Short Title:  Mathematics 5 

Full Title:  Mathematics 5 (Differential Equations) 

Language of Instruction:  English 

Field of Study:  Mechanics and metal work 

Reviewed By:  DIARMUID RUSH 

Module Author:  CIARAN TAYLOR 

Module Description:  The first aim of Mathematics 5 is to reinforce the student’s competence in a range of mathematical techniques to support the analytical content of other modules in the course. The second aim is to enable the student to apply these mathematical techniques to the solution of engineering problems, such as the analysis of system behaviour and solution of control problems. 

Learning Outcomes 
On successful completion of this module the learner will be able to: 
LO1 
Solve first order differential equations by separating the variables. [POa, POb] 
LO2 
Solve first order linear differential equations by the integrating factor method. [POa, POb] 
LO3 
Solve second order linear differential equations with constant coefficients using the complementary equation. [POa, POb,POd] 
LO4 
Find and invert Laplace transforms using a standard table, linearity, shift theorems. [POa, POb] 
LO5 
Invert a Laplace transform by partial fraction techniques. [POa, POb] 
LO6 
Solve first and second order linear differential equations with constant coefficients using the Laplace transform method. [POa, POb, POd] 
LO7 
Solve a system of first order linear differential equations using Laplace transforms. [POa, POb] 
LO8 
Use differential equation techniques to create and solve models of engineering systems. [POa, POb, POd] 
LO9 
Interpret the solutions of differential equation models of engineering systems appropriately. [POa, POb, POd] 
Prerequisite learning 

Corequisite Modules
 No Corequisite modules listed 
Module Content & Assessment
Content (The percentage workload breakdown is inidcative and subject to change) 
% 
First Order Ordinary Differential Equations Separable FirstOrder. General and particular solutions. Initial conditions. Existence and uniqueness of solutions. Classification of ODE’s. Integrating factor method for first order linear ODEs.

28.00% 
Second Order Ordinary Differential Equations Modelling oscillation and circuits by second order ODE’s. Complementary function.Transient and steady state solutions. Free, damped and forced oscillation. Beats and resonance. Applications to circuits and motion with resistance proportional to speed.

22.00% 
The Laplace Transform: Definition and simple examples. Existence of the Laplace Transform. Table of Laplace Transforms of common functions. Linearity of the Laplace Transform. Laplace Transform of unit step function. Inverting Laplace Transforms – use of partial fractions. Shift theorems. Laplace Transform method for first order linear ODE’s with constant coefficients and systems of first order linear ODE’s with constant coefficients. Laplace Transform Method for Second Order Linear ODE’s with constant coefficients.

50.00% 
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 
Other 
High threshold test on solution of differential equations. 

15.00 
Week 5 
Other 
High threshold test on Laplace transform techniques. 

15.00 
Week 9 
End of Module Formal Examination 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Formal Exam 
EndofSemester Final Examination 

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 
No Description 
4.00 
Every Week 
4.00 
Independent Learning Time 
No Description 
4.00 
Every Week 
4.00 
Total Weekly Learner Workload 
8.00 
Total Weekly Contact Hours 
4.00 
Workload: Part Time 
Workload Type 
Workload Description 
Hours 
Frequency 
Average Weekly Learner Workload 
Lecture 
No Description 
2.00 
Every Week 
2.00 
Lecture 
No Description 
6.00 
Week 13 
0.46 
Independent Learning Time 
No Description 
6.00 
Every Week 
6.00 
Total Weekly Learner Workload 
8.46 
Total Weekly Contact Hours 
2.46 
Module ResourcesRecommended Book Resources 

 Anthony Croft, Robert Davison, James Flint, Martin Hargreaves 2017, Engineering Mathematics, 5th ed. Ed., Pearson [ISBN: 1292146656]
 K. A. Stroud, Dexter J. Booth 2013, Engineering Mathematics, 7th ed. Ed., Palgrave MacMillan [ISBN: 1137031204]
 K. A. Stroud, Dexter J. Booth 2011, Advanced Engineering Mathematics, 5th ed. Ed., Palgrave MacMillan [ISBN: 0230275486]
 Erwin Kreyszig 2011, Advanced Engineering Mathematics, 10th ed. Ed., John Wiley and Sons [ISBN: 0470646136]
 This module does not have any article/paper resources 

This module does not have any other resources 

Module Delivered in
