Short Title:  Technical Mathematics 3 

Full Title:  Technical Mathematics 3 

Field of Study:  Mechanics and metal work 

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 1variable
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. 
Prerequisite learning 

Corequisite Modules
 No Corequisite 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 Work  45.00% 
End of Module Formal Examination  55.00% 
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 
EndofSemester Final Examination 
1,2,3,4,5,6,7,8,10,12,13 
55.00 
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. 
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 ResourcesRequired 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
