# Heaviside/Unit Step Function and other piecewise functions

• Nov 19th 2010, 09:53 AM
Noxide
Heaviside/Unit Step Function and other piecewise functions
let f(t) be an elementary function defined for every real number t
denote the unit step function as U(t-a), t >= 0, a real
such that U(t-a) = {0 if 0<=t<a, and 1 if t>= a

then

f(t)U(t-a) = {0 if 0<=t<a, and f(t) if t >= a

No problem.

What happens when we compute the product U(t-a)p(t), where p(t) is itself a piecewise function? i.e. p(t) = { condition 1, 2, ..., n
• Nov 19th 2010, 11:20 AM
CaptainBlack
Quote:

Originally Posted by Noxide
let f(t) be an elementary function defined for every real number t
denote the unit step function as U(t-a), t >= 0, a real
such that U(t-a) = {0 if 0<=t<a, and 1 if t>= a

then

f(t)U(t-a) = {0 if 0<=t<a, and f(t) if t >= a

No problem.

What happens when we compute the product U(t-a)p(t), where p(t) is itself a piecewise function? i.e. p(t) = { condition 1, 2, ..., n

Exactly as before:

U(t-a)p(t) = {0 if 0<=t<a, and p(t) if t >= a

CB
• Nov 19th 2010, 04:48 PM
Noxide
lol, ty