From 3e1c9cfa3dc9aabcf66fb8f93ccdf816ee4459f7 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Fri, 23 Aug 2019 17:02:38 -0400 Subject: functionalfunctional functional --- main.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'main.tex') diff --git a/main.tex b/main.tex index 895c9a5..d0184d5 100644 --- a/main.tex +++ b/main.tex @@ -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 -- cgit v1.2.3-70-g09d2