From d80351979bd0a173ff2bc8ab9f4af38dfbfe8b0f Mon Sep 17 00:00:00 2001 From: "Jiri (George) Lebl" Date: Fri, 18 Dec 2020 10:56:59 -0800 Subject: [PATCH] New version --- ca.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/ca.tex b/ca.tex index ede6db5..aca15b4 100644 --- a/ca.tex +++ b/ca.tex @@ -408,7 +408,7 @@ Ji{\v r}\'i Lebl\\[3ex]} \today \\ -(version 1.0) +(version 1.1) \end{minipage}} %\addtolength{\textwidth}{\centeroffset} @@ -21896,7 +21896,7 @@ \subsection{Differentiation under the integral} \end{thm} The hypotheses on $f$ and $\frac{\partial f}{\partial y}$ can be -weakened to some degree, see e.g.\ \exerciseref{exercise:strongerleibniz}. +weakened to a degree, see e.g.\ \exerciseref{exercise:strongerleibniz}. The proof below requires that $\frac{\partial f}{\partial y}$ exists and is continuous as a function of two variables, and the $x$ interval must be the entire @@ -23347,7 +23347,7 @@ \chapter{Basic Notation and Terminology} \label{ap:basicnotation} \lim_{t \downarrow a} f(t) \quad \Bigl( = \lim_{\substack{t \to a\\t > a}} f(t) \Bigr) , \end{equation*} -as these seemed clearer in some of the situations in this book. +as these seemed the clearer option in some of the situations in this book. We may write $\{ x_n \}$ for a sequence $\{x_n\}_{n=1}^\infty$ and similarly $\lim x_n$ instead of $\lim_{n\to \infty} x_n$ when it is clear that $n$ is the index of the sequence.