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Unformatted text preview: A ( M,y ), B ( x,N ) and C ( M,N ). [Note that A ( M,y ) is pathological and will have an extremely simple answer. This is a result of using such a simple and easily tractable function for z ( x,y ).] (d) Write the dierentials corresponding to dA , dB and dC . (e) Explain and show that B N x = C N M . List all the equivalent relationships that should exist between derivatives of z,A,B and C . 5. Given a function z, and its Legendre transforms a = zxM , b = zyN and c = zxMyN , show why following relationships hold and what they both equal (these are simple results from the denition of the dierentials): (a) z x y = b x N (b) a M y = c M N (c) M y x = N x y (d) z y x = a y M (e) b N x = c N M (f) x N M = y M N 1...
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 Fall '04
 THOMPSON

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