Module Details

Module Code: STAT8002
Title: Mathematics for Engineers
Long Title: Mathematics for Engineers
NFQ Level: Advanced
Valid From: Semester 1 - 2016/17 ( September 2016 )
Duration: 1 Semester
Credits: 5
Field of Study: 4620 - Statistics
Module Delivered in: 3 programme(s)
Module Description: Design and analysis of experiments (DOE), topics from the field of Operations Research along with some partial differential equations and their applications.
 
Learning Outcomes
On successful completion of this module the learner will be able to:
# Learning Outcome Description
LO1 evaluate the possible experimental designs for a given problem, select a suitable design and analyse the resultant data.
LO2 formulate, solve and interpret the solution to linear programming problems.
LO3 conduct sensitivity analysis on the solution to a LP problem.
LO4 formulate and solve special category LP problems such as transportation problems.
LO5 solve partial differential equations relevant to mechanical engineering.
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).
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.
Statistics for Engineering 301
 
Indicative Content
Analysis of Variance
ANOVA fundamentals; sums of squares, degrees of freedom, F-ratios.
Design and analysis of experiments
The need for experimental design, independent and dependent variables, factors, levels, treatment, error, randomisation, confounding, replication, one-way and two-way analysis of variance, factorial and fractional factorial designs, Taguchi concepts.
Introduction to Linear Programming
Assumptions underlying the L.P. model, formulating L.P. problems, graphical representation and solution by graphical means.
The Simplex Method.
Representing L.P. problems as a set of linear equations, use of slack and artificial variables, basic solutions, Simplex tableau format, Simplex routine, M-technique, two-phase method, infeasible problems, unbounded problems.
Duality and Sensitivity Analysis
Primal and dual problems, formulating the dual, relationships between solutions to primal and dual, Dual Simplex method, complementary slackness, sensitivity analysis.
Special category L.P. problems
Formulation and solution of special category problems such as transportation problems and assignment problems.
Partial differential equations
Half Range Fourier series. One dimensional heat flow. One dimensional wave equation. Laplace's equation.
Module Content & Assessment
Assessment Breakdown%
Coursework20.00%
End of Module Formal Examination80.00%

Assessments

Coursework
Assessment Type Short Answer Questions % of Total Mark 10
Timing Week 7 Learning Outcomes 1,2,3
Assessment Description
In class test
Assessment Type Short Answer Questions % of Total Mark 10
Timing Week 12 Learning Outcomes 4,5
Assessment Description
In-class test
End of Module Formal Examination
Assessment Type Formal Exam % of Total Mark 80
Timing End-of-Semester Learning Outcomes 1,2,3,4,5
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 Lecture Every Week 3.00 3
Tutorial Contact Tutorial Every Week 1.00 1
Independent & Directed Learning (Non-contact) Non Contact Independent learning 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
Independent & Directed Learning (Non-contact) Non Contact Independent learning Every Week 3.00 3
Tutorial Contact Tutorial Every Week 1.00 1
Total Hours 7.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
 
Module Resources
Recommended Book Resources
  • Douglas C. Montgomery. (2012), Design and Analysis of Experiments, 8th. Wiley, [ISBN: 978-111814692].
  • E Kreyszig. (2011), Advanced Engineering Mathematics, 10th. Wiley, [ISBN: 978-047064613].
Supplementary Book Resources
  • Jiju Antony. (2003), Design of Experiments for Engineers and Scientists, Butterworth-Heinemann, [ISBN: 0750647094].
  • Hamdy A. Taha. (2010), Operations Research, an introduction, 9th. Prentice Hall, [ISBN: 978-013255593].
  • D.G. Zill & R.Cullen. (2000), Advanced Engineering Mathematics, 2nd. Mac Millian, [ISBN: 0-333-6574-4].
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_EBIOM_8 Bachelor of Engineering (Honours) in Biomedical Engineering 7 Mandatory
CR_EMECH_8 Bachelor of Engineering (Honours) in Mechanical Engineering 7 Mandatory
CR_EMECE_9 Master of Engineering in Mechanical Engineering 7 Mandatory