Short Title:  Technical Mathematics 6 

Full Title:  Technical Mathematics 6 

Field of Study:  Electricity and energy 

Module Author:  PAUL ROBINSON 

Module Description:  This module aims to:
To support Semester 6 modules by introducing Laplace Transforms and their use in solving linear differential equations.
2. To deepen the students knowledge of geometry, by introducing the formulation and solution of 3D problems involving lines and planes in vector notation. To be able
to calculate the divergence, gradient and curl and relate these to ideas in geometry and physics.
3. To use iterative techniques to solve equations numerically and as an introduction to material they may cover in year 4. 

Learning Outcomes 
On successful completion of this module the learner will be able to: 
LO1 
To find and invert Laplace transforms directly and
indirectly from Tables 
LO2 
To use Laplace Transforms in the solution of
linear first and second order differential equations
with constant coefficients 
LO3 
To write the coordinates of points in i, j, k notation
from a diagram 
LO4 
To find the equations of lines, line segments and
planes and solve problems involving these 
LO5 
To find the divergence, gradient and curl for
polynomially defined functions 
LO6 
To use the gradient to find the directional
derivative, maximum rate of change, tangent
planes and normal lines 
LO7 
Use Newton’s Method and the Bisection Method
in one variable to numerically solve an equation 
LO8 
To use the first order Euler method to numerically solve a first order differential equation 
Prerequisite learning 

Corequisite Modules
 No Corequisite modules listed 
Module Content & Assessment
Content (The percentage workload breakdown is inidcative and subject to change) 
% 
The Laplace Transform: Definition. The Laplace transform of common
functions. Linearity rules. Transform of derivatives. Application: Solution of
first and second order linear ODE’s with constant coefficients.

40.00% 
Vector Calculus i, j, k notation. Equations of lines and planes in 3D. Intersection point of line with a plane. Gradient, divergence, curl. Directional derivatives and maximum rate of change. Tangent planes and normal lines to a surface.

35.00% 
Numerical Methods NewtonRaphson and Bisection methods. First order Euler method for a first order differential equation

25.00% 
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 the Laplace Transform and 3D lines and planes 
1,2,3,4 
15.00 
Week 7 
Continuous Assessment 
CA to use a spreadsheet to implement bisection, Newton or Euler methods and high threshold Keyskills test 
3,4,5,6,7,8 
15.00 
Week 12 
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 
70.00 
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 
Classwork 
3.00 
Every Week 
3.00 
Lecturer/Lab 
Computing practical 
1.00 
Every Week 
1.00 
Independent Learning Time 
Outside of Class 
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 

 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 macmillian UK [ISBN: 9781403903129]
 This module does not have any article/paper resources 

This module does not have any other resources 

Module Delivered in
