Photo of Philip Maini lecturing

Our YouTube student lectures elicit all sorts of comments:

- What's with the crazy rolling boards?

- I knew this stuff at high school

- Didn't understand a thing

17 million views later, here's our latest: the Heat Equation with Philip Maini.

The heat equation, also known as the diffusion equation, is central to many areas in applied mathematics. In this series of four lectures, forming part of the first year undergraduate mathematics course, 'Fourier Series and PDEs', the heat equation is derived and the boundary value problem is solved using the method of separation of variables.

Students are then shown how they can use the theory of Fourier series, taught in the preceding lectures, to solve the initial value problem. The behaviour of the solutions is discussed mathematically and in the context of physical applications. Some of the accompanying materials (slides and problem sheets) are publicly available via this link:

Here is the first of four lectures. The next three are also available via the playlist

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