5Second-order differential equations
IA Differential Equations
5.7 Heaviside step function
Definition (Heaviside step function). Define the Heaviside step function as:
H(x) =
Z
x
−∞
δ(t) dt
We have
H(x) =
0 x < 0
1 x > 0
undefined x = 0
x
y
By the fundamental theorem of calculus,
dH
dx
= δ(x)
But remember that these functions and relationships can only be used inside
integrals.