PS4 - assume that F ( x ) = sin kx , where k is some...

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MATH 412: Problem Set 4 due Thursday, March 6, 2008 1. Strauss 2.5 #4 - Gaussian transform of the wave equation 2. Strauss 3.1 #5(b) - heat equation on the half line with Robin boundary conditions - we will go over #4 and #5(a) in class 3. (standing waves, separation of variables) As a warmup for the next problem, find a solution u ( x, t ) to the wave equation u tt = c 2 u xx by assuming that u ( x, t ) = F ( x ) G ( t ); this is called separation of variables. Here let’s
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Unformatted text preview: assume that F ( x ) = sin kx , 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 unaected. 4. Strauss 3.2 #9 -wave equation on a nite interval 5. Strauss 3.3 #2 - postponed to PS 5 Version 1.1...
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