Tabeddilt n Laplaṣ

Deg tusnakt, Tabeddilt n Laplaṣ, tettwasemma-d ɣef Pierre-Simon Laplace, d tabeddilt tuɣridt, i d smutti n tesɣent n umutti ilaw ( s tuget $t$) ar tasɣent n umutti asemlal $s$.

Amezruy

Pierre-Simon Laplace

Tabeddilt n Laplaṣ tewwi isem-is seg umusnak afransis Pierre-Simon Laplaṣe (1749-1827). Laplaṣe yessiweḍ ad d-yefk tabadut n tbeddilt-agi deg useggas n 1785, mi yella yeţţnadi ɣef tlufa n tmikanikt tagennawt. Seg yimir-nni, tabeddilt n Laplaṣ tuɣal d allal aseklan deg waṭas n yiḥricen n tusnakt d tussna.

Tabadut tamsalɣa

$\mathrm{\Re }(e^{-st})$

Tabeddilt n Laplaṣ n tesɣent $f(t)$, yettwasbedun i wakk imḍanen ilawen $t\ge 0$ , d nettat d tesɣunt $F(t)$ am akka:

$F(x)=\underset{0}{\overset{+\mathrm{\infty }}{\int }}f(t)*e^{-st}dt$

anda  :$$s=\sigma +i\omega ,$$

Tabeddilt n Laplaṣ n sin idisen

ma neqqar "tabeddilt n Laplaṣ" akken s tḥerfit, ad negg srid tabeddilt n Laplaṣ n yiwen idis i t-nezwar deg uḥric amezwaru (seg yilem ar ifeḍ n ufella). Ama yella useɣzef n tbeddilt agi akken ad yecmel akk imḍanen ilawen seg yifeḍ n wadda ar ifeḍ n ufella, wagi neqqar-as "Tabeddilt n Laplaṣ n sin idisen".

Tabedddilt n Laplaṣ n sin idisen tettwasbedu am akka :

$F(x)=\underset{-\mathrm{\infty }}{\overset{+\mathrm{\infty }}{\int }}f(t)*e^{-st}dt$