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##### APM346--Lectures & Home Assignments / Re: Exam Practice: Prob 69-72

« Last post by**Rhamel**on

*April 09, 2019, 10:09:58 PM*»

yes

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yes

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You understand, that in the left there is summation with respect to $j$?

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When we are asked to "find the Euler-Lagrange of [some functional T[v]]" are we supposed to :

a) differentiate T[v+$\epsilon$ w] w.r.t to w and evaluate at $\epsilon = 0$ to get the EL, or

b) just plug the Lagrangian into

$$\frac{\partial}{\partial x_j} \frac{\partial \mathcal{L}}{\partial v_{x_j}} = \frac{\partial \mathcal{L}}{\partial v}$$

a) differentiate T[v+$\epsilon$ w] w.r.t to w and evaluate at $\epsilon = 0$ to get the EL, or

b) just plug the Lagrangian into

$$\frac{\partial}{\partial x_j} \frac{\partial \mathcal{L}}{\partial v_{x_j}} = \frac{\partial \mathcal{L}}{\partial v}$$

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Thank you, Professor.

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Anyone can give me a hint about Q4 uxy=0 uyz=0 and uzx=1? Thank you.

For Q13, my answer is u=1 if x=t<0,x-t<0; u=t if x+t>0,x-t>0;u=1/2+1/2(x+t) if x-t<0,x+t>0. I don't know whether it is right or not.

For Q13, my answer is u=1 if x=t<0,x-t<0; u=t if x+t>0,x-t>0;u=1/2+1/2(x+t) if x-t<0,x+t>0. I don't know whether it is right or not.

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See practice problems and announcements

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Yes

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What does it mean solution depend on 𝜌? Is it equivalent to say “depend on r”?

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What is the scope of the final exam?

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Here is my solution for solving A.