Upon successful completion of the module you will be able to:
· Identify flows and maps, linear and non-linear
· Describe the response of linear systems to simple periodic inputs
· Give examples of chaotic systems and the non-linearity driving them
· Describe and use simple techniques to characterise complicated dynamics, such as bifurcation diagrams, Poincare sections and attractor reconstruction techniques.
· Distinguish chaotic from purely random systems
· Describe fractals and give appropriate examples
· Describe and use simple methods to determine fractal dimension
· Describe and give examples of the mathematical concept of complexity
· Calculate the mean, variance, skewness and kurtosis of a list of numbers
· Define and give examples of common probability density functions
· Calculate a list of numbers that follow a given pdf
· Set up a Monte Carlo simulation for a simple system
· Use Maple to manipulate simple equations, solve them numerically and plot the results.
· Use Excel for a variety of simple numerical and statistical tasks.