Born2bwire said:Just draw them out and do the additions and subtractions that way. The step function is rather simple so a quick pictoral representation should show you your answer.
veralika said:i still don't get it. could u just tell me that when u subtract 2 unit step functions, will there or will there not be a discontinuity at the last point?
A unit step function, also known as the Heaviside function, is a mathematical function that represents a sudden jump in value from 0 to 1 at a specific point. It is often used in engineering and physics to model the behavior of systems that experience a sudden change or impulse.
The unit step function is typically denoted by the symbol u(t) and is defined as:
u(t) = 0 for t < 0
u(t) = 1 for t ≥ 0
In other words, the function has a value of 0 for all negative inputs and a value of 1 for all non-negative inputs.
The unit step function allows us to model real-world situations that involve sudden changes or impulses. By using this function, we can analyze and understand the behavior of systems that experience these types of changes, which can be useful in various fields such as engineering, physics, and economics.
The unit step function is closely related to the Dirac delta function, which represents an infinitely sharp pulse. The unit step function can be thought of as the integral of the Dirac delta function, and is often used to smooth out the sharp edges of the delta function in practical applications.
Yes, the unit step function can be extended to multiple dimensions, such as the Heaviside step function in two dimensions or the Heaviside ramp function in three dimensions. These functions are used to model sudden changes or impulses in systems with more than one independent variable.