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Math Help - simple step function

  1. #1
    Newbie
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    simple step function

    Hi, I just want to make sure I understand the step function.

    given that
    f(t) =
    cost, t < pi
    0, t >= pi (>= is my notation for greater than or equal to)

    Is the the correct way to write the above in heaviside notation:

    f(t) = cost + u_pi_(t)(-cost)

    Thanks. Also, does any know of any good resources out there that explain heaviside/step functions? Ive used Pauls Online notes and some youtube videos, just wondering if there are other suggestions out there.
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  2. #2
    MHF Contributor

    Joined
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    Quote Originally Posted by plopony View Post
    Hi, I just want to make sure I understand the step function.

    given that
    f(t) =
    cost, t < pi
    0, t >= pi (>= is my notation for greater than or equal to)

    Is the the correct way to write the above in heaviside notation:

    f(t) = cost + u_pi_(t)(-cost)

    Thanks. Also, does any know of any good resources out there that explain heaviside/step functions? Ive used Pauls Online notes and some youtube videos, just wondering if there are other suggestions out there.
    Yes, it is easy to check that that is correct. If t< pi, then u_pi(t)= 0 so u_pi(t)= 0(-cos(t))= 0 and f(t)= cos(t)+ 0= cos(t). If t> pi, then u_pi(t)= 1 so u_pi(t)(- cos(t))= -cos(t) and f(t)= cos(t)- cos(t)= 0.
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  3. #3
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    thank you =)
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