preparing for exerciseset environment

Author: teepeemm

Calculus.tex

@@ -20,8 +20,6 @@
 
 \mainmatter
 
-\pagestyle{fancy}
-
 \include{CalculusI}
 
 \include{CalculusII}

CalculusII.tex

@@ -74,7 +74,7 @@ \part*{Calculus II}
 
 \apexchapter{Sequences and Series}{chapter:sequences_series}
 
-This chapter introduces \sword{sequences} and \sword{series}, important mathematical constructions that are useful when solving a large variety of mathematical problems. The content of this chapter is considerably different from the content of the chapters before it. While the material we learn here definitely falls under the scope of ``calculus,'' we will make very little use of derivatives or integrals. Limits are extremely important, though, especially limits that involve infinity. 
+This chapter introduces \textbf{sequences} and \textbf{series}, important mathematical constructions that are useful when solving a large variety of mathematical problems. The content of this chapter is considerably different from the content of the chapters before it. While the material we learn here definitely falls under the scope of ``calculus,'' we will make very little use of derivatives or integrals. Limits are extremely important, though, especially limits that involve infinity. 
 
 One of the problems addressed by this chapter is this: suppose we know information about a function and its derivatives at a point, such as  $f(1) = 3$, $\fp(1) = 1$, $\fp'(1) = -2$, $\fp''(1) = 7$, and so on. What can I say about $f(x)$ itself? Is there any reasonable approximation of the value of $f(2)$? The topic of Taylor Series addresses this problem, and allows us to make excellent approximations of functions when limited knowledge of the function is available.
 

CalculusIII.tex

@@ -3,7 +3,7 @@ \part*{Calculus III}
 
 \apexchapter{Vectors}{chapter:vectors}
 
-This chapter introduces a new mathematical object, the \sword{vector}. Defined in \autoref{sec:vector_intro}, we will see that vectors provide a powerful language for describing quantities that have magnitude and direction. A simple example of such a quantity is force: when applying a force, one is generally interested in how much force is applied (i.e., the magnitude of the force) and the direction in which the force is applied. Vectors will play an important role in many of the subsequent chapters in this text. 
+This chapter introduces a new mathematical object, the \textbf{vector}. Defined in \autoref{sec:vector_intro}, we will see that vectors provide a powerful language for describing quantities that have magnitude and direction. A simple example of such a quantity is force: when applying a force, one is generally interested in how much force is applied (i.e., the magnitude of the force) and the direction in which the force is applied. Vectors will play an important role in many of the subsequent chapters in this text. 
 
 This chapter begins with moving our mathematics out of the plane and into ``space.'' That is, we begin to think mathematically not only in two dimensions, but in three. With this foundation, we can explore vectors both in the plane and in space. 
 

apexNotes.txt

@@ -1,7 +1,3 @@
-### simple group (level 3) entered at line 589 ({)  was in 08_Series
-### simple group (level 2) entered at line 131 ({)  was in 07_Fluid_Force.tex
-### simple group (level 1) entered at line 496 ({)  was in 07_Disk_Washer_Method.tex
-
 
 Ally complains that "This HTML file contains an invalid heading structure"
 (image?) directories in Windows use a separator \ which becomes %5C in html, and breaks
@@ -61,20 +57,16 @@ Should the notebook be distributed with the text?  Eventually.  CC-BY-NC, same a
 
 
 My to do:
-  find big|?
-  pdfsizeopt to python 3?
+  pdfsizeopt to python 3? or just get it working again?
   5.2: use something other than $\Delta x$ to represent a partition
   check units in center of mass calculations
   \exerciseset -> \begin{exerciseset} 423 times. interacted weirdly with enumerate
-  \example -> \begin{example} 596 times
   \ d, \,d, d become \dd
   rearrange text/ to have chapter subfolders? and figure???
   kill [over|under]full hboxes
-  spellcheck:
-	cat text/*tex | aspell list -t --ignore=3 --ignore-case --add-texinfo-ignore=youtubeVideo | sort | uniq > misspell.txt
   ifthen -> etoolbox ?
   use subfig
-  flexible vertical page length??
+  hyphenation rules at beginning
 
   | to norm/abs
   Watch out for extra !
@@ -84,13 +76,4 @@ My to do:
   vspace to addvspace, [small|med|big]skip to [small|med|big]break ?
 
 
-13.7 p832 margin note: "will may"
 
-Fencing mismatches: \Big vs \big vs normal
-Example 5.5.1
-Key Idea 5.5.1
-Example 7.3.2
-Equation 12.2 (Section 12.5)
-Example 13.2.2
-Example 13.2.4
-Example 14.3.4

changes.md

@@ -4,7 +4,7 @@ List Of Changes
 Changes for the 2020-06 version:
 --------------------
 
-* A careful reading of Definition 3.3.1 shows that intervals of increasing and decreasing are usually closed within the domain.  We often had open intervals instead.
+* A careful reading of Definition 3.3.1 shows that intervals of increasing and decreasing are usually closed within their domain.  We often had open intervals instead.
 
