The heat equation, also known as the diffusion equation, is central to many areas in applied mathematics. In this series of four lectures - this is the first - 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.

You can watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists):
https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE

All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.