chapter  53
An introduction to partial differential equations
Pages 13

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.