hw6[1] - 3 Compute two terms in the expansion of the...

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MAE294B/SIO203B: Methods in Applied Mechanics Winter Quarter 2010 http://maecourses.ucsd.edu/mae294b Homework VI Due February 18, 2010. 1 Calculate the asymptotic expansion of the function E 1 ( x ) = Z x e - t t d t for large positive x using integration by parts. Do the same using Watson’s lemma. 2 Compute two terms in the expansion of the integral Z 0 d x ( ε + x )( 1 + ε x ) for small positive ε . Compare with the exact solution.
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Unformatted text preview: 3 Compute two terms in the expansion of the integral Z e-xt 1 + t 2 d t for both large positive and small positive x . 4 Compute two terms in the asymptotic expansion for large positive x of the integral Z e-xt f ( t ) d t where the function f ( t ) satises f 00 + 1 t f-e-t t 2 f = , f ( ) = 1 . 1...
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