Week 5

Section 3.6 describes an elementary uniqueness theorem for an initial value problem for the heat equation.

Section 3.7 describes the method of shifting the data to handle inhomogeneous Dirichlet boundary conditions.

Section 3.8 discusses the impact of imposing homogeneous Neumann boundary conditions.

Section 3.9 describes how to generalise Fourier’s method to solve an initial boundary value problem for the inhomogeneous heat equation subject to inhomogeneous Neumann boundary conditions. This provides a stepping stone to eigenfunction expansions and Fourier transforms methods that may be studied later on in the degree.