The wave and heat equations. Elements of distribution theory: derivative, Fourier transform, convolution, fundamental solutions. The wave and heat equations on a interval, Fourier series. The Dirichlet and Neumann problems for the Laplace equation on a bounded domain. Green’s functions. The wave and heat equations in a bounded domain. The Dirichlet’s principle. The variational characterization of eigenvalues. The Weyl’s theorem on the asymptotic behaviour of eigenvalues