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A couple of fixes to index
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jirilebl committed May 15, 2019
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4 changes: 2 additions & 2 deletions ch-der.tex
Original file line number Diff line number Diff line change
Expand Up @@ -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 $f(x) \leq f(c)$.
Expand Down Expand Up @@ -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
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4 changes: 2 additions & 2 deletions ch-riemann.tex
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Expand Up @@ -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*}
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