Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

\begin{align} f(t) = \begin{cases} 3t &\mbox{if } t \leq 3 \\ 12 & \mbox{if } 3<t\leq 7 \\ 0 & \mbox{if } t\geq 7 \end{cases} \end{align}

I'm confused as to how I can write this in terms of the unit step function with the first f(t) has $\leq 3$ instead of just $\lt 3$. Any help with this problem?

share|cite|improve this question
I edited your latex, please check if this is still consistent – k1next Dec 14 '12 at 11:15
This is besides the question, but your function is slightly flawed. At $t=7$, is $f(t)$ equal to 12 or 0? – Paresh Dec 14 '12 at 11:34
up vote 1 down vote accepted

Depends on the definition of the Heaviside function - it can be either 0, 1 or 0.5 at H(0).

If you take it to be zero, I think the following works:

[3tH(3-t) + 12 H(7-t) H(t-3)]H(7-t)

share|cite|improve this answer
Indeed,… – lhf Dec 14 '12 at 12:23

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.