\documentclass[]{article}
\usepackage{lmodern}
\usepackage{amssymb,amsmath}
\usepackage{ifxetex,ifluatex}
\usepackage{fixltx2e} % provides \textsubscript
\ifnum 0\ifxetex 1\fi\ifluatex 1\fi=0 % if pdftex
  \usepackage[T1]{fontenc}
  \usepackage[utf8]{inputenc}
\else % if luatex or xelatex
  \ifxetex
    \usepackage{mathspec}
  \else
    \usepackage{fontspec}
  \fi
  \defaultfontfeatures{Ligatures=TeX,Scale=MatchLowercase}
\fi
% use upquote if available, for straight quotes in verbatim environments
\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
% use microtype if available
\IfFileExists{microtype.sty}{%
\usepackage{microtype}
\UseMicrotypeSet[protrusion]{basicmath} % disable protrusion for tt fonts
}{}
\usepackage{hyperref}
\hypersetup{unicode=true,
            pdftitle={Homework 6},
            pdfborder={0 0 0},
            breaklinks=true}
\urlstyle{same}  % don't use monospace font for urls
\IfFileExists{parskip.sty}{%
\usepackage{parskip}
}{% else
\setlength{\parindent}{0pt}
\setlength{\parskip}{6pt plus 2pt minus 1pt}
}
\setlength{\emergencystretch}{3em}  % prevent overfull lines
\providecommand{\tightlist}{%
  \setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
\setcounter{secnumdepth}{0}
% Redefines (sub)paragraphs to behave more like sections
\ifx\paragraph\undefined\else
\let\oldparagraph\paragraph
\renewcommand{\paragraph}[1]{\oldparagraph{#1}\mbox{}}
\fi
\ifx\subparagraph\undefined\else
\let\oldsubparagraph\subparagraph
\renewcommand{\subparagraph}[1]{\oldsubparagraph{#1}\mbox{}}
\fi

\title{Homework 6}

\input{preamble.tex}
\title{Homework}



\begin{document}
\maketitle

Please answer the following questions in complete sentences in submit
the solution on Blackboard November 22, 2016 by 5pm.

\section{Homework 6}\label{homework-6}

\subsection{Problem 1: Derive a method (20
points)}\label{problem-1-derive-a-method-20-points}

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
  Chapter 10, Exercise 2 (10 points)
\item
  Chapter 10, Exercise 3 (10 points)
\end{enumerate}

\subsection{Problem 2: An error study (10
points)}\label{problem-2-an-error-study-10-points}

Complete chapter 10, Problem 6c.

\subsection{Problem 3: A new hire (15
points)}\label{problem-3-a-new-hire-15-points}

You have just been hired at Aperature Science Labs, one of the premier
institutes of numerical computing. One of their specialities is
evaluating numerical representations of complex phenomenon. You've been
brought on in a top-secret project that is going to study the basics of
numerical integration that underlie Aperature's advanced simulations.
Your goal: produce a report on the accuracy and computational cost of
evaluating \[ \int_0^1 \cos(x^2) \, dx \] via numeric integration. Your
report should contain a summary recommendation on your findings with
state-of-the-art methods to evaluate this routine. It should include at
least three different methods; and some form of chart that your boss can
present to the weekly meeting.

\subsection{Problem 4: Sleepless nights (20
points)}\label{problem-4-sleepless-nights-20-points}

\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
  Chapter 11, Problem 3 (10 points)
\item
  Chapter 11, Problem 8 (10 points)
\end{enumerate}

\subsection{Problem 5: A choice! (15
points)}\label{problem-5-a-choice-15-points}

Please choose your own adventure! You only need to do one of the
following problems.

\textbf{Theory} Chapter 11, Problem 11 (You will have to read in the
book about how to show multi-step methods are convergent.)

\textbf{Experiment} Chapter 11, Problem 14. Here, you should use the
version of 4th order Runge-Kutta in Section 11.2.5. Make sure you show
at least one illustration of the numerical problem described with small
\(w(0)\).

\subsection{Problem 6: Look and explain! (10
points)}\label{problem-6-look-and-explain-10-points}

Take a look at the raptorchase code from the start of class. Go through
it an explain what each segment does! You may use as much or as little
granularity as you want.

\end{document}
