Probleme 1:[7 points] (a) Trouver la serie de Fourier de la fonction de periode 4 f(x) = 2x3-x, -2 0. Conditions aux limites: u(0, t)
Probleme 1:[7 points] (a) Trouver la serie de Fourier de la fonction de periode 4 f(x) = 2x3-x, -2 0. Conditions aux limites: u(0, t) = 2 , u(3, t) = 5. Conditions initiales: u(x, 0) = 3 sin 2 71 - 2 sin(x). Probleme 3:[10 points] Resoudre le probleme d'onde suivant (faire toutes les etapes): Utt = 4urx , 00, Conditions aux limites: ux(0, t) = 0, ux(4, t) =0, t> 0. 371 Conditions initiales: u(x, 0) = cos -x) , u(x, 0) = 2 - 4 sin 4
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