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Unformatted text preview: , where [ ] [ ] âˆ« âˆ« + + = 1 2 1 ) sin( ) cos( ) sin( ) cos( 250 dx x x dx x x D n n n n n n n Question 5 a) The substitution leads to the same PDE for f(r,Î¸) and C=10. b) Eigenvalues are n = n Î» , where n= 1,3,5, â€¦ and the eigenfunctions are ) cos( Î¸ Î· n A n n = c) n n n n n r D r C-+ = Ï† d) âˆ‘ âˆž = + = ... 5 , 3 , 1 ) cos( 10 ) , ( n n n n r c r T Î¸ , where âˆ« âˆ« = 2 / 2 2 / ) ( cos ) cos( 90 Ï€ d n d n R c n n e) The same substitution as in part (a) will lead to an eigenvalue problem for that is not a Sturm-Liouville type of problem. Thus, cannot solve the PDE with such BCs using SofV method....
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- Spring '10
- Cos, Trigraph, Eigenvalue, eigenvector and eigenspace