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Using Taylor Polynomial for Laplace Transforms

  1. Sep 20, 2011 #1
    Ive attached the problem and my work in the pic.

    Questions:

    Am I even applying the taylor polynomial the correct way? (I never learned taylor series, but I was supposed to be taught in the pre-requisite class)

    Am I suppose to plug in c=4? Im not so sure about how the U4(t) works.

    After I have found the taylor polynomial, do I just take the laplace transform of it, and then that is my answer?

    thanks
     

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    Last edited: Sep 20, 2011
  2. jcsd
  3. Sep 20, 2011 #2

    LCKurtz

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    In this problem you want to make use of the forumula

    [tex]\mathcal L(f(t-a)u(t-a) = e^{-as}\mathcal Lf(t)[/tex]

    but you need to take the transform of f(t)u4(t) = f(t)u(t-4), which isn't in that form. So to use the above formula, you need to express f(t) in powers of (t-4).

    Once you have the Taylor polynomial, you would take its transform as though all the t-a terms were t and multiply the result by e-as.

    I didn't check your arithmetic but be sure you go up through the 4th derivative since you have a 4th degree polynomial and the 5th derivative and above would be 0.

    [Edit] Your numbers are OK but you need that last term to get the 4th degree.
     
    Last edited: Sep 20, 2011
  4. Sep 20, 2011 #3
    ok, I see now. Thanks for the help!
     
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