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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
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