A unit step function, also known as the Heaviside step function, is a mathematical function that represents a sudden change in value from 0 to 1. It is defined as 0 for all negative values and 1 for all positive values.
A unit step function is commonly used in science to model sudden changes or events, such as the activation of a gene or the sudden release of a chemical in a reaction. It is also used in differential equations to model step-like changes in a system.
A unit impulse function, also known as the Dirac delta function, is a mathematical function that represents an infinitely narrow pulse with an area of 1. It is defined as 0 for all values except at 0, where it is infinite.
A unit impulse function is commonly used in science to model sudden, short-lived events such as collisions or explosions. It is also used in signal processing to represent a single point in a continuous signal.
The unit step function can be thought of as the integral of the unit impulse function. In other words, the unit step function is the accumulated effect of multiple unit impulses over time. This relationship is often used in the analysis of systems and signals in science and engineering.