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# HW4soln - EAS 4101 S08 HW solutions 4th Homework 1(1.2...

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EAS 4101 S08 HW solutions 1/10 HW#4 02/22/08 4 th Homework 1. (1.2 Anderson) Starting with Equations (1.7), (1.8), and (1.11), derive in detail Equations (1.15), (1.16), and (1.17). ( ) ( ) ( ) ( ) ( ) ( ) ( ) ' cos sin cos sin cos sin ' ' TE TE u u u l l l LE LE TE TE u l u l LE LE TE TE u l u l LE LE N p ds p ds ds dx ds dy N p p dx dy N p p p p dx dy θ τ θ θ τ θ θ θ τ τ τ τ = − + + = = − = − + + = − + + Divide by ( ) 1 q S q c = ( ) ( ) 0 ' 1 1 1 1 l u u l TE TE u l u l LE LE c TE n p p f f LE p p p p N dx dy q c c q q c q q c c c dx c c dy c c τ τ = − + + = + + This is Eq. (1.15). ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 0 ' sin cos sin cos ' ' ' 1 1 1 u l TE TE u u u l l l LE LE TE TE u l u l LE LE TE c u l u l LE TE c u l u l LE TE a p p LE A p ds p ds A p p dy dx A p p p p dy dx p p p p A dy dx q c c q q c q q c c c dy c θ τ θ θ τ θ τ τ τ τ τ τ = + + + = + + = + + = + + =

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