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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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- Summer '08