527ass9 - compute the series for (c). For 17.4:2(d) do the...

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642:527 ASSIGNMENT 9 FALL 2009 Turn in starred problems Thuesday 11/10/2009. Section 17.3: 4 (g), 16 (b)* Section 17.4: 1 (b), 2 (c)* (d)* (see comment 1 below!) Section 18.3: 6 (c), (h), (n) (See comments 2 and 3 below). 9.A* Do problem 18.3.6(e) but change the boundary conditions to u (0 , t ) = u x (4 , t ) = 0. Keep the same initial condition f ( x ) = 25. 9.B* (a) Let F ( t ) = | t | on ( - 2 π, 2 π ]. Note that we studied this function on Assignment 8, Problem 17.3.4(b); you can use the solution to that problem without recomputing it (see the posted solution). Solve problem 17.3:18 for this function F ( t ). Comments, hints, instructions: 1. For 17.4:2(c), do only the part of the problem requiring the sketches; you are not required to
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Unformatted text preview: compute the series for (c). For 17.4:2(d) do the entire problem. 2. Section 18.3: We have not covered all of this section, but in lecture Tuesday 11/3 we discussed using Fourier series in solving the one-dimensional diusion equation on an nite interval with homogeneous boundary conditions. The parts of 18.3:6 assigned (including 9.A) are of this type. In approaching such a problem you must rst decide what sort of series to use: half range? quarter range? sine? cosine? 3. Section 18.3: For the parts of problem 18.3:6 assigned (including 9.A) you do not have to nd the steady state solution, since we have not yet discussed this....
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