Module Title: Mathematics 2 English
 Credits: 5
 NFQ Level: 6
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 differentiating a variety single variable and multi variable functions.
LO2 Demonstrate a competence in integrating a variety of functions.
LO3 Apply basic operations to matrices and vectors. Use matrix methods to solve simultaneous equations.
LO4 Recognise arithmetic and geometric series and find their sums.
LO5 Apply basic laws of probability. Calculate mean and standard deviation for a simple discrete probability distribution.
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 1” or equivalent

## Module Content & Assessment

Indicative Content
(a)Differentiation
Review of basic rules of differentiation. Implicit, parametric and logarithmic differentiation. Partial differentiation, rates of changes and small changes of multi-variable functions.
(b)Integration
The integral as an anti-derivative. Integration of basic functions by rule. Integration of functions using the special methods of partial fractions, algebraic substitutions and integration by parts. Areas under curves, average and RMS values using the definite integral. Application of integration to areas of engineering
(c) Matrices
Arithmetic operations on matrices. Matrix inverse using cofactors. Simultaneous equations using Matrix inverse and Cramer's Rule.
(d) Vectors
Addition and subtraction of vectors in two and three dimensions. Dot and cross product of vectors
(e) Sequences and Series
Arithmetic and geometric progressions. Sum of a series
(f) Statistics and Probability
Mean, Median, Mode and Standard Deviation of a sample. Laws of probability. Random variables. Introduction to a discrete probability distribution.
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 programme. 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 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