Short Title:Mathematics 5
Full Title:Mathematics 5 (Differential Equations)
Module Code:MATH H3010
 
Credits: 5
NFQ Level:7
Field of Study:Mechanics and metal work
Module Delivered in 2 programme(s)
Reviewed By:FIONA CRANLEY
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 Find and invert Laplace transforms using a standard table, linearity, shift theorems. [POa, POb]
LO2 Invert a Laplace transform by partial fraction techniques. [POa, POb]
LO3 Solve first order linear differential equations by the integrating factor method. [POa, POb]
LO4 Solve first and second order linear differential equations with constant coefficients using the Laplace transform method. [POa, POb, POd]
LO5 Solve second order linear differential equations with constant coefficients using the complementary equation. [POa, POb,POd]
LO6 Solve a system of first order linear differential equations using Laplace transforms. [POa, POb]
LO7 Use differential equation techniques to create and solve models of engineering systems. [POa, POb, POd]
LO8 Interpret the solutions of differential equation models of engineering systems appropriately. [POa, POb, POd]
Pre-requisite learning
Co-requisite Modules
No Co-requisite modules listed
 

Module Content & Assessment

Content (The percentage workload breakdown is inidcative and subject to change) %
First Order Ordinary Differential Equations
Separable First-Order. 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 Work30.00%
End of Module Formal Examination70.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Other High threshold test on Laplace transform techniques.   15.00 Week 4
Other High threshold test on solution of differential equations.   15.00 Week 10
End of Module Formal Examination
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Formal Exam End-of-Semester Final Examination   70.00 End-of-Semester

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 Resources

Recommended Book Resources
  • Anthony Croft, Robert Davison, Martin Hargreaves, Engineering mathematics, A Foundation for Electronic, Electrical, Communications and Systems Engineers,, Prentice Hall [ISBN: ISBN 0130268585]
  • Dexter J. Booth, 2008, Engineering Mathematics, 6th Ed., Dexter Booth Palgrave Macmillan [ISBN: ISBN 9781403942463]
  • KA Stroud with additions by Dexter J 2003, Advanced Engineering Mathematics, Booth Palgrave Macmillan
  • Ed Erwin Kreyszig 1999, Advanced Engineering Mathematics, 8th Ed., John Wiley and Sons
This module does not have any article/paper resources
This module does not have any other resources
 

Module Delivered in

Programme Code Programme Semester Delivery
TA_EAMEC_B B.Eng(Hons) in Mechanical Engineering [Ab Initio] 5 Mandatory
TA_EAMEC_D Bachelor of Engineering in Mechanical Engineering 5 Mandatory