The Dirac delta function, often represented as , is a mathematical object (not technically a function) that is defined as
which has the integral
for all .
It has the Laplace transform
The Dirac delta function is often used in differential equations to approximate physical actions that take place over very short time intervals, such as a bat striking a ball. The 3D Dirac delta function, defined as
is useful in physics for modelling systems of point charges.