• 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 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 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