Hello all,
By definition, we are taught that the derivative of the unit step function is the impulse function (or delta function, which is another name).
u(t) = 1 for t>0
= 0 otherwise
So when t is equal to some infinitesimal point to the right of 0, then u(t) shoots up to equal to a constant 1. From that point on, u(t) = 1 for all time (to positive infinity).
So the derivative of a constant we know is equal to 0. And also the derivative of an infinite slope is not defined. The infinite slope occurs when
u(t) goes from magnitude 0 to 1.
So how is the derivative defined to be equal to 1.
Thanks
By definition, we are taught that the derivative of the unit step function is the impulse function (or delta function, which is another name).
u(t) = 1 for t>0
= 0 otherwise
So when t is equal to some infinitesimal point to the right of 0, then u(t) shoots up to equal to a constant 1. From that point on, u(t) = 1 for all time (to positive infinity).
So the derivative of a constant we know is equal to 0. And also the derivative of an infinite slope is not defined. The infinite slope occurs when
u(t) goes from magnitude 0 to 1.
So how is the derivative defined to be equal to 1.
Thanks