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Homework Help: Laplace convolution properties

  1. Nov 25, 2008 #1
    1. The problem statement, all variables and given/known data

    Prove the associativity law and the distributive law for convolution:
    (1) prove F*(G+H)=(F*G)+(F*H)
    (2) prove: F*(G*H)=(F*G)*H

    2. Relevant equations


    3. The attempt at a solution

    (1) proof: using the definition of the laplace using convolution
    Left hand side: =integral(F(u)(G(t-u)+H(t-u))du
    =laplace(F)xlaplace(G)+Laplace(F)xlaplace(H)
    Right hand side: =integral(F(u)G(t-u))du + integral(F(u)H(t-u)du
    =laplace(F)xlaplace(G)+laplace(F)laplace(H) = left hand side

    I dont know how to prove the second one. Any help would be v much appreciated.
     
  2. jcsd
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