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teepeemm · Nov 21, 2024 · 5fdb69b · 5fdb69b
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diff --git a/README.md b/README.md
@@ -17,6 +17,8 @@ Running `./make.py -n` will use latexml to make a complete website version of th
 (Unfortunately, latexmk appears to be a little too agressive in ignoring compilation errors.
 I recommend compiling using your regular method first, and once you know it compiles, then use latexmk.)
 
+A solutions manual is available upon request.
+
 This work is covered with a Creative Commons 4.0 By-NC copyright.
 
 #### Rearrangements from ET

diff --git a/apexNotes.txt b/apexNotes.txt
@@ -12,6 +12,7 @@ III: F15.4.8 ?
 9.8 p529: all series tests require positivity?
 D11.4.1: Maybe give the box method for computing?
 12.5 better arc length parameterization? Frenet frame?
+F14.2.8: use axis equal image
 C15: should 2d curl match 3d curl?
 15.4: Green's Theorem on region with holes
 

diff --git a/errata/Errata.tex b/errata/Errata.tex
@@ -85,6 +85,34 @@
 
 \maketitle
 
+\noindent
+The following errors exist in the in June 2023 printed version of Apex LT Calculus I:
+\begin{enumerate}
+\item \S1.2 p18 Example 1.2.1: The solution requires $\epsilon<4$ in order for $\delta>0$.
+\item \S3.3 p168\#25 solution: While the function is decreasing on $(-\infty,-2)$, $(-2,4)$, $(4,\infty)$; and this is the entirety of the domain; it is incorrect to say that the function is ``decreasing on [its] entire domain'' because it is not necessarily decreasing from one interval to another.
+\label{2023-06-00I}
+\end{enumerate}
+
+\startMarkdownTable
+\begin{table}[ht]
+\caption{Errata Tally (``+'' indicates systemic errata)}
+\begin{tabular}{lccc}\toprule
+Version & Calculus I & Calculus II & Calculus III \\\midrule
+\errorrow{2023-06-00} \\
+\errorrow{2021-06-00} \\
+\errorrow{2019-06-00} \\
+\errorrow{2018-07-13} \\
+\errorrow{2017-11-13} \\
+\errorrow{2017-07-27} \\
+\errorrow{2017-05-00} \\
+\errorrow{2017-01-00} \\
+\errorrow{2016-08-00} \\
+\midrule
+\errorTotals \\
+\bottomrule
+\end{tabular}
+\end{table}
+
 \noindent
 The following errors exist in the in June 2021 printed version of Apex LT Calculus I:
 \begin{enumerate}
@@ -147,25 +175,6 @@
 \label{2021-06-00III}
 \end{enumerate}
 
-\startMarkdownTable
-\begin{table}[ht]
-\caption{Errata Tally (``+'' indicates systemic errata)}
-\begin{tabular}{lccc}\toprule
-Version & Calculus I & Calculus II & Calculus III \\\midrule
-\errorrow{2021-06-00} \\
-\errorrow{2019-06-00} \\
-\errorrow{2018-07-13} \\
-\errorrow{2017-11-13} \\
-\errorrow{2017-07-27} \\
-\errorrow{2017-05-00} \\
-\errorrow{2017-01-00} \\
-\errorrow{2016-08-00} \\
-\midrule
-\errorTotals \\
-\bottomrule
-\end{tabular}
-\end{table}
-
 \noindent
 The following errors exist in the in June 2019 printed version of Apex LT Calculus I:
 \begin{enumerate}

diff --git a/errata/README.md b/errata/README.md
@@ -5,6 +5,7 @@ If you are interested in a particular error, you can look through [Errata.tex](E
 
 Version | Calculus I | Calculus II | Calculuc III
 ---|---|---|---
+2023-06-00|2||
 2021-06-00|2|30|10
 2019-06-00|6+|7|22
 2018-07-13|47|56+|13+
@@ -14,7 +15,7 @@ Version | Calculus I | Calculus II | Calculuc III
 2017-01-00|9+|19+|
 2016-08-00|19+||
 ---|---|---|---
-Total|94+|146+|103+
+Total|96+|146+|103+
 
 "+" indicates a systemic error.  
 (The totals for a row may be higher than what's listed in [changes.md](../changes.md) due to double counting.)
diff --git a/exercises/03-03-exset-02.tex b/exercises/03-03-exset-02.tex
@@ -44,7 +44,7 @@
 
 \exercise{$\ds f(x) =\frac{x}{x^2-2x-8}$}{domain=$(-\infty,-2)\cup(-2,4)\cup(4,\infty)$;\\
 no c.p.;\\
-decreasing on entire domain, $(-\infty,-2)$; $(-2,4)$; $(4,\infty)$.}
+decreasing on $(-\infty,-2)$; $(-2,4)$; $(4,\infty)$.}
 
 \exercise{$\ds f(x) =\frac{(x-2)^{2/3}}{x}$}{domain=$(-\infty,0)\cup(0,\infty)$;\\
 c.p. at $c=2,6$;\\

diff --git a/slurm-apex.sh b/slurm-apex.sh
@@ -53,10 +53,10 @@ latexmlscripts="$HOME/git/LaTeXML/blib/script"
 singularitydir="$HOME/latexml"
 printf '\\newcommand{\\thetitle}{Calculus}\n\\printincolor\n\\usethreeDgraphics\n\\renewcommand{\\monthYear}{June 2023}\n' > options.tex
 
-#singularity exec $singularitydir/latexml.sif $latexmlscripts/latexml \
-#    --destination=$base.xml \
-#    --nocomments \
-#    $base
+singularity exec $singularitydir/latexml.sif $latexmlscripts/latexml \
+    --destination=$base.xml \
+    --nocomments \
+    $base
 
 exit_code=$?
 
