Unformatted text preview: 3. Find the adjoint problem of x 2 y 00xy + 3 y = 0 , y (1) = y (2) = 0 . Is it selfadjoint? 4. Consider the linear operator L [ y ] = y (4) , deﬁned on the set of functions having continuous derivatives up to order 4, that satisfy the following periodic boundary conditions: y ( i ) (0) = y ( i ) (1) , i = 0 , 1 , 2 , 3 . Show that L is selfadjoint, ie show that ( L [ y 1 ] , y 2 ) = ( y 1 , L [ y 2 ]) for all y 1 and y 2 in the domain of L where ( y 1 , y 2 ) denotes the usual inner product of the functions y 1 and y 2 . * Instructor: Patrick De Leenheer. 1...
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This note was uploaded on 09/12/2011 for the course MAP 4305 taught by Professor Deleenheer during the Summer '06 term at University of Florida.
 Summer '06
 DeLeenheer

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