| Title: | Maths for Control and Quality |
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| Long Title: | Mathematics for Control and Qu |
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| Field of Study: |
Mathematics
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| Valid From: |
Semester 1 - 2016/17 ( September 2016 ) |
| Module Coordinator: |
AINE NI SHE |
| Module Author: |
AINE NI SHE |
| 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: |
| 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. |
| 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). |
| 9461 |
MATH7020 |
Technological Mathematics 301 |
| 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 |
Co-requisites
|
| No Co Requisites listed |
Module Content & Assessment
| 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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| Assessment Breakdown | % |
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| Course Work | 30.00% |
| End of Module Formal Examination | 70.00% |
| Course Work |
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| Assessment Type |
Assessment Description |
Outcome addressed |
% of total |
Assessment Date |
| Short Answer Questions |
Test 1 - Laplace Transforms, Differential Equations |
1 |
10.0 |
Week 4 |
| Short Answer Questions |
Test 2 - Z-transforms, Difference Equations |
2 |
10.0 |
Week 8 |
| Short Answer Questions |
Test 3 - Acceptance Sampling |
3 |
10.0 |
Week 11 |
| 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 |
Lecture |
3.0 |
Every Week |
3.00 |
| Tutorial |
Problem Solving |
1.0 |
Every Week |
1.00 |
| Lecturer Supervised 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 |
| Workload: Part Time |
| Workload Type |
Workload Description |
Hours |
Frequency |
Average Weekly Learner Workload |
| Lecture |
Lecture |
3.0 |
Every Week |
3.00 |
| Tutorial |
Tutorial |
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 |
Module Resources
| Recommended Book Resources |
|---|
- G.James 2010, Advanced Modern Engineering Mathematics, 4th Ed., Prentice Hall [ISBN: 978-0273719236]
- Douglas C. Montgomery, George C. Runger 2007, Applied Statistics and Probability for Engineers, 6th Ed., John Wiley & Sons Hoboken, NJ [ISBN: 978-111853971]
| | Supplementary Book Resources |
|---|
- E.Kreyszig 2011, Advanced Engineering Mathematics, 10th Ed., Wiley [ISBN: 0-470-64613-6]
- D. W. Jordan and P. Smith 2008, Mathematical techniques, 4th Ed., OUP [ISBN: 978-0199282012]
- Reza Malek-Madani 1998, Advanced Engineering Mathematics with Mathematica and MATLAB, Addison-Wesley Reading, Mass. [ISBN: 0-201-59881-7]
- A. C. Grove 1991, An introduction to the Laplace transform and the z transform, Prentice Hall New York [ISBN: 0-13-488933-9]
- Dennis G. Zill, Michael R. Cullen 2000, Advanced Engineering Mathematics, 2nd Ed., Jones and Bartlett Sudbury, Mass [ISBN: 0-7637-1357-0]
- R.L. Scheaffer & J.T. McClave 1990, Probability and Statistics for Engineers, 3rd Ed., PWS-Kent Publishing Co. Boston [ISBN: 0-534-98216-6]
| | This module does not have any article/paper resources |
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| This module does not have any other resources |
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Module Delivered in
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