Short Title:Technical Mathematics 3
Full Title:Technical Mathematics 3
Module Code:MATH H2091
 
Credits: 5
NFQ Level:6
Field of Study:Mechanics and metal work
Module Delivered in 2 programme(s)
Reviewed By:JOHN ANDREW DONNELLAN
Module Author:Ciaran O Sullivan
Module Description:The first aim of Technical Mathematics 3 is to develop the students’ competence in a range of mathematical techniques in discrete mathematics, probability as applied to reliability, array handling and basic calculus in such a way as to support other engineering modules. The second aim is to deepen the students understanding of key mathematical ideas regarding number systems, logic, probability, rates of change and matrices as a basis for further mathematical study in semester 4. The third aim is to extend the students use of software applications in the manipulation and processing of engineering data.
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1 Translate numbers between binary, decimal and hexadecimal bases.
LO2 Perform simple calculations in binary and hexadecimal number systems.
LO3 Construct simple truth tables.
LO4 Calculate probabilities.
LO5 Apply discrete probability distributions: (binomial, Poisson) to problems in reliability engineering.
LO6 Apply the multiple, sum, product, quotient and chain rules to engineering functions.
LO7 Use differential calculus to find and classify the stationary points of a function.
LO8 Apply the differential calculus to simple 1-variable problems in engineering.
LO9 Use appropriate software to carry out differentiation.
LO10 Write down geometric transformations as matrices and use matrices to implement geometric transformations.
LO11 Use appropriate software to determine inverse matrices
LO12 Use matrix techniques to solve systems of linear equations of the type occurring in engineering problems.
LO13 Use appropriate software to implement row reduction to solve systems of linear equations of the type occurring in engineering problems.
Pre-requisite learning
Co-requisite Modules
No Co-requisite modules listed
 

Module Content & Assessment

Content (The percentage workload breakdown is inidcative and subject to change) %
Computing :
Number bases: binary decimal hexadecimal. Translation between them.
6.00%
Discrete Mathematics:
Simple and compound propositions. Truth tables. Simple logic circuits: AND, OR, NAND, NOR, EXCLUSIVE Tabular simplification technique.
8.00%
Probability (Reliability)
Definition of probability. Calculating probabilities. The laws of probability. Reliability engineering: components in series and in parallel ( use of AND/OR).
10.00%
Discrete probability distributions:
recognise the binomial and Poisson distributions and their engineering applications in relation to defectives and defects.
8.00%
Differentiation:
Use of a table of derived functions. Use of the multiple, sum, product, quotient and chain rules. Average and instantaneous rate of change. Definition of derivative of a function at a point. Geometric interpretation of the derivative.
25.00%
Function investigation using differentiation:
Increasing and decreasing functions. Stationary points. Classifying stationary points and the second derivative test. Applied Maximum / minimum and approximate error problems.
16.00%
Software skills:
Spreadsheets: Selection. Logic. Simple macros. Data manipulation package (eg.Matlab): Basic array manipulation.
10.00%
Geometry and Matrices:
Matrix definition. Matrix algebra. Matrix determinant, special matrices and the matrix of a geometric transformation. Inverse matrix formula for 2´2. Systems of linear equations in matrix form. Row reduction for finding the inverse of a matrix. Solution of system of linear equations using row reduction (Gaussian elimination).
17.00%
Assessment Breakdown%
Course Work45.00%
End of Module Formal Examination55.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Continuous Assessment High threshold ‘Key Skills’ quiz, testing key basic mathematical techniques needed for this semester. (Week 1 first test but repeatable through the semester) 4,5,6,7,8,10,12 15.00 Ongoing
Assignment Assignment on constructing a spreadsheet for reliability engineering (using IF then Else and AND /OR) 4,5,6 10.00 Week 5
Practical/Skills Evaluation Laboratory based test on the use of appropriate software to manipulate matrices and solve simultaneous equations (for example using MATLAB) 1,2,3,4,5,9,11,13 10.00 Week 12
Continuous Assessment High threshold criterion referenced test on basic calculus 6,7,8 10.00 Week 8
End of Module Formal Examination
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Formal Exam End-of-Semester Final Examination 1,2,3,4,5,6,7,8,10,12,13 55.00 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.

IT Tallaght 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 No Description 3.00 Every Week 3.00
Lab Computer lab on excel and Matlab, augmented by tutorial work on problem sheet questions. 1.00 Every Week 1.00
Independent Learning Review of lecture material between lectures, completion of problem sheet questions, completion of computer assignments. Synthesis of course material ahead of final semester exam. 3.00 Every Week 3.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
This module has no Part Time workload.
 

Module Resources

Required Book Resources
  • Kuldeep Singh, Engineering mathematics through applications, 1st ed Ed. [ISBN: 0 - 333 – 92224 – 7]
  • James Reilly,, Using Statistics [ISBN: 9780717140220]
Recommended Book Resources
  • 2006, CALMAT Learning Environment, CALMAT Team, 4th ed Ed., Glasgow Caledonian Uni UK
  • Tony Croft,, Foundation Maths [ISBN: 9780131979215]
  • Glyn James... [et al.], Modern engineering mathematics, Pearson Prentice Hall Harlow [ISBN: 9780132391443]
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
TA_EAEEE_B Bachelor of Engineering (Honours) in Sustainable Energy Engineering 3 Mandatory
TA_EAEEE_D Bachelor of Engineering in Sustainable Energy & Environmental Engineering 3 Mandatory