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\begin{document}
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\title{My Capstone Project}
\author{Template Writer}
\maketitle
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\chapter{Introduction} Take some time here to inform the reader about the contents of this report. This could include structural details and an outline description. More importantly it could include details about the contents and discourse on motivation, methods, findings, difficulties, resolutions, etc.
The reamainder of this example report includes chapters devoted to homework problems, capstone enrichment, and synthesizing concluding discussion.
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\chapter{Homework Problems}
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\section{Concept Discussion} Tell the reader your philosophy and approach to formulating and writing solutions. What can the reader expect to see? How might this be different or similar to the work of others? What benefits or drawbacks are associated with your style and methods? Write something personal and informative.
Notice that each example problem shown below has the complete problem statement and a full solution. Solutions to problems are not simply answers. A full solution must include all relevant details and explanations, and it must use accurate and appropriate mathematical language.
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\section{Problems with Solutions}
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\subsection{Problem A.1}
The railroad track from Chicago to Minneapolis is 400 miles long. The SteamKing train leaves Chicago at noon heading for Minneapolis and the IceBreaker train leaves Minneapolis at noon heading for Chicago. The SteamKing travels at 70 miles per hour and the IceBreaker travels at 55 miles per hour. Answer the following questions:
\begin{enumerate}
\item At what time do the two trains pass each other?
\item At what location along the track to the two trains pass each other?
\end{enumerate}
\paragraph{Solution}
Let $x$ be the distance along the track from Chicago (mile zero) to Minneapolis (mile 400). Let $t$ be the time in hours from noon. The location of the SteamKing is
\begin{equation}\label{eq:SK}
x_{sk}(t)=70t
\end{equation}
and the location of the IceBreaker is
\begin{equation}\label{eq:IB}
x_{ib}(t)=400-55t.
\end{equation}
The trains meet after a time $t$ when $x_{sk}=x_{ib}$.
\begin{align}
x_{ib}&=x_{sk}\\
400-55t&=70t\\
400&=15t\\
\frac{8}{3}&=t \label{eq:MeetTime}
\end{align}
We see that the time the two trains meet is $\frac{8}{3}$ hours past noon, or 2:40 PM. We can use the travel time (Equation~\ref{eq:MeetTime}) and either of Equations~\ref{eq:SK} or~\ref{eq:IB} to determine the location $x$ where the trains meet.
\begin{equation}
x=70t=(70)(8/3)=\frac{560}{3}.
\end{equation}
That is, the trains meet $560/3\approx187$ miles from Chicago.
\textcolor{blue}{Note: You may wish to add some concluding discussion which touches on any Capstone project goals you have. Or perhaps not.}
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\subsection{Problem B.3}
A person walks/runs along a straight road due west. Figure~\ref{fig:plotexample} shows her position in miles west of her starting point as a function of time in hours. Estimate the time at which she is traveling at the fastest speed. Estimate this fastest speed.
\begin{figure}[h!]
\begin{centering}
\includegraphics[width=0.7\textwidth]{speed.png}
\caption{Position (miles west) relative to a starting point as a function of time (hours). \label{fig:plotexample} }
\end{centering}
\end{figure}
\paragraph{Solution}
The person is traveling at the fastest speed when the distance versus time curve is steepest -- increasing implies traveling west, decreasing implies traveling east. This steepest location appears to occure in hour 13 during which she travels six miles. Thus, her fastest speed is 6 miles per hour (traveling west).
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\section{Concluding Discussion}
Here is your opportunity to discuss the homework problems as a whole, identify common aspects, relate problems to other questions you have considered, etc. The sky is the limit!
And, because it might be helpful, here is an example of constructing a simple (un-labeled and un-numbered) table in LaTeX. Notice that columns one and four are aligned centered, column two is aligned right justified and column three is aligned left justified.
\begin{center}
%\caption{Table of Miscellaneous Numbers}
\begin{tabular}{c|rlc}
one & two & three & four \\ \hline
33 & 44 & 55 & 66 \\
-4 & 365 & 1033 & 0 \\
$\pm 16$ & $\sqrt{7}$ & $\pi$ & 471.77 \\
\end{tabular}
\end{center}
Table~\ref{table:simple} is an example of a numbered table that can be referenced.
\begin{table}[h!]
\begin{center}
\caption{Table of Miscellaneous Numbers. \label{table:simple}}
\vspace{3mm}
\begin{tabular}{c|rlc}
one & two & three & four \\ \hline
33 & 44 & 55 & 66 \\
-4 & 365 & 1033 & 0 \\
$\pm 16$ & $\sqrt{7}$ & $\pi$ & 471.77 \\
\end{tabular}
\end{center}
\end{table}
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\chapter{A Place for a Project}
Perhaps you have chosen to relate the class material to an applied or theoretical problem taken from another field of study. This would be a good place insert details of this project. It might be a research report in itself and using the same techniques as used in solving the homework problems. It might be a research project. It might be an extended discussion and exploration of one or more homework problems. Whatever this section turns out to be, keep in mind the Capstone goals.
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\chapter{Conclusion}
Here is your summary section for the entire report. Be sure and convince the reader that your work addresses the Capstone goals. \textcolor{red}{Do not use the word ``Capstone'' anywhere within this document!}
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