THIS MODULE IS RESERVED FOR VISITING STUDENTS: 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 Forbenius. Legendre's and Bessel's equations: Legendre polynomials, Bessel functions and their recurrence relations.