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fixes a few more ND errors, typos and the like.
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APEXCalculus committed Sep 17, 2018
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11 changes: 11 additions & 0 deletions _ErrataTracker.tex
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pA.47 In Algebra / Taylor Series: should end with $+ . . .$ and pA.47 In Algebra / Maclaurin Series: same
% 9/16/18 both fixed, plus other uses of ``...'' instead of ``\cdots'' on same page

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You mentioned that all exercise sets now start with an odd and end with an even. There are a few sets with an odd number of problems:
01_04_exset_03
02_06_exset_02
Expand All @@ -204,17 +207,25 @@
2.3#26 doesn’t seem to belong to that instruction set, leaving the set with an odd number of problems
7.1#19,20: These don’t really belong to their exercise set
10.2#21 throws off the parity
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Grammar:
p423 8.2 just before Thm 8.2.2: $p$ is not in math mode
p496 8.8#12 solution: an open quote is never closed
p793 Def&Thm 13.4.2: (x_2,y_2) should have a comma after it
% 9/17/18 All three of above fixed


Misspellings. The good news is I figured out how to spell check in my editor (and from the command line:
cat text/*tex | aspell list -t --ignore=3 --ignore-case | sort | uniq > misspell.txt
The bad news is I figured out how to spell check.

Multiple places: The units Newtons and Joules should be capitalized
% 9/17/18 Pretty sure that no, they are not. Look at Wikipedia entry on Newton.
% Removed a few cases at first of capitalized Newton, used \emph{newton} and
% \emph{joule} for their first use.

p292 6.2#4: original is misspelled.
p557 9.5#34 solution: Pythagorean is misspelled
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2 changes: 1 addition & 1 deletion exercises/08_08_ex_12.tex
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Expand Up @@ -2,7 +2,7 @@
}
{The derivatives of $\sin x$ are $\pm \cos x$ and $\pm \sin x$; at $x=\pi/4$, these derivatives evaluate to $\pm \sqrt{2}/2$.

The Taylor series starts $\frac{\sqrt{2}}2+\frac{\sqrt{2}}2(x-\pi/4) - \frac{\sqrt{2}}2\frac{(x-\pi/4)^2}{2}-\frac{\sqrt{2}}2\frac{(x-\pi/4)^3}{3!}+\frac{\sqrt{2}}2\frac{(x-\pi/4)^4}{4!}+\frac{\sqrt{2}}2\frac{(x-\pi/4)^5}{5!}\cdots$. Note how the signs are ``even, even, odd, odd, even, even, odd, odd,$\ldots$ We saw signs like these in Example \ref{ex_seq1} of Section \ref{sec:sequences}; one way of producing such signs is to raise $(-1)$ to a special quadratic power. While many possibilities exist,
The Taylor series starts $\frac{\sqrt{2}}2+\frac{\sqrt{2}}2(x-\pi/4) - \frac{\sqrt{2}}2\frac{(x-\pi/4)^2}{2}-\frac{\sqrt{2}}2\frac{(x-\pi/4)^3}{3!}+\frac{\sqrt{2}}2\frac{(x-\pi/4)^4}{4!}+\frac{\sqrt{2}}2\frac{(x-\pi/4)^5}{5!}\cdots$. Note how the signs are ``even, even, odd, odd, even, even, odd, odd,$\ldots$'' We saw signs like these in Example \ref{ex_seq1} of Section \ref{sec:sequences}; one way of producing such signs is to raise $(-1)$ to a special quadratic power. While many possibilities exist,
one such quadratic is $(n+3)(n+4)/2$.

Thus the Taylor series is $\ds \sum_{n=0}^\infty (-1)^{\frac{(n+3)(n+4)}{2}}\frac{\sqrt2}{2}\frac{(x-\pi/4)^n}{n!}$.
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2 changes: 1 addition & 1 deletion text/07_Work.tex
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Expand Up @@ -2,7 +2,7 @@ \section{Work}\label{sec:work}

\textit{Work} is the scientific term used to describe the action of a force which moves an object. When a constant force $F$ is applied to move an object a distance $d$, the amount of work performed is $W=F\cdot d$.

The SI unit of force is the Newton, (kg$\cdot$m/s$^2$), and the SI unit of distance is a meter (m). The fundamental unit of work is one Newton--meter, or a joule (J). That is, applying a force of one Newton for one meter performs one joule of work. In Imperial units (as used in the United States), force is measured in pounds (lb) and distance is measured in feet (ft), hence work is measured in ft--lb.
The SI unit of force is the \emph{newton}, (kg$\cdot$m/s$^2$), and the SI unit of distance is a meter (m). The fundamental unit of work is one newton--meter, or a \emph{joule} (J). That is, applying a force of one newton for one meter performs one joule of work. In Imperial units (as used in the United States), force is measured in pounds (lb) and distance is measured in feet (ft), hence work is measured in ft--lb.

\mnote{.7}{\textbf{Note:} \textit{Mass} and \textit{weight} are closely related, yet different, concepts. The mass $m$ of an object is a quantitative measure of that object's resistance to acceleration. The weight $w$ of an object is a measurement of the force applied to the object by the acceleration of gravity $g$.

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2 changes: 1 addition & 1 deletion text/08_Series.tex
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Expand Up @@ -162,7 +162,7 @@ \section{Infinite Series}\label{sec:series}
\end{enumerate}
}

Like geometric series, one of the nice things about p--series is that they have easy to determine convergence properties.
Like geometric series, one of the nice things about $p$--series is that they have easy to determine convergence properties.

\theorem{thm:pseries}{$p$--Series Test}
{A general $p$--series $\ds\sum_{n=1}^\infty \frac{1}{(an+b)^p}$ will converge if, and only if, $p>1$.\index{series!p@$p$-series}\index{p@$p$-series}
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2 changes: 1 addition & 1 deletion text/13_Center_of_Mass.tex
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Expand Up @@ -191,7 +191,7 @@ \section{Center of Mass}\label{sec:center_of_mass}
We can extend the concept of the center of mass of discrete points along a line to the center of mass of discrete points in the plane rather easily. To do so, we define some terms then give a theorem.

\definition{def:moment}{Moments about the $x$- and $y$- Axes.}
{Let point masses $m_1$, $m_2,\ldots,m_n$ be located at points $(x_1,y_1)$, $(x_2,y_2)\ldots,(x_n,y_n)$, respectively, in the $x$-$y$ plane. \index{moment}
{Let point masses $m_1$, $m_2,\ldots,m_n$ be located at points $(x_1,y_1)$, $(x_2,y_2),\ldots,(x_n,y_n)$, respectively, in the $x$-$y$ plane. \index{moment}
\begin{enumerate}
\item The \textbf{moment about the $y$-axis}, $M_y$, is
$\ds M_y = \sum_{i=1}^n m_ix_i.$
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