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MATH8005 - Maths for Control and Quality

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Title:Maths for Control and Quality
Long Title:Mathematics for Control and Qu
Module Code:MATH8005
 
Duration:1 Semester
Credits: 5
NFQ Level:Advanced
Field of Study: Mathematics
Valid From: Semester 1 - 2016/17 ( September 2016 )
Module Delivered in 6 programme(s)
Module Coordinator: David Goulding
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
 

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.
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.
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.
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.
Assessment Breakdown%
Course Work30.00%
End of Module Formal Examination70.00%
Course Work
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
This module does not have any other resources
 

Module Delivered in

Programme Code Programme Semester Delivery
CR_EAMTE_8 Bachelor of Engineering (Honours) in Advanced Manufacturing Technology 1 Mandatory
CR_EBENS_8 Bachelor of Engineering (Honours) in Building Energy Systems 7 Mandatory
CR_EPPTE_8 Bachelor of Engineering (Honours) in Process Plant Technology 1 Mandatory
CR_EMASD_8 Certificate in Manufacturing Systems Design 1 Mandatory
CR_EMESY_8 Certificate in Mechanical Engineering Systems 1 Mandatory
CR_EPPSY_8 Certificate in Process Plant Systems 1 Mandatory

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