vecteur, calcul intergal et equa dif Flashcards

1
Q

produit scalaire

A

U.V = U x V x cos (UV)

= UxVx + UyVy+ UzVz

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2
Q

projection orthogonal

A

->v = v.cos(angle

= ->u.v / [u]

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3
Q

calcul integral

geometrie

A

Aire sous la courbe

pour un trapeze = (B+b)h/2

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4
Q

integral par partie

A

i f(x)g’(x) dx = [fg] - if’g dx

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5
Q

valeur moyenne

A

m= 1/ b-a x i f(x)dx

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6
Q

equa dif
y’ = y
y’ = ky

A
y' = y = Aexp(x)
y' = ky  Aexp(kx)
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7
Q

methode séparation de variable

A
y'=ky 
dy/dx = ky 
dy/y = kdx 
-> integration 
ln(y) = kx + cst 
y = exp (kx + cst) 
y = K exp(kx)
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8
Q

integration des fonctions rationnelle

si ° numerateur < ° dénominateur

A

P(X) / Q(X)
Q(X) = (x-a)(x-b)
P(x) / (x-a)(x-b) = A /(x-a) + B /(x-b)
= A (x-b) + B (x-a) / (x-a)(x-b)

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9
Q

integration des fonctions rationnelle

si ° numerateur > ° dénominateur

A

P(x) / Q(x) = M(x) + R(x) / Q(x)
1) diviser le x^n le plus grand de P par le x^n le + gd de Q note ax
2) soustraitre P(x) par ax x x^n de Q
3) recommencer jusqua avoir un reste de degres < Q
M = quotient R = reste

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10
Q

equa dif lineaire du 1er ordre a coef cst

ay’ + by = r(x)

A

1) ayo’ + byo = 0
solution : Kexp(- bt /a)
2) méthode d’identification et on trouve Y de aY’ + bY = r(x)
3) y = yo + Y

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11
Q

equa dif lineaire du 2eme ordre a coef cst

ay’’ + by’ + cy = g(x)

A
1) ayo'' + byo' + cyo' = 0 
yo'' = r^2 exp (rx) 
yo' = r exp (rx) 
yo = exp (rx) 
=> ar^2 + br + c = 0 
calcul D = b^2 - 4ac 
si D > 0 r = -b +- racine (D) / 2a
si D = 0 r = -b / 2a
 si D < 0 r = -b +- i racine (D) / 2a = alpha + beta i 
solution dans le formulaire 
2) méthode d'identification et on trouve Y de aY' + bY = r(x) 
3) y = yo + Y
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