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author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2019-08-23 17:02:38 -0400 |
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committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2019-08-23 17:02:38 -0400 |
commit | 3e1c9cfa3dc9aabcf66fb8f93ccdf816ee4459f7 (patch) | |
tree | 1622cdc9f94b1ea5b3d234496c00f6df31e8f8c5 /main.tex | |
parent | c94d723e095fc34137bc50efe41a082949f926fd (diff) | |
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functionalfunctional functional
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-rw-r--r-- | main.tex | 2 |
1 files changed, 1 insertions, 1 deletions
@@ -314,7 +314,7 @@ cannot be solved explicitly, we can make use of the inverse function theorem. First, denote by $\eta^{-1}[\eta]$ the inverse functional of $\eta$ implied by \eqref{eq:implicit.eta}, which gives the function $\epsilon_\X$ corresponding to each solution of \eqref{eq:implicit.eta} it receives. Now, we use the inverse function -theorem to relate the functional reciprocal of the functional derivative of $\eta[\epsilon]$ with respect to $\epsilon_\X$ to the functional derivative of $\eta^{-1}[\eta]$ with respect to $\eta$, yielding +theorem to relate the functional reciprocal of the derivative of $\eta[\epsilon]$ with respect to $\epsilon_\X$ to the derivative of $\eta^{-1}[\eta]$ with respect to $\eta$, yielding \begin{equation} \begin{aligned} \bigg(\frac{\delta\eta(x)}{\delta\epsilon_\X(x')}\bigg)^\recip |