Module Title: Mathematics 3 English
 Credits: 5
 NFQ Level: 7
Module Delivered In 2 programme(s)
Teaching & Learning Strategies: A series of lectures will be delivered using whiteboard and data projector. The Institute Managed Learning Environment will be used to interactively communicate with students e.g. on-line test, discussion forums, reference information Mathematical software (e.g. Matlab) will be used by students to re-enforce the mathematical principles and practices
Module Aim: To give the student sufficient mathematical knowledge to support the other modules of the course and provide a solid foundation for further studies
Learning Outcomes
On successful completion of this module the learner should be able to:
LO1 Find the partial derivatives and total differentials of multivariable functions and use them to calculate small changes
LO2 Perform vector operations and apply them in an engineering context
LO3 Solve first order ODEs by various methods and solve engineering problems that involve first order ODEs
LO4 Solve second order ODEs (linear, constant coefficients) and apply them to the solution of initial value and boundary value problems in an engineering context
LO5 Apply probability laws and statistical techniques to practical engineering situations
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.
Year 2 Mathematics or equivalent

## Module Content & Assessment

Indicative Content
Partial Differentiation
First and second order partial derivatives Small change and total differential in engineering
Vectors
Vectors in two and three dimensions Dot and cross products Engineering problems with vectors
Laplace Transforms
Introduction to differential equations and their solutions. Use Laplace Transforms to solve first and second order differential equations.
Statistics and Probability
Representation of data. Evaluation of mean and standard deviation of ordinary data and data in a frequency distribution Probability rules and applications Random variables and simple probability distributions Binomial and Poisson probability distributions Continuous random variables. The Normal distribution.
Assessment Breakdown%
Continuous Assessment30.00%
End of Module Formal Examination70.00%
Continuous Assessment
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Examination Each student will be obliged to complete a continuous assessment program 1,2,3,4,5 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 open book examination at the end of the module. 1,2,3,4,5 70.00 End-of-Semester

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