Short Title:  Technical Mathematics 4 

Full Title:  Technical Mathematics 4 

Field of Study:  Electricity and energy 

Reviewed By:  JOHN ANDREW DONNELLAN 

Module Author:  Ciaran O Sullivan 

Module Description:  The first aim of Technical Mathematics 4 is to develop the students’ competence in a range of
mathematical techniques in probability as applied to process capability, pattern manipulation
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 the application of the
normal distribution to engineering problems, sequence and the convergence of a mathematical
sequence, basic integration of engineering functions (including indefinite integrals, definite
integrals, and numerical integration). The third aim is to extend the students use of software
applications in the processing of engineering data and understanding engineering concepts.
Finally the module aims to encourage self awareness and independent learning as mathematics
students through maintaining a reflective diary on their work. 

Learning Outcomes 
On successful completion of this module the learner will be able to: 
LO1 
Use the standard normal table to solve problems about
the general normal distribution. 
LO2 
Construct and interpret an SPC chart. 
LO3 
Construct confidence intervals for means and
proportions. 
LO4 
Recognise arithmetic and geometric sequences and
calculate terms in them. 
LO5 
Test simple sequences for convergence or divergence
and determine the limit (steady state) of simple
convergent sequences 
LO6 
Calculate the sum of n terms in a series. 
LO7 
Use software tools appropriately to generate a
sequence, the limit of a sequence and the sum of the
first n terms of a sequence. 
LO8 
Use software tools appropriately to generate a series,
the sum of the first n terms of a series. 
LO9 
Use a table of indefinite integrals and linearity to find
antiderivatives of simple functions. 
LO10 
Calculate definite integrals including the area under a
graph. 
LO11 
Use the technique of substitution to integrate a
composition of two functions, the first of which is linear.Use the tableau method of integration by parts and integrate rational integrands using partial fractions. 
LO12 
Solve a simple variable separable differential equationand solve first order linear differential equations using an integrating factor. 
LO13 
Use the trapezoidal rule and Simpson’s rule to
approximate the value of a definite integral. 
LO14 
Maintain a reflective learning diary. 
Prerequisite learning 

Corequisite Modules
 No Corequisite modules listed 
Module Content & Assessment
Content (The percentage workload breakdown is inidcative and subject to change) 
% 
Probability Distributions: The normal distribution. The standard normal table. Using the standard normal table to solve problems for general normal distributions. Confidence intervals. Statistical Process Control: XBar charts.

25.00% 
Software skills: Control structures (loops). Recursion (sequences and series).

13.00% 
Sequences and Series: Ordinary, explicit, and recursive forms of sequences. Arithmetic and geometric sequences. Convergence and divergence of sequences. Series as a sequence of partial sums. The ratio test.

21.00% 
Integration: Antiderivatives of simple functions. The constant of integration. Integration of linear combinations of simple functions. Definite integrals. The area under a graph, including area below the horizontal axis. Integration of the composition of two functions, the first being a linear function. Integration using the tableau method. Integration using partial fractions. Solution of simple variable separable differential equations. Solution of first order differential equations using the integrating factor method.

29.00% 
Numerical Integration: The trapezoidal rule. Simpson’s rule.

12.00% 
Assessment Breakdown  % 
Course Work  40.00% 
End of Module Formal Examination  60.00% 
Course Work 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Practical/Skills Evaluation 
High threshold ‘Key Skills’ quiz, testing key basic mathematical techniques needed for this semester. ( First opportunity to do test in week 1). 
1,2,3,4,5,6,7,8,10,13 
15.00 
Ongoing 
Continuous Assessment 
Written test on integration. 
2,6,9,10,11,12,14 
7.00 
Week 8 
Project 
Assignment on the use of SPC charts and control structures in sequences or numerical integration using appropriate software. 
1,2,3,5,6,7,8,13 
8.00 
Week 10 
Continuous Assessment 
Submission of Reflective Learning Diary, detailing student’s perception of how they met the learning outcomes of the syllabus. 
2,6,9,10,11,12,14 
10.00 
Sem 2 End 
End of Module Formal Examination 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Formal Exam 
EndofSemester Final Examination 
1,3,4,5,6,9,10,11,12,13 
60.00 
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 use of excel and Matalb for relaiablilty, sequences and integartion, augnmented by tutorial work on problem sheet questions. Also Selected opportunities to do Keyskills tests. 
1.00 
Every Week 
1.00 
Independent Learning 
Review of lecture material between lectures, completion of problem sheet questions, completion of computer assignments. Reflection on and revison for Keyskills test. 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, Palgrave, Engineering Mathematics through Applications, 1st ed Ed., Macmillan [ISBN: 0 333– 92224 –7]
 James Reilly,, Using Statistics, 1st ed Ed. [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
