TAM310hw07 - TAM 310 Advanced Engineering Analysis I Spring...

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Unformatted text preview: TAM 310 Advanced Engineering Analysis I Spring 2008 Prof.R.Rand Homework No.7 (Due Tuesday March 11) 1. Beginning with the equation A ( x ) y primeprime + B ( x ) y prime + C ( x ) y + D ( x ) y = 0 first divide by A ( x ) and then multiply by p ( x ) = exp parenleftBigg integraldisplay B ( x ) A ( x ) dx parenrightBigg Show that the resulting equation can be written in the Sturm-Liouville form: d dx bracketleftBigg p ( x ) dy dx bracketrightBigg- q ( x ) y + w ( x ) y = 0 and obtain expressions for q ( x ) and w ( x ) in terms of p ( x ), A ( x ), C ( x ) and D ( x ). 2a. Use your results from problem 1 to put the following equation in Sturm-Liouville form: y primeprime- 2 xy prime + 2 y = 0 2b. Let y 1 ( x ) and 1 be an eigenfunction and associated eigenvalue of this equation, and let y 2 ( x ) and 2 be a different eigenfunction and associated eigenvalue. State the orthogonality of y 1 ( x ) and y 2 ( x ) on the interval- < x < ....
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