ABSTRACT
A partial differential equation is an equation that contains one or more partial derivatives. Examples include:
(i) a ∂u ∂x
+ b∂u ∂y
= c
(ii) ∂ 2u
∂x2 = 1
c2 ∂u
∂t
(known as the heat conduction equation)
(iii) ∂ 2u
∂x2 + ∂
∂y2 = 0
(known as Laplace’s equation) Equation (i) is a first order partial differential equation, and equations (ii) and (iii) are second order partial differential equations since the highest power of the differential is 2.
