Skip to main content\(\newcommand{\vf}[1]{\mathbf{\boldsymbol{\vec{#1}}}}
\renewcommand{\Hat}[1]{\mathbf{\boldsymbol{\hat{#1}}}}
\let\VF=\vf
\let\HAT=\Hat
\newcommand{\Prime}{{}\kern0.5pt'}
\newcommand{\PARTIAL}[2]{{\partial^2#1\over\partial#2^2}}
\newcommand{\Partial}[2]{{\partial#1\over\partial#2}}
\newcommand{\tr}{{\mathrm tr}}
\newcommand{\CC}{{\mathbb C}}
\newcommand{\HH}{{\mathbb H}}
\newcommand{\KK}{{\mathbb K}}
\newcommand{\RR}{{\mathbb R}}
\newcommand{\HR}{{}^*{\mathbb R}}
\renewcommand{\AA}{\vf A}
\newcommand{\BB}{\vf B}
\newcommand{\CCv}{\vf C}
\newcommand{\EE}{\vf E}
\newcommand{\FF}{\vf F}
\newcommand{\GG}{\vf G}
\newcommand{\HHv}{\vf H}
\newcommand{\II}{\vf I}
\newcommand{\JJ}{\vf J}
\newcommand{\KKv}{\vf Kv}
\renewcommand{\SS}{\vf S}
\renewcommand{\aa}{\VF a}
\newcommand{\bb}{\VF b}
\newcommand{\ee}{\VF e}
\newcommand{\gv}{\VF g}
\newcommand{\iv}{\vf\imath}
\newcommand{\rr}{\VF r}
\newcommand{\rrp}{\rr\Prime}
\newcommand{\uu}{\VF u}
\newcommand{\vv}{\VF v}
\newcommand{\ww}{\VF w}
\newcommand{\grad}{\vf\nabla}
\newcommand{\zero}{\vf 0}
\newcommand{\Ihat}{\Hat I}
\newcommand{\Jhat}{\Hat J}
\newcommand{\nn}{\Hat n}
\newcommand{\NN}{\Hat N}
\newcommand{\TT}{\Hat T}
\newcommand{\ihat}{\Hat\imath}
\newcommand{\jhat}{\Hat\jmath}
\newcommand{\khat}{\Hat k}
\newcommand{\nhat}{\Hat n}
\newcommand{\rhat}{\HAT r}
\newcommand{\shat}{\HAT s}
\newcommand{\xhat}{\Hat x}
\newcommand{\yhat}{\Hat y}
\newcommand{\zhat}{\Hat z}
\newcommand{\that}{\Hat\theta}
\newcommand{\phat}{\Hat\phi}
\newcommand{\LL}{\mathcal{L}}
\newcommand{\DD}[1]{D_{\textrm{$#1$}}}
\newcommand{\bra}[1]{\langle#1|}
\newcommand{\ket}[1]{|#1/rangle}
\newcommand{\braket}[2]{\langle#1|#2\rangle}
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\newcommand{\INT}{\LargeMath{\int}}
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\newcommand{\Partials}[3]
{\displaystyle{\partial^2#1\over\partial#2\,\partial#3}}
\newcommand{\Jacobian}[4]{\frac{\partial(#1,#2)}{\partial(#3,#4)}}
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\newcommand{\ii}{\ihat}
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\)
Section 12.6 Examples from Thermodynamics
** COMING SOON **