 * Definition 10.3.1 (Tangent line to a parametric curve) has been rearranged to no longer have an unnecessary "provided x'≠0".
 

errata/Errata.tex

@@ -4,8 +4,7 @@
 \usepackage{booktabs}
 \usepackage{url}
 
-\title{Errata %and Addenda
-to Apex LT}
+\title{Errata to Apex LT}
 \date{\today}
 
 \newcommand{\ds}{\displaystyle}
@@ -41,30 +40,30 @@
 \maketitle
 
 \noindent
-The following errors exist in the in June 2019 printed version of Apex LT Calculus I:%\\[-2\baselineskip]
+The following errors exist in the in June 2019 printed version of Apex LT Calculus I:
 \begin{enumerate}
 \item \S1.4 p41: Theorem 1.4.1 needs to say ``except possibly at $c$''.
 \item \S1.6\#14,16: To be continuous at a point, the function needs to be defined in a neighborhood of the point.  This means that the functions are not continuous at the indicated points.
-\item \S3.3: A careful reading of Definition 3.3.1 shows that intervals of increasing and decreasing are usually closed.  We often had open intervals instead.
+\item \S3.3: A careful reading of Definition 3.3.1 shows that intervals of increasing and decreasing are usually closed within the domain.  We often had open intervals instead.
 \item \S5.4 p262: In order for Theorem 5.4.1 (FTC1) to help with the MVT later on, this needs to also include that $F$ is continuous at the endpoints.
 \item In the integration formulas at the back of the book, \#13 is missing its $dx$.
 \label{2019-06-00Iplus}
 \end{enumerate}
 
 \noindent
-The following errors exist in the in June 2019 printed version of Apex LT Calculus II:%\\[-2\baselineskip]
+The following errors exist in the in June 2019 printed version of Apex LT Calculus II:
 \begin{enumerate}
 \item \S7.4 p364 Line -1: as $x\to\infty$, both $\sinh x$ and $\cosh x$ approach $e^x/2$.
 \item \S7.5 p382\#40: $\ds\lim_{x\to1^+}$ should be $\ds\lim_{x\to1^-}$.
 \item \S8.6 p438 Figure 8.6.3: The graph is $f(x)=1/x$, not $1/x^2$.
-\item The chapter headings in \S10.2--10.5 show Chapter 9. % todo
+\item The chapter headings in \S10.2--10.5 show Chapter 9.
 \item \S10.3 p608\#40: In order to be integrable, we should have $y=4e^{t/2}$.  The length is then $e^3+11-e^{-8}$.
 \item In the integration formulas at the back of the book, \#13 is missing its $dx$.
 \label{2019-06-00II}
 \end{enumerate}
 
 \noindent
-The following errors exist in the in June 2019 printed version of Apex LT Calculus III:%\\[-2\baselineskip]
+The following errors exist in the in June 2019 printed version of Apex LT Calculus III:
 \begin{enumerate}
 \item \S11.2 p659 Definition 11.2.3 refers to $c\vec v$ as a scalar product, whereas most authors use ``scalar product'' as a synonym for the dot product.
 \item \S11.2 p660 Line 17: This is the definition of $\vec u-\vec v$; it does not follow from anything.
@@ -302,7 +301,7 @@ \section*{Digital Math Resources}
 \item \S8.1 p385 Example 6 Line -3: The $\ln(1+x^2)$ at the end should be $\frac12\ln(1+x^2)$.
 \item \S8.1\#25 Solution: The second term $x\left(\ln\abs{x+1}\right)$ should be $x\left(\ln\abs{x+1}\right)^2$.
 \item \S8.2\#5 Solution: The solution should be $\frac38 x+\frac14\sin2x+\frac1{32}\sin4x+C$.
-\item \S8.2 p402: Most of the definite integrals \emph{do not} ``appear in the previous set''. % todo do we want them to?
+\item \S8.2 p402: Most of the definite integrals \emph{do not} ``appear in the previous set''.
 \item \S8.3\#17 Solution: $\tan^{-1}\left(\frac{x+2}2\right)$ should be $\tan^{-1}\left(\frac{x+2}3\right)$.
 \item \S8.4\#31 Solution: The first and third term should be negative.
 \item \S8.5\#1: $\int \sin^{-1}x\ dx=x\sin^{-1}x+\sqrt{1-x^2}+C$, whereas\\

exercises/01_00_exercises.tex

@@ -4,6 +4,8 @@
 
 \input{exercises/01_00_exset_02}
 
+\questioncolumnbreak
+
 \input{exercises/01_00_exset_03}
 
 \input{exercises/01_00_exset_04}

exercises/01_00_exset_02.tex

@@ -56,4 +56,4 @@
 \node [above] at (myplot.above origin) {\scriptsize $y$};
 \end{tikzpicture}}
 
-}
+}

exercises/01_00_exset_03.tex

@@ -1,86 +1,70 @@
 \exerciseset{In Exercises}{, evaluate the expressions for the given $f$.}{
 
