Module Title: Mathematics 3 English
 Credits: 5
 NFQ Level: 7
Module Delivered In 2 programme(s)
Teaching & Learning Strategies: 1. A series of lectures will be delivered using whiteboard and data projector. 2. The Institute Managed Learning Environment will be used to interactively communicate with students e.g. on-line tests, discussion forums, reference information 3. Mathematical software (e.g. MATLAB) may be used by students to reinforce the mathematical principles and practices
Module Aim: To familiarise the student with the mathematical concepts and techniques that s/he will encounter in the other modules of the programme.
Learning Outcomes
On successful completion of this module the learner should be able to:
LO1 Solve systems of linear equations using various matrix methods and calculate the eigenvalues and eigenvectors of a matrix.
LO2 Solve first order separable and first order linear differential equations and apply them to simple problems in mechanics and electrical circuits.
LO3 Solve second order linear differential equations with constant coefficients and apply them to the analysis of spring-mass systems.
LO4 Apply Laplace transforms to the solutions of first and second order initial value problems
Pre-requisite learning
Module Recommendations

This is prior learning (or a practical skill) that is recommended before enrolment in this module.

No recommendations listed
Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module.
No incompatible modules listed
Co-requisite Modules
No Co-requisite modules listed
Requirements
This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed.
No requirements listed

## Module Content & Assessment

Indicative Content
• Matrices
Solution of simultaneous equations by matrix methods The rank of a matrix. Eigenvectors & eigenvalues of a matrix.
• Ordinary Differential Equations
First order ordinary differential equations. Applications of first order ODEs in mechanics. Second order linear ODEs with constant coefficients. Free and forced oscillations. Spring-mass systems.
• Laplace Transforms
o The Laplace transform and its inverse. First shift theorem. Laplace transforms of derivatives. Solution of first order initial value problems.Solution of second order initial value problems.
Assessment Breakdown%
Continuous Assessment30.00%
End of Module Formal Examination70.00%
Continuous Assessment
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Other Each student will be obliged to complete a continuous assessment program for which 30% will be awarded. This will consist of class tests and other assigned tasks, which will assess the achievement of all learning outcomes. 1,2,3,4 30.00 n/a
 No Project
 No Practical
End of Module Formal Examination
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Formal Exam A final written examination, for which 70% will be awarded, will assess the extent to which the student has achieved all the module learning outcomes. 1,2,3,4 70.00 End-of-Semester

ITCarlow reserves the right to alter the nature and timings of assessment