It's been a long time since I last used Laplace so please forgive me if this is a dumb question.
Assuming I take the first and second derivatives of a function should the Laplace transforms of those derivatives be the same?
It's been a long time since I last used Laplace so please forgive me if this is a dumb question.
Assuming I take the first and second derivatives of a function should the Laplace transforms of those derivatives be the same?
If you have a function $\displaystyle f(t)$, with corresponding Laplace transform $\displaystyle F(s)$, then the Laplace transform of $\displaystyle f'(t)$ is $\displaystyle s F(s)-f(0)$, where the upper- and lower-case letters are very carefully typed. Similarly, the second derivative of $\displaystyle f(t)$ would have the Laplace transform $\displaystyle s^{2}F(s)-sf(0)-f'(0)$. So you gain two things by Laplace transformation: differentiation becomes multiplication, and the initial conditions are automatically included in your answer! Of course, not all functions even have a Laplace transform, so this method can only get you so far.