TD_6 - ondes u 00 tt = a 2 u 00 xx a u = sin kx sin akt b u...

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TD 6 Mohammed Saddoune AUTOMNE 2009 Exercice 1 Soit la fonction f ( x, y ) = e x + y a) Donner une fonction linéaire L ( x, y ) qui approxime f ( x, y ) au point P o = (0 , 0) . b) Trouver l’équation du plan tangent à la surface d’équation z = e x + y au point (0,0,1). Exercice 2 Soit f ( x, y ) une fonction satisfaisant 2 f ∂x 2 = 12. (*) En utilisant le changement de variables x = s + t et y = s - t , Transformer l’équation (*) dans le systeme de coordonnées { s, t } . Exercice 3 Donner l’expression de ∂z ∂x et ∂z ∂y pour: a) z = f ( x ) g ( y ) . b) z = f ( x/y ) . 1
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Exercice 4 Montrer que chacune des fonctions suivantes est une solution de l’équation des
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Unformatted text preview: ondes u 00 tt = a 2 u 00 xx a) u = sin ( kx ) sin ( akt ) . b) u = ( x-at ) 6 + ( x + at ) 6 . Exercice 5 Expliquer pourquoi la fonction est différentiable au point donné. Chercher ensuite la linéarisation L ( x,y ) de la fonction en ce point a) f ( x,y ) = yln ( x ) au point (2 , 1) . b) f ( x,y ) = e x cos ( xy ) au point (0 , 0) . 2...
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