Module Title: Mathematics 3 English
 Credits: 10
 NFQ Level: 7
Module Delivered In 2 programme(s)
Teaching & Learning Strategies: (a) A series of lectures will be delivered using whiteboard and data projector. (b) The Institute Managed Learning Environment will be used to interactively communicate with students e.g. on-line test, discussion forums, reference information (c) Mathematical software (e.g. Matlab) will be used by students to re-enforce the mathematical principles and practices
Module Aim: To give the students the knowledge, competencies and skills necessary to support the mathematical procedures encountered in the other modules of this course.
Learning Outcomes
On successful completion of this module the learner should be able to:
LO1 Demonstrate a competence in solving First and Second order differential equations.
LO2 Use Fourier series to analyse periodic functions.
LO3 Use Laplace transforms to solve first and second order IVP's.
LO4 Use probability distributions to model uncertainty.
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.
Mathematics 2 or equivalent

## Module Content & Assessment

Indicative Content
A.Differential Equations
Solve variable separable and linear first order differential equations. Solve second order homogeneous and non-homogeneous differential equations.
B.Fourier Series
Recognise periodic functions. Even and odd functions. Be able to obtain the Fourier Series of a periodic function. Derive half-range sine and cosine series
C.Laplace Transforms
Find the Laplace Transform of standard functions. Find inverse Laplace Transforms. Find the Laplace Transform of derivatives and use Laplace Transforms to solve IVP's.
D.Probability
Use probability distributions to calculate probability values.
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 a maximum of 30% will be awarded. 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 Each student will sit a formal written examination at the end of the module for which 70%will be awarded 1,2,3,4 70.00 End-of-Semester

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