A linear partial differential equation is a partial differential equation that is linear in the unknown function and all of its derivatives. It can be written
 |
where 
is a linear operator whose
coefficients depend only on the independent variables and 
is a given function. The equation is homogeneous when 
.
Solutions of a homogeneous linear partial differential equation obey the superposition
principle. Examples include Laplace's equation,
the heat conduction equation, and the
wave equation (Evans 2010).
