Website owner:  James Miller

Prove: Linearity property. Let c₁ and c₂ be any constants and F₁(t) and F₂(t) be functions with Laplace transforms f₁(s) and f₂(s) respectively. Then

            L[c₁ F₁(t) + c₂ F₂(t)] = c₁ L [F₁(t)] + c₂ L [F₂(t)] = c₁ f₁(s) + c₂ f₂(s)

Proof. Let

and

Let c₁ and c₂ be any constants. Then

Website owner:  James Miller