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Differential Equations Lecture Work Solutions 117

Differential Equations Lecture Work Solutions 117 - 1 b = 0...

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1 b. Θ + µ Θ = 0 Z λ Z = 0 r ( r R ) + ( λ r 2 µ ) R = 0 Z (0) = Z ( H ) = 0 | R (0) | < µ m = m 2 Z n = sin n π H z Θ m = sin m θ cos m θ λ n = n π H 2 m = 1 , 2 , · · · r ( r R ) + n π H 2 r 2 m 2 R µ 0 = 0 extra minus sign Θ 0 = 1 R nm = I m n π H r u ( r, θ, z ) = m =0 n =1 ( a nm cos m θ + b nm sin m θ ) sin n π H z I m n π H r u r ( a, θ, z ) = γ ( θ, z ) = m =0 n =1 ( a nm cos m θ + b nm sin m θ ) sin n π H z · n π H I m n π H a constant a nm n π H I m n π H a = 2 π 0 H 0 γ ( θ, z ) cos m θ sin n π H z dz dθ 2 π 0 H 0 cos 2 m θ sin 2 n π H z dz dθ
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