Module Details
| Module Code: |
MATH8005 |
| Title: |
Maths for Control and Quality
|
|
Long Title:
|
Mathematics for Control and Qu
|
| NFQ Level: |
Advanced |
| Valid From: |
Semester 1 - 2016/17 ( September 2016 ) |
| Field of Study: |
4610 - Mathematics
|
| Module Description: |
This module develops the theory of Laplace Transforms, and introduces the learner to Z-transforms, with applications to difference equations. There is also coverage of statistics relevant to quality control: acceptance sampling and hypothesis testing.
|
| 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 and impulsive inputs. |
| LO2 |
Solve first-order and second-order difference equations using the method of Z-transforms. |
| LO3 |
Apply probability distributions to Acceptance Sampling. |
| LO4 |
Formulate and carry out appropriate hypothesis testing procedures. |
| 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).
|
| 10178 |
STAT6010 |
Intro. to Probability & Stats |
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 |
|
Laplace Transforms and Differential Equations
Review of Laplace transform theory. Unit-step function - definition, notation, Laplace transform. Second Shift Theorem, application to delayed signals. Unit-impulse function - definition, notation, unit area property, sifting property, Laplace transform. Solution of differential equations subject to step inputs and impulsive inputs.
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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.
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Acceptance Sampling
Review of the Binomial, Poisson and Normal distributions. Sampling with/without replacement. The Hypergeometric distribution. Acceptance sampling - rationale. Sample size, percentage defective, critical number, acceptance number. Operating characteristic curve. Double sampling plans. Producer's risk, consumer's risk.
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Hypothesis Testing
Null hypothesis, alternative hypothesis. One-tailed test, two-tailed test. Significance level. Test statistic, p-value. Power of a test. Type I error, Type II error. Test on the mean when variance is known/unknown. Two-sample tests for difference between means.
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Module Content & Assessment
|
| Assessment Breakdown | % |
|---|
| Coursework | 30.00% |
| End of Module Formal Examination | 70.00% |
Assessments
| End of Module Formal 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 |
Lecture |
Every Week |
3.00 |
3 |
| Tutorial |
Contact |
Problem Solving |
Every Week |
1.00 |
1 |
| Lecturer Supervised 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 |
| Workload: Part Time |
| Workload Type |
Contact Type |
Workload Description |
Frequency |
Average Weekly Learner Workload |
Hours |
| Lecture |
Contact |
Lecture |
Every Week |
3.00 |
3 |
| Tutorial |
Contact |
Tutorial |
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 |
|
Module Resources
|
| Recommended Book Resources |
|---|
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G.James. (2010), Advanced Modern Engineering Mathematics, 4th. Prentice Hall, [ISBN: 978-0273719236].
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Douglas C. Montgomery, George C. Runger. (2007), Applied Statistics and Probability for Engineers, 6th. John Wiley & Sons, Hoboken, NJ, [ISBN: 978-111853971].
| | Supplementary Book Resources |
|---|
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E.Kreyszig. (2011), Advanced Engineering Mathematics, 10th. Wiley, [ISBN: 0-470-64613-6].
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D. W. Jordan and P. Smith. (2008), Mathematical techniques, 4th. OUP, [ISBN: 978-0199282012].
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Reza Malek-Madani. (1998), Advanced Engineering Mathematics with Mathematica and MATLAB, Addison-Wesley, Reading, Mass., [ISBN: 0-201-59881-7].
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A. C. Grove. (1991), An introduction to the Laplace transform and the z transform, Prentice Hall, New York, [ISBN: 0-13-488933-9].
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Dennis G. Zill, Michael R. Cullen. (2000), Advanced Engineering Mathematics, 2nd. Jones and Bartlett, Sudbury, Mass, [ISBN: 0-7637-1357-0].
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R.L. Scheaffer & J.T. McClave. (1990), Probability and Statistics for Engineers, 3rd. PWS-Kent Publishing Co., Boston, [ISBN: 0-534-98216-6].
| | This module does not have any article/paper resources |
|---|
| This module does not have any other resources |
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