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PS4soln - §0DH7F7§AJS MATH 412 Problem Set 4 due Thursday...

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Unformatted text preview: / §0DH7F7§AJS // MATH 412: Problem Set 4 due Thursday, March 6, 2008 l. Strauss 2.5 #4 — Gaussian tmnsfonn of the wave equation 2. Strauss 3.1 #5(b) — heat equation on the half line with Robin boundary conditéom - we will go over #4 and #5(a) in class 3. (standing waves, sepamtton of variables) As a warmup for the next problem, find a solution u(z, t) to the wave equation utt = 62153:: by assuming that u(a:,t) : F(x)G(t); this is called separation of variables. Here let’s assume that F(a:) = sin km, where k is some constant. Find the equation for G, and solve it. For this problem u(0, t) = 0 already. How could we also get u(L,t) = 0? Notice that the function G is unaffected. 4. Strauss 3.2 #9 - wave equation on a finite interval Version 1.1 . I >4 ) 22W W/fifl": figs/5A ($7334; % {D hoax W bnjlefféi‘ft g) wc/fi fl?(‘€ ( / '1 K (AX E 9} [M V/ynL ‘> (/39 Q vQWLflSZ‘ #240 DA c g; Wm) :g/g) :: few» fig“) ”/XABfi qé/R fifl I '€‘>O ,5: (J4 m s: Dfimv'S/(B §9[u“l‘1w-x \fii a?!“ venat/J-C €fi6/‘JLO/L 07L 6% gr A? / ”9+: {fii/g‘fif/fii"? g M 51’? W “4?) +¢fiM3 ...
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