@@ -69,10 +69,10 @@ if [ "$exit_code" -ne "0" ]; then
     exit "$exit_code"
 fi
 
-#singularity exec $singularitydir/latexml.sif $latexmlscripts/latexmlpost \
-#    --split \
-#    --destination=web/index.html \
-#    $base.xml
+singularity exec $singularitydir/latexml.sif $latexmlscripts/latexmlpost \
+    --split \
+    --destination=web/index.html \
+    $base.xml
 
 exit_code=$?
 
@@ -91,6 +91,7 @@ singularity exec $singularitydir/latexml.sif $latexmlscripts/latexmlc \
     --split \
     --timeout=36000 \
     --css=style-narrow.css \
+    --stylesheet=apexepub.xsl \
     $base
 
 exit_code=$?

diff --git a/standalone.tex b/standalone.tex
@@ -25,13 +25,13 @@
 
 %\clearpage
 
-\setcounter{chapter}{10}
+\setcounter{chapter}{1}
 
-\setcounter{section}{4}
+\setcounter{section}{1}
 
-\setcounter{figure}{6}
+%\setcounter{figure}{6}
 
-\input{text/09_Polar_Intro}
+\input{text/01_Limit_Definition}
 
 %%\printexercises{exercises/14-03-exercises}
 %

diff --git a/text/01_Limit_Definition.tex b/text/01_Limit_Definition.tex
@@ -139,7 +139,9 @@ \section{Epsilon-Delta Definition of a Limit}\label{sec:limit_def}
 \end{align*}
 
 The ``desired form'' in the last step is ``$-\textit{something} < x-4 < \textit{something}$.''
-Since we want this last interval to describe an $x$ tolerance around 4, we have that either $\delta \leq 4\epsilon - \epsilon^2$ or $\delta \leq 4\epsilon + \epsilon^2$, whichever is smaller: \[\delta \leq \min\{4\epsilon - \epsilon^2, 4\epsilon + \epsilon^2\}\text{.}\]  Since $\epsilon > 0$, the minimum is $\delta \leq 4\epsilon - \epsilon^2$.  That's the formula: given an $\epsilon$, set $\delta \leq 4\epsilon-\epsilon^2$. 
+Since we want this last interval to describe an $x$ tolerance around 4, we have that either $\delta \leq 4\epsilon - \epsilon^2$ or $\delta \leq 4\epsilon + \epsilon^2$, whichever is smaller:
+\[\delta \leq \min\{4\epsilon - \epsilon^2, 4\epsilon + \epsilon^2\}\text{.}\]
+Since $\epsilon > 0$, the minimum is $\delta \leq 4\epsilon - \epsilon^2$.  That's the formula: given an $\epsilon$, set $\delta \leq 4\epsilon-\epsilon^2$. (We also need $\epsilon<4$ so that $\delta>0$.  But there's no problem assuming $\epsilon$ is smaller than what we were given.)
 
 We can check this for our previous values.  If $\epsilon=0.5$, the formula gives
 $\delta \leq 4(0.5) - (0.5)^2 = 1.75$ and when $\epsilon=0.01$, the formula gives $\delta \leq 4(0.01) - (0.01)^2 = 0.399$.

diff --git a/text/04_NewtonsMethod.tex b/text/04_NewtonsMethod.tex
@@ -91,7 +91,7 @@ \section{Newton's Method}\label{sec:newton}
 x_4 &= 1.48579 - \frac{f(1.48579)}{\fp(1.48579)} \approx  1.46596,\\
 x_5 &= 1.46596 - \frac{f(1.46596)}{\fp(1.46596)} \approx 1.46557
 \end{flalign*}
-We performed 5 iterations of Newton's Method to find a root accurate to the first 3 places after the decimal; our final approximation is $1.465.$ The exact value of the root, to six decimal places, is $1.465571$;  It turns out that our $x_5$ is accurate to more than just 3 decimal places.
+We performed 5 iterations of Newton's Method to find a root accurate to the first 3 places after the decimal; our final approximation is $1.465.$ The exact value of the root, to six decimal places, is $1.465571$; it turns out that our $x_5$ is accurate to more than just 3 decimal places.
 
 \mtable{A graph of $f(x) = x^3-x^2-1$ in \autoref{ex_newt2}.}{fig:newt2}{\begin{tikzpicture}
 \begin{axis}[width=\marginparwidth,tick label style={font=\scriptsize},