(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 Assessment

30.00%

End of Module Formal Examination

70.00%

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