In this video, the probability transformation rule is used to show that the Box-Muller transformation can convert two uniform random variables into two independent Gaussian random variables.…

This video extends the probability transformation rule from the scalar case to the vector case for vector functions of random vectors. The video discusses how the Jacobian determinant needs to be…

Here we look at how the the same (or a very similar) differential equation applies to several different engineering problems. We consider cantilevers, pendulums and a floating buoy.

Here we look at some more general oscillators and their phase portraits and consider how plotting vector plots can be useful for understanding autonomous systems.

In the last part of the lecture we look at real numerical methods that can be used for real engineering problems. Looking briefly at Runge-Kutta methods and an application modelling methane-air…

What happens when the method in the first part of the lecture fails. We look at why and find a way of dealing with the problem.

In this lecture we extend the ideas in lecture 2 to allow us to solve inhomogeneous equations.

Representing Music with Fourier Coefficients