THIS MODULE IS RESERVED FOR STUDENTS ON U1N323401- ACTUARIAL SCIENCES AND U1G390301 - BUSINESS STATISTICS- Differential Equations: Fourier series. Partial differential equations (PDEs): diffusion equation, wave equation, Laplace's equation. Solution by separation of variables in Cartesian and polar co-ordinates. Ordinary differential equations (ODEs): solution by reduction of order and variation of parameters. Series solution and the method of Frobenius. Legendre's and Bessel's equations: Legendre polynomials, Bessel functions and their recurrence relations.