Website owner:  James Miller

Prove. Laplace transform of ∂U/∂x. Given the function U(x, t) defined for a x b, t > 0. Let the Laplace transform of U(x, t) be

Then the Laplace transform of ∂U/∂x is given by

Proof. Using Leibnitz’s rule for differentiating under the integral sign we obtain

Website owner:  James Miller