problemset10

D since k only appears in the k terms of dk we obtain

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Unformatted text preview: wk , iDk ∂∂ kk � + �wk , i ∂∂ kk wk � �wk , iDk wk � ∂ wk ∂ �wk , iDk wk � ∂ wk � = ∂k − � , wk � + �wk , ∂ k �wk , wk � �wk , wk � �wk , wk �2 ∂k ∂k � � ˆ ∂ wk ∂ wk ∂ Dk ˆ ˆ ˆ � , iDk wk � + �iDk wk , ∂k � + �wk , i ∂ k wk � �wk , iDk wk � ∂ wk ∂ wk � = ∂k − � , wk � + �wk , �wk , wk � �wk , wk �2 ∂k ∂k � � � ∂w � � ˆk ��wk � �� D � ω � ∂kk ,�k � �� k , ∂∂ k � + �wk ,...
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This note was uploaded on 01/22/2014 for the course MATH 18.303 taught by Professor Hancock during the Fall '06 term at MIT.

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