4038HW24_Su2010 - unctions A ( p ) and B ( p ) or which ( x...

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Homework #24 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. Question This question has two parts. a. Let φ ( x )= e k | x | where k> 0and φ is defned on the whole real line. Find the Fourier coefficient
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Unformatted text preview: unctions A ( p ) and B ( p ) or which ( x ) = Z o A ( p ) cos px + B ( p ) sin px dp . (Suggestion, write cos px = < e ipx and sin px = = e ipx .) b. Use ormula (6), rom section 12.6 in the text, to write the solution o the heat equation u t = c 2 u xx or an infnite rod provided that the initial temperature distribution on the rod is given by u ( x, 0) = f ( x ) = 1 1 + x 2 . (Suggestion: Part (a) actually tells you the value o Z o f ( x ) cos px dx .) 1...
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