4038HW22_Su2010 - Question (a) (8 points) Use separation of...

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Homework #22 Math 4038 Summer 2010 Print Your Name: S how all work: We can give credit only for what you write! Hand in only your own work—nothing copied! Please do not convert exact answers into decimal approximations. Please write neatly so that the grader can read your work easily. You may print a copy of this Fle and write on it, or use a blank paper with your name at the top. The maximum score possible is 10.
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Unformatted text preview: Question (a) (8 points) Use separation of variables to solve the partial diFerential equation u t = 2 u x 2 (1) with the following boundary conditions and initial conditions: x u (0 , t ) x u ( L, t ) for all t > 0. u ( x, 0) = x for all x [0 , L ]. (b) (2 points) inally, nd lim t u ( x, t ) on the interval [0 , L ]. 1...
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