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Differentiation is the set of techniques and results from Differential Calculus, concerning the calculation of derivatives of functions or distributions.
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Showing that intensive parameters obtain by considering molar quantities
In Callen's Thermodynamics textbook, he writes that
$$\left(\frac{\partial u}{\partial s}\right)_v = \left(\frac{\partial U}{\partial S}\right)_{V,N}$$
where $u = U/N$, $s = s/N$, and $v = V/N$ and, m …
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Accepted
Showing that intensive parameters obtain by considering molar quantities
Observe that
$$ \left(\frac{\partial U}{\partial S}\right)_{V,N} \equiv \left(\frac{\partial (Nu(S/N,V/N))}{\partial S}\right)_{V,N} = N\left(\frac{\partial (u(S/N,V/N))}{\partial S}\right)_{V,N} $$
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"To order $n$ of" arguments
Often one finds in physics textbooks that arguments will be made "to order $n$". I am not sure on what the procedure or argument ought to be when we have some denominator dependence though. As an exam …
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Is the time derivative of the adjoint equal to the adjoint of the time derivative?
This is hopefully straightforward. Starting from the Schrödinger equation as an axiom, one obtains the operator differential equation for the $U$ such that $| \psi(t) \rangle = U(t,t_0) | \psi(t_0) \r …