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Math Help - Find the laplace transformation.

  1. #1
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    Find the laplace transformation.

    Find the Laplace transformation of the piecewise function.

    f(t) = t+1, 0≤t≤1
    f(t) = t^2, t>1

    Sketch the graph of f(t)

    i use the g(t)[u(t-a)-u(t-b)] and i get:

    (t+1)[u(t-0)-u(t-1)]+(t^2)u(t-1)
    and that gives:
    (t+1)-(t+1)u(t-1)+(t^2)u(t-1)
    and then i can take the Laplace
    L[t]+L[1]+L[(t+1)u(t-1)]+L[(t^2)u(t-1)]

    after much calculation i got answer which was wrong
    I'm pretty sure i messed up trying to take the laplace of "L[(t+1)u(t-1)]+L[(t^2)u(t-1)]"

    Any help?
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  2. #2
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    Re: Find the laplace transformation.

    Quote Originally Posted by Aquameatwad View Post
    Find the Laplace transformation of the piecewise function.

    f(t) = t+1, 0≤t≤1
    f(t) = t^2, t>1

    [snip]
    Why not substitute f(t) into the definition of the Laplace transform and calculate the answer from 'first principles' ....
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    Re: Find the laplace transformation.

    You have intrigued me... What are "first principles"? I haven't heard my teacher use that term with laplace transformations.
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    Re: Find the laplace transformation.

    Quote Originally Posted by Aquameatwad View Post
    You have intrigued me... What are "first principles"? I haven't heard my teacher use that term with laplace transformations.
    Equation (1) here: Laplace Transform -- from Wolfram MathWorld

    I'd be amazed if your class notes and textbook don't have it, together with examples.
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    Re: Find the laplace transformation.

    This class should be taught in 2 semesters than just one. Our teacher does the best he can in this short amount of time. thanks for the insight , i will look into it
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