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Laplace transformation

  1. Jul 28, 2017 #1
    1. The problem statement, all variables and given/known data
    You have to calculated the Laplace transformation for 1/ cos(t)

    2. Relevant equations
    That's all

    3. The attempt at a solution
    i tryed whit some trigonometric formulas but i don't get anywhere : 1/cos(t) = cos(t) / (1- sin ^2 (t)) or 1/cos(t) = cos(t) + sin(t) x tg(t) or 1/cos(t)= (tg(t))' cos(t) ...
     
  2. jcsd
  3. Jul 28, 2017 #2

    Mark44

    Staff: Mentor

    Did you try using the definition of the Laplace Transform?
    Note that ##\frac 1 {\cos(t)} = \sec(t)##, so using the definition would entail evaluating this integral:
    $$ \int_0^\infty \sec(t)e^{-st}dt$$
    I haven't attempted doing this integration, so don't know how easy or difficult it would be. Possibly it could be done using integration by parts.
     
  4. Jul 28, 2017 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    I don't know whether the Laplace transform of your ##f(t) = 1/ \cos(t) ## exists in any sense, either as an ordinary function or as a "generalized function". The problem is that ##f(t)## has singularities at ##t = (2n+1) \pi/2, n = 0,2,3, \ldots## because ##\cos(t)## passes through ##0## at those values of ##t##. Maybe something like an infinite sum of principal-value integrals will work, but it will not be straightforward at all!

    Where did you get this problem? It looks ill-conceived to me.
     
  5. Jul 28, 2017 #4

    vela

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    Staff Emeritus
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    Is this even defined? Secant is undefined at odd multiples of ##\pi/2##.
     
  6. Jul 28, 2017 #5
    Now i know that the Laplace transform dose'nt exist , there was a diferential ecuation but i solved it without this transformation , thank you
     
  7. Jul 28, 2017 #6
    This transformation does'nt exist , i find this on other website , thank you
     
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