From de018de07aafbb2469f8f2544c3432262ac00f08 Mon Sep 17 00:00:00 2001 From: "Jiri (George) Lebl" Date: Wed, 15 May 2019 13:05:59 -0500 Subject: [PATCH] A couple of fixes to index --- ch-der.tex | 4 ++-- ch-riemann.tex | 4 ++-- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/ch-der.tex b/ch-der.tex index 471fa91..55eb29f 100644 --- a/ch-der.tex +++ b/ch-der.tex @@ -518,7 +518,7 @@ \subsection{Relative minima and maxima} \begin{defn} Let $S \subset \R$ be a set and let $f \colon S \to \R$ be a function. The function $f$ is said to have -a \emph{\myindex{relative maximum}}\index{minimum!relative} +a \emph{\myindex{relative maximum}}\index{maximum!relative} at $c \in S$ if there exists a $\delta>0$ such that for all $x \in S$ where $\abs{x-c} < \delta$ we have $f(x) \leq f(c)$. @@ -1353,7 +1353,7 @@ \subsection{Taylor's theorem} of $f$ at $c$, we mean that there exists a $\delta > 0$ such that $f(x) > f(c)$ for all $x \in (c-\delta,c+\delta)$ where $x\not=c$. -A \emph{\myindex{strict relative maximum}}\index{minimum!strict relative} +A \emph{\myindex{strict relative maximum}}\index{maximum!strict relative} is defined similarly. Continuity of the second derivative is not needed, but the proof is more difficult and is left as an exercise. The proof also generalizes diff --git a/ch-riemann.tex b/ch-riemann.tex index c107a9c..455b121 100644 --- a/ch-riemann.tex +++ b/ch-riemann.tex @@ -119,9 +119,9 @@ \subsection{Partitions and lower and upper integrals} \inf \, \bigl\{ U(P,f) : P \text{ a partition of $[a,b]$} \bigr\} . \end{align*} We call $\underline{\int}$\glsadd{not:lowerdarboux} -the \emph{\myindex{lower Darboux integral}}\index{Darboux integral!lower} and +the \emph{\myindex{lower Darboux integral}} and $\overline{\int}$\glsadd{not:upperdarboux} the -\emph{\myindex{upper Darboux integral}}\index{Darboux integral!upper}. +\emph{\myindex{upper Darboux integral}}\index{Darboux integral}. To avoid worrying about the variable of integration, we often simply write \begin{equation*}