Module Title: Mathematics 2 English
 Credits: 5
 NFQ Level: 6
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 Plot and interpret graphs of logarithmic and exponential functions
LO2 Differentiate common mathematical functions and apply differential calculus to the solution of engineering-type problems
LO3 Find the indefinite and definite integrals and apply integration in solving engineering-type problems
LO4 Be able to perform basic algebraic manipulation with complex numbers and understand the geometric interpretation of complex numbers.
LO5 Perform operations on matrices and use matrices to solve systems of linear equations
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 1 mathematics or equivalent

## Module Content & Assessment

Indicative Content
Logarthmic and Exponential
Exponential function Application of the exponential function to engineering problems Logarithmic function Application of the logarithmic function to engineering problems Application of logarithms to experimental data
Differentiation
Derivative in terms of the limit of a function Derivatives of common engineering functions and apply rules of differentiation Second order derivatives and application to engineering problems Second derivative test to find maxima, minima and points of inflection and applications in engineering and kinematics
Integration
Integration as reverse of differentiation Concept of indefinite integration and find indefinite integrals Integration using substitution, partial fractions and parts formula Use of integration to find areas under a graph, mean and root mean square values of functions Use of integration to find the displacement and velocity of a particle
Complex Numbers
General arithmetic operations on complex numbers Graphical representation of complex numbers Multiplication and division in polar form Various representations of complex numbers such as rectangular and polar form
Matrices
General arithmetic operations on matrices Solution of equations by using the matrix inverse method and application to engineering problems Various types of solutions of linear equations such as no solution, unique solution and infinite number of solutions. Applications of matrices in electrical principles and mechanics
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. 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 n/a 1,2,3,4,5 70.00 End-of-Semester

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