pset_6 - G(1,x = 0(b Using the Greens function write down...

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ACM 95/100b Problem Set 6 February 22, 2009 Due by 5:00PM on 2/27/2009 All problems are worth 10 points on this set. Please deposit your problem set in the slot in 303 Firestone or upload it via Moodle. In either case please keep a copy of your problem set. Please remember to include your section number and section instructor. Collaboration is allowed on all problems but please write up the solutions yourself. Problem 1 Consider the boundary value problem y 00 + 2 y 0 + y = x 0 x 1 y (0) = 0 y (1) = 0 The objective of this problem is to solve the BVP above using Greens functions. (a) Find the Greens function for this ODE. That is, solve the boundary value prob- lem G 00 + 2 G 0 + G = δ ( x - x 0 ) G (0 ,x 0 ) = 0
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Unformatted text preview: G (1 ,x ) = 0 (b) Using the Greens function write down the formal solution to the problem y 00 + 2 y + y = f ( x ) ≤ x ≤ 1 Your answer should be in the form of an integral. (c) Finally, using the results above solve y 00 + 2 y + y = x ≤ x ≤ 1 Problem 2 Solve for the Green’s function for G 00 + λG = δ ( x-x ) ≤ x ≤ π G (0 ,x ) = 0 , G ( π,x ) = 0 1 in closed form (that is, not a Fourier series). Show that the poles of the Green’s function are located at the eigenvalues of the corresponding Sturm-Liouville problem y 00 + λy = 0 ≤ x ≤ π y (0) = 0 , y ( π ) = 0 2...
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pset_6 - G(1,x = 0(b Using the Greens function write down...

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