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Need to split function into terms and then plot


I am a newbie and need help please. I hope I can express myself clearly enough, so you can understand me.

#I have a function:
u[x_]:=c0+c1 * x +c2 * x^2

#And I am interested in these three points 0,le/2 and le (length)
points={0,le/2,le}

#When I map the above together
c=Map[u,points]

#I'll get c0, c0+c1*le/2+c2*le^2/4, c0+c1*le + c2 * le^2

#define my deflection vector
r={u1,u2,u3}

#Solve for c0,c1,c2
c=Solve[c==r,{c0,c1,c2}]
#I'll get c0->u1, c1->(3u1-4u2+u3)/le and c2-> 2(u1-2u2+u3)/le^2


#replace c into u[x_]
u[x]/.c

# separate by variable u1,u2,u3
Collect[%,{u1,u2,u3}]

#I'll get {u1(1+2x^2/le^2-3x/le)+u3(2x^2/le^2-x/le)+u2(-4x^2/le^2+4x/le)}

#Now I need to separate the above like this (le=1.5):

# n1=(1+2x^2/le^2-3x/le)
# n2=(-4x^2/le^2+4x/le)
# n3=(2x^2/le^2-x/le)

# And I don't know how.

# So I can plot it: Plot[{n1,n2,n3},{x,0,1}]
# Thanks for your help.

Honza



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