Short Title:  Technical Mathematics 5 

Full Title:  Technical Mathematics 5 

Field of Study:  Electricity and energy 

Reviewed By:  DIARMUID RUSH 

Module Author:  PAUL ROBINSON 

Module Description:  This module has two aims:
1. to introduce basic matrix techniques for the formulation and solution of engineering problems. These techniques include the representation of geometric transformations, the power method to find eigenvalues and the solution of systems of differential equations.
2. to use partial differentiation to formulate and solve optimisation problems in several variables and to perform error analysis.


Learning Outcomes 
On successful completion of this module the learner will be able to: 
LO1 
Use matrices to construct and analyse geometric
transformations in 2D 
LO2 
Find the eigenvalues of a 2 by 2 matrix and apply to diagonalisation and power of a matrix 
LO3 
Find the largest and smallest eigenvalue of a matrix using the Power Method 
LO4 
Solve a system of first order
differential equations (homogeneous and none homogeneous) with constant coefficients
(2D) using matrix techniques both analytically and numerically (Euler Method). 
LO5 
Convert a higher order DE into a system of first
order DE’s 
LO6 
Use matrix techniques to find the normal modes and frequencies of undamped coupled oscillators 
LO7 
Calculate partial derivatives of polynomials to solve max/min problems in 2D and do error analysis 
Module Content & Assessment
Course Work 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Continuous Assessment 
CA Test covering Linear Transformations and coupled first order differential equations 
1,2,3,4 
10.00 
Week 7 
Continuous Assessment 
High threshold Keyskills test in lab 
1,2,3,4,5,6,7 
10.00 
Week 11 
Assignment 
Implement the Power Method and Euler's Method in the lab 
3,4 
10.00 
Week 7 
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 
70.00 
EndofSemester 
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 
Classwork 
3.00 
Every Week 
3.00 
Independent Learning Time 
Outside of Class 
4.00 
Every Week 
4.00 
Lecturer/Lab 
Session in Computing Laboratory 
1.00 
Every Week 
1.00 
Total Weekly Learner Workload 
8.00 
Total Weekly Contact Hours 
4.00 
This module has no Part Time workload. 

Module ResourcesRecommended Book Resources 

 K. A. Stroud,Dexter J. Booth, Engineering Mathematics, 4th ed Ed. [ISBN: 9780831133276]
 K. A. Stroud,Dexter J. Booth, Advanced Engineering Mathematics, 4th ed Ed., Palgrave MacMillan [ISBN: 9781403903129]
 Michael E. Mortenson, Geometric Transformations for 3D Modeling [ISBN: 9780831133382]
 This module does not have any article/paper resources 

This module does not have any other resources 

Module Delivered in
