Practical Analytical Methods for Partial Differential Equations

This chapter runs through some techniques that can be used to tackle partial differential equations (PDEs) in practice. It is not a theoretical work — there will be no proofs — instead I will demonstrate a range of tools that you might want to try. We begin with first-order PDEs and the method of characteristics; classification of second-order PDEs and solution of the wave equation; and separation of variables. Finally, there is a section on perturbation methods which can be applicable to both ordinary differential equations (ODEs) and PDEs of any order as long as there is a small parameter