Преобразование Лапласа
4)
5) f1 ∗ f2 = f1(τ)f2(t − τ)dτ e−ptf1(τ)f2(t − τ)dτ dt =
= e−ptf1(τ)f2(t − τ)dt dτ =
= e−pτf1(τ)e−p(t−τ)f2(t − τ)dt dτ =
= e−pτf1(τ)dτe−psf2(s)ds ≡ F1(p)F2(p).
4)
5) f1 ∗ f2 = f1(τ)f2(t − τ)dτ e−ptf1(τ)f2(t − τ)dτ dt =
= e−ptf1(τ)f2(t − τ)dt dτ =
= e−pτf1(τ)e−p(t−τ)f2(t − τ)dt dτ =
= e−pτf1(τ)dτe−psf2(s)ds ≡ F1(p)F2(p).