Prove the convolution theorem. Hint: First write F(s)G(s)
Chapter 3, Problem 3.96(choose chapter or problem)
Prove the convolution theorem. Hint: First write F(s)G(s) = 0 F(s)es g( ) d.Show that F(s)G(s) = 0 L[H(t ) f (t )](s)g( ) d. Use the definitions of the Heaviside function and of the transform to obtain F(s)G(s) = 0 est g( ) f (t ) d. Reverse the order of integration to obtain F(s)G(s) = 0 t 0 est g( ) f (t ) d dt = 0 est( f g)(t) dt. From this, show that L[ f g](s) = F(s)G(s). 3.5
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