Abstract
This chapter explains Duhamel's principle applicable to linear parabolic and hyperbolic partial differential equations. It yields an integral representation in terms of the solution of a more tractable partial differential equation. The idea is that to solve a parabolic partial differential equation with a time varying source function and time varying boundary conditions, only a parabolic partial differential equation with a constant source term and constant boundary conditions needs to be solved. The chapter describes the detailed procedure as well as examples. It also highlights that the procedure for hyperbolic partial differential equations is analogous to the procedure for parabolic partial differential equations.
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