module Formal Examination
Assessment Type Formal Exam % of Total Mark 70
Timing End-of-Semester Learning Outcomes 1,2,3
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 Conventional Lecture Every Week 3.00 3
Tutorial Contact Based on exercise sheets Every Week 1.00 1
Independent & Directed Learning (Non-contact) Non Contact No Description 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 Conventional Lecture Every Week 3.00 3
Lecture Contact Lecturer-Supervised Learning Every Week 1.00 1
Independent & Directed Learning (Non-contact) Non Contact No Description Every Week 3.00 3
Total Hours 7.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
 
Module Resources
Recommended Book Resources
  • John Bird. (2017), Higher Engineering Mathematics, 8th. Routledge, Oxon, [ISBN: 9781138673571].
  • A.C.Grove. (1991), An Introduction to the Laplace transform and the Z-transform, Prentice Hall, New York, [ISBN: 0763713570].
Supplementary Book Resources
  • Dennis G. Zill and Michael R. Cullen. (2006), Advanced Engineering Mathematics, 3rd. Jones and Bartlett, Sudbury, MA, [ISBN: 9780763739140].
  • Erwin Kreyszig. (2011), Advanced Engineering Mathematics, 10th. John Wiley & Sons, Jefferson City, MO, [ISBN: 0980470458365].
This module does not have any article/paper resources
Other Resources
 
Module Delivered in
Programme Code Programme Semester Delivery
CR_SINEN_8 Bachelor of Science (Honours) in Instrument Engineering 5 Mandatory