laplace.py

Created on April 17, 2022
756 Bytes
FORMULE:

 Division euclédienne:
   diviseur * résulta droite + reste      / diviseur 
  


F(p)= 28/(p+2)**4        => 3!/(p+2)**4 
nb au dessus div par x!     3!=6
f(t)= 28/6* t**3 *   e**-2t U(t)

L[f'(t)] = p×F(p) – f(0+)
L[f''(t)] = p**2 × F(p) – p × f(0+) – f’(0+)

L[-t*f(t)U(t)] = F'(p)
L[(f*g)(t)] = F(p) * G(p) ; (f*g)*h =g(f*h)

L[f(t)*U(t)] = F0(p) * 1/ 1-e**-pt
        T
F0(p)= S f(t)e**-pt * dt
        0
        
τ=retard
L [f(t-τ) U(t-τ)] = F(p) * e**-τp
 
Theoreme valeur initiale
limf(t)=lim[p*F(p)]
t->0+     p-> +OO
Theoreme valeur finale
limf(t)=lim[p*F(p)]
t->+00     p-> 0 
 
 
        
EXO:    x(O+)=0 y(0+)=1
  (x'= -2x+y  => p*X(p)-0 = -2X(p)+ Y(p)
  (y'= x-2y      pY(p)-1 = X(p)-2Y(p)
   

2pi paire symetrique