# Mathematics 3

## Description

This module will equip students with the mathematical concepts and techniques to solve problems in differentiation, integration, differential equations, Fourier series and Laplace transforms, and model the solutions with computer software.

## Learning Outcomes

1. Identify and differentiate a range of functions including the inverse trigonometric functions, the hyperbolic functions, implicit and parametric functions, functions requiring logarithmic differentiation and multivariable functions.

2. Select and apply the appropriate techniques and concepts required to evaluate a variety of integrals.

3. Solve first-order separable and linear differential equations arising from applied problems.

4. Recognise and solve linear second order differential equations with constant coefficients and appreciate their role in the modelling of oscillations.

5. Determine the Laplace Transform of a function from the definition, the table and using the First Shift Theorem.

6. Invert Laplace Transforms using the table, completion of the square and partial fractions.

7. Employ Laplace Transforms to solve differential equations.

8. Obtain the Fourier series representation of a periodic function.

9. Apply computational software to solve mathematical problems and to visualize solutions.

Credits
05
% Coursework 40%
% Final Exam 60%