Chem Differential Eq HW Solutions Fall 2011 98

Chem Differential Eq HW Solutions Fall 2011 98 - λ k a )...

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98 Chapter 6 Sturm-Liouville Theory with Engineering Applications But y satisfes the boundary condition y ± ( a )= - κy ( a ), so 2 λ 2 ± a 0 [ y ( r )] 2 rdr = a 2 κ 2 [ y ( a )] 2 + λ 2 a 2 [ y ( a )] 2 ; ± a 0 [ y ( r )] 2 rdr = a 2 2 ² κ 2 [ J 0 ( λ k a )] 2 λ 2 k +[ J 0 ( λ k a )] 2 ³ = a 2 2 ´ [ J 0 ( λ k a )] 2 +[ J 1 ( λ k a )] 2 µ , because, by (7), [ J 0 ( λ k a )] 2 = ´ λ k κ J 1 (
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Unformatted text preview: λ k a ) µ 2 . (b) Reproduce the sketch oF prooF oF Theorem 1. The given Formula For the coeﬃ-cients is precisely Formula (5) in this case....
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This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.

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