Buscar

Loading [MathJax]/jax/output/HTML-CSS/jax.js

13.4: Propiedades de Laplace transform
https://espanol.libretexts.org/Matematicas/Analisis/Variables_complejas_con_aplicaciones_(Orloff)/13%3A_Transformaci%C3%B3n_de_Laplace/13.04%3A_Propiedades_de_Laplace_transform
$\mathcal{L} (f''; s) = \mathcal{L} ((f')'; s) = s \mathcal{L} (f'; s) - f'(0) = s(sF(s) - f(0)) - f'(0) = s^2 F(s) - sf(0) - f'(0). \text{ QED}$ \(\begin{array} {rcl} {\mathcal{L} (f(t - a); s)} & ... $\mathcal{L} (f''; s) = \mathcal{L} ((f')'; s) = s \mathcal{L} (f'; s) - f'(0) = s(sF(s) - f(0)) - f'(0) = s^2 F(s) - sf(0) - f'(0). \text{ QED}$ $\begin{array} {rcl} {\mathcal{L} (f(t - a); s)} & = & {\int_{0}^{\infty} f(t - a) e^{-st}\ dt = \int_{a}^{\infty} f(t - a) e^{-st}\ dt} \\ {} & = & {\int_{0}^{\infty} f(\tau) e^{-s(\tau + a)} \ d \tau = e^{-sa} \int_{0}^{\infty} f(\tau) e^{-s \tau} \ d \tau = e^{-sa} F(s).} \end{array}$

Search