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 is also the derivative of the Heaviside function, which can be written as It can be defined as the limit of a normal distribution as it gets steeper and steeper, or the limit as of the function It has the Laplace transform for . 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