Title:  Maths for Control and Quality 
Long Title:  Mathematics for Control and Qu 
Field of Study: 
Mathematics

Valid From: 
Semester 1  2016/17 ( September 2016 ) 
Module Coordinator: 
David Goulding 
Module Author: 
AINE NI SHE 
Module Description: 
This module develops the theory of Laplace Transforms, and introduces the learner to Ztransforms, 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 firstorder and secondorder linear differential equations subject to unitstep and impulsive inputs. 
LO2 
Solve firstorder and secondorder difference equations using the method of Ztransforms. 
LO3 
Apply probability distributions to Acceptance Sampling. 
LO4 
Formulate and carry out appropriate hypothesis testing procedures. 
Prerequisite 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 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).

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 
Corequisite Modules

No Corequisite 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. Unitstep function  definition, notation, Laplace transform. Second Shift Theorem, application to delayed signals. Unitimpulse function  definition, notation, unit area property, sifting property, Laplace transform. Solution of differential equations subject to step inputs and impulsive inputs.

ZTransforms and Difference Equations
Sequences, discrete functions  direct formula, recursive formula. Ztransform  definition and notation. Discussion of properties of the Ztransform to include linearity, first and secondshift properties. Ztransform of sampled signals. Determination of the inverse transform using table lookup and partial fractions. Use of the Ztransform to solve first and secondorder 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. Onetailed test, twotailed test. Significance level. Test statistic, pvalue. Power of a test. Type I error, Type II error. Test on the mean when variance is known/unknown. Twosample tests for difference between means.

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 
Short Answer Questions 
Test 1  Laplace Transforms, Differential Equations 
1 
10.0 
Week 4 
Short Answer Questions 
Test 2  Ztransforms, 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 
EndofSemester Final Examination 
1,2,3,4 
70.0 
EndofSemester 
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 (Noncontact) 
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 (Noncontact) 
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: 9780273719236]
 Douglas C. Montgomery, George C. Runger 2007, Applied Statistics and Probability for Engineers, 6th Ed., John Wiley & Sons Hoboken, NJ [ISBN: 978111853971]
 Supplementary Book Resources 

 E.Kreyszig 2011, Advanced Engineering Mathematics, 10th Ed., Wiley [ISBN: 0470646136]
 D. W. Jordan and P. Smith 2008, Mathematical techniques, 4th Ed., OUP [ISBN: 9780199282012]
 Reza MalekMadani 1998, Advanced Engineering Mathematics with Mathematica and MATLAB, AddisonWesley Reading, Mass. [ISBN: 0201598817]
 A. C. Grove 1991, An introduction to the Laplace transform and the z transform, Prentice Hall New York [ISBN: 0134889339]
 Dennis G. Zill, Michael R. Cullen 2000, Advanced Engineering Mathematics, 2nd Ed., Jones and Bartlett Sudbury, Mass [ISBN: 0763713570]
 R.L. Scheaffer & J.T. McClave 1990, Probability and Statistics for Engineers, 3rd Ed., PWSKent Publishing Co. Boston [ISBN: 0534982166]
 This module does not have any article/paper resources 

This module does not have any other resources 

Module Delivered in
