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supplement to BOB p10-1 - Supplement to BOB(page 10 5.7...

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Supplement to BOB (page 10) 5.7, extra problems (1) C œ C œ sin cos sin $B $ $ PP P P P 11 1 1 1 ww w # Š‹ C Cœ œ! ww ## # $$ $ B $ $ B P P P 1 1 1 sin sin 9 (2) is an eigenvalue corresponding to the eigenfunction Case 1 - Cœ" no eigenvalues or eigenfunctions Case 2 - ! Case 3 - ! eigenvalues: , - 8 # œ 8œ"ß#ß$ßá 8 P 1 eigenfunctions: , C œ 8 œ "ß #ß $ß á 8 cos 8B P 1 (3) (formula 9) ' ! # ! # sin sin sin sin B " " % # .B œ  # B  B œ ! ’“ ¹ 9 (4) (formula 7) ' ! # ! % $ 4 cos sin % " $B " %$ # % % # 1 1 .B œ œ # mC m œ # ’Š ¹ È 11.2, extra problems (1) ' P P P P cos cos sin sin 7B P P # Ð 7 8 Ñ P # Ð 7 8 Ñ P Ð78Ñ B Ð78Ñ B .B œ ¹ 9 (formula 10) (2) (formula 8) '' ‹‹ P ! ! P sin sin sin ŠŠ
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