-\exercise{$f(x)=3x^2-2x+6$\\
-\begin{minipage}{.5\linewidth}
+\exercise{$f(x)=3x^2-2x+6$\\[-1.5\baselineskip]
+\begin{multicols}{2}
 \begin{enumerate}
 \item $f(2)$
 \item $f(-1)$
 \item $f(a)$
-\end{enumerate}
-\end{minipage}%
-\begin{minipage}{.5\linewidth}
-\begin{enumerate}
-\setcounter{enumii}{3}
 \item $f(x+h)$
 \item $\dfrac{f(x+h)-f(x)}{h}$
+\item[]
 \end{enumerate}
-\end{minipage}}{\mbox{}\\[-2\baselineskip]\begin{enumerate}
+\end{multicols}}{\mbox{}\\[-2\baselineskip]\begin{enumerate}
 \item 14
 \item 11
 \item $3a^2-2a+6$
 \item $3(x+h)^2-2(x+h)+6$
 \item $\dfrac{h(3 h+6 x-2)}h$
 \end{enumerate}}
 
-\exercise{$f(x)=\sqrt{x-2}$\\
-\begin{minipage}{.5\linewidth}
+\exercise{$f(x)=\sqrt{x-2}$\\[-1.5\baselineskip]
+\begin{multicols}{2}
 \begin{enumerate}
 \item $f(4)$
 \item $f(-3)$
 \item $f(t)$
-\end{enumerate}
-\end{minipage}%
-\begin{minipage}{.5\linewidth}
-\begin{enumerate}
-\setcounter{enumii}{3}
 \item $f(x+h)$
 \item $\dfrac{f(x+h)-f(x)}{h}$
+\item[]
 \end{enumerate}
-\end{minipage}}{\mbox{}\\[-2\baselineskip]\begin{enumerate}
+\end{multicols}}{\mbox{}\\[-2\baselineskip]\begin{enumerate}
 \item $\sqrt2$
 \item undefined
 \item $\sqrt{t-2}$
 \item $\sqrt{x+h-2}$
 \item $\dfrac{\sqrt{x+h-2}-\sqrt{x-2}}h\\=\dfrac h{h(\sqrt{x+h-2}+\sqrt{x-2})}$
 \end{enumerate}}
 
-\exercise{$f(x)=\dfrac1x$\\
-\begin{minipage}{.5\linewidth}
+\exercise{$f(x)=\dfrac1x$\\[-1.5\baselineskip]
+\begin{multicols}{2}
 \begin{enumerate}
 \item $f(-1)$
 \item $f(9)$
 \item $f(t+3)$
-\end{enumerate}
-\end{minipage}%
-\begin{minipage}{.5\linewidth}
-\begin{enumerate}
-\setcounter{enumii}{3}
 \item $f(x+h)$
 \item $\dfrac{f(x+h)-f(x)}{h}$
+\item[]
 \end{enumerate}
-\end{minipage}}{\mbox{}\\[-2\baselineskip]\begin{enumerate}
+\end{multicols}}{\mbox{}\\[-2\baselineskip]\begin{enumerate}
 \item $-1$
 \item $\dfrac19$
 \item $\dfrac1{t+3}$
 \item $\dfrac1{x+h}$
 \item $\dfrac{\frac1{x+h}-\frac1x}h=-\dfrac h{hx(x+h)}$
 \end{enumerate}}
 
-\exercise{$f(x)=e^x$\\
-\begin{minipage}{.5\linewidth}
+\exercise{$f(x)=e^x$\\[-1.5\baselineskip]
+\begin{multicols}{2}
 \begin{enumerate}
 \item $f(-2)$
 \item $f(3)$
 \item $f(t+1)$
-\end{enumerate}
-\end{minipage}%
-\begin{minipage}{.5\linewidth}
-\begin{enumerate}
-\setcounter{enumii}{3}
 \item $f(x+h)$
 \item $\dfrac{f(x+h)-f(x)}{h}$
+\item[]
 \end{enumerate}
-\end{minipage}}{\mbox{}\\[-2\baselineskip]\begin{enumerate}
+\end{multicols}}{\mbox{}\\[-2\baselineskip]\begin{enumerate}
 \item $e^{-2}$
 \item $e^3$
 \item $e^{t+1}$

exercises/02_06_exset_04.tex

@@ -1,4 +1,4 @@
-% todo Tim check line break of directions
+% todo Tim check line break of directions in 2.6
 \exerciseset{In Exercises}{, an implicitly defined function is given. Find $\ds \frac{d^2y}{dx^2}$. Note: these are the same problems used in Exercises~\ref{exer:02_06_ex_09}--\ref{exer:02_06_ex_12}.}{
 
 \exercise{$x^4+y^2+y=7$}{$\frac{d^2y}{dx^2} = \frac{(2y+1)(-12x^2) + 4x^3\left(2\frac{-4x^3}{2y+1}\right)}{(2y+1)^2}$}