TAM310hw07

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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- &amp;lt; x &amp;lt; ....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online