(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Laplace convolution properties

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**