ABSTRACT
This chapter seems logical to discuss first order partial differential equations (PDEs) before we discuss higher order. However, historically, investigation of partial differential equations starts with second order, as many physical problems, like wave propagation, heat diffusion, and incompressible and irrotational flow, have to be modelled by second order PDEs. They include the work of Bernoulli, Euler, D’Alembert, Laplace and many others. Because of its importance in physical applications, most of the available results for PDEs are developed for second order. The chapter shows that the canonical forms of second order PDEs with constant coefficients can always convert to nonhomogeneous Klein-Gordon equations, nonhomogeneous diffusion equation and nonhomogeneous Helmholtz equations. In view of the importance of the biharmonic equation in elasticity and in fluid flows, Selvadurai considered the solution of the biharmonic equation in detail whereas higher order PDEs with constant coefficients were considered.
