# Mathematics for Civil Engineering 3

## Description

In this module students learn to solve and model higher order differential equations which allow for further applications to sustainable systems. Further Integration covers the calculation of work, force and energy.

## Learning Outcomes

1. Implement the method of  LU decomposition to solve a system of equations, Determine the rank of a matrix and hence determine the nature of the solutions of a system of equations. Recognise homogenous systems and calculate eigenvalues and eigenvectors.

2. Determine the unit vector normal to a particular surface. Recognise a scalar and vector field function. Find the gradient, divergence and curl of a scalar or vector field. Appreciate the use of vectors in fluid mechanics, hydraulic engineering and structural mechanics.

3. Solve intial valued first order, bounday valued, Bernoulli and second order equations using differential methods.

4. Determine Laplace transforms and inverse Laplace transforms. Apply Laplace transforms to solve first order, second order and simultaneous differential equations.

Credits
05
% Coursework 30%
% Final Exam 70%