Review of Implicit Functions

From equations A2.14.1 to A2.14.3, further relationships among partial derivatives can be obtained, such as 

If we let X and y vary while holding z constant, we get, from the partial derivative in dx of equation A2.18, 

Equation A2.19 is one of the possible ways to switch from a couple of variables to another conjugate couple. Most transforms adopted in the thermodynamics of systems with two independent variables are based on equation A2.19 and its modifications (Legendre transforms, cf section 2.4). 

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