Short Title:  Technical Mathematics 5 

Full Title:  Technical Mathematics 5 

Field of Study:  Electricity and energy 

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 
LO3 
Diagonalise a 2 by 2 matrix. Find the power of a 2
by 2 matrix. 
LO4 
Find the largest and smallest eigenvalue of a matrix using the Power Method 
LO5 
Solve a system of homogeneous first order
differential equations with constant coefficients
(2D) using matrix techniques. 
LO6 
Convert a higher order DE into a system of first
order DE’s 
LO7 
Use matrix techniques to find the normal modes and frequencies of undamped coupled oscillators 
LO8 
Calculate partial derivatives of polynomials and solve max/min problems in 2D 
LO9 
Use Lagrange multipliers to solve max/min problems. 
LO10 
Use partial differentiation to do error analysis 
Prerequisite learning 

Corequisite Modules
 No Corequisite modules listed 
Module Content & Assessment
Content (The percentage workload breakdown is inidcative and subject to change) 
% 
Linear transformations: Representation by matrices. Dilation,
projection,rotation and translation. Parametrized transformations. Inverse of
a matrix. Eigenvalues and eigenvectors and their geometric interpretation.

31.00% 
Linear Algebra: Calculation of maximum
and minimum eigenvalue using the Power Method for 2D and 3D matrices.

7.00% 
Systems of first order ODE’s: Review of first order and one variable ODE’s.
Coupled first order DE’s – application to heat transfer. Conversion of higher
order DE’s to systems of first order ones.

23.00% 
Coupled second order DE’s without friction terms : Application to coupled
spring systems. Application of matrix techniques to find normal modes and
frequencies.

12.00% 
Applications: Functions of more than one variable: Geometrical representation. Partial
Differentiation. Higher derivatives. Optimisation for functions of
several variables, Calculation of experimental error.

27.00% 
Assessment Breakdown  % 
Course Work  30.00% 
End of Module Formal Examination  70.00% 
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 
2,6,9,10 
15.00 
Week 7 
Continuous Assessment 
High threshold Keyskills test and lab practical 
1,2,3,4,5,6,7,8,9,10 
15.00 
Week 11 
End of Module Formal Examination 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Formal Exam 
EndofSemester Final Examination 
1,2,3,4,5,6,7,8,9,10 
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 ResourcesRequired Book Resources 

 K. A. Stroud, with additions by Dexter J. Booth 2007, Engineering mathematics, 4th ed Ed., Industrial Press New York [ISBN: 9780831133276]
 Recommended Book Resources 

 K.A. Stroud, Dexter J. Booth, 2003, Advanced Engineering Mathematics, 4th ed Ed., Palgrave Macmillan, UK [ISBN: 9781403903129]
 Michael E. Mortenson 2007, Geometric transformations for 3D modeling, Industrial Press New York [ISBN: 9780831133382]
 This module does not have any article/paper resources 

This module does not have any other resources 

Module Delivered in
