Graphical Methods Summary

Linearizing and analyzing graphs are tricky skills for students to pick up when doing physics.  I enjoyed the discussion of a poster created by Paul Jebb, on the Modeling Physics listserve, but I wanted to create my own.  The result is here:

graph-analysis-beamer-poster-18x24
graph-analysis-beamer-poster-18×24

It would be nice to add the Hestenes’ descriptions of the change in the graph, but perhaps that deserves another poster.

Incidentally, I found the LaTeX beamerposter package quite easy to use.  As usual with LaTeX, the sizes of margins and things required tweaking, but it should work to print out as an 18″ by 24″ poster.

The source code is clearly cribbed from the beamerposter template.  PGF/TikZ is used for the graphs.

Update: You can now find source code for this and other posters in my GitHub repository.

  \documentclass[final]{beamer} % beamer 3.10: do NOT use option hyperref={pdfpagelabels=false} !
 %\documentclass[final,hyperref={pdfpagelabels=false}]{beamer} % beamer 3.07: get rid of beamer warnings
  	\mode {  %% check http://www-i6.informatik.rwth-aachen.de/~dreuw/latexbeamerposter.php for examples
	\usetheme{default}    %% you should define your own theme e.g. for big headlines using your own logos
	\beamertemplatenavigationsymbolsempty
	\definecolor{royalblue}{rgb}{0,0.13725490196078433,0.4}
	\definecolor{royalblueweb}{rgb}{0.25490196078431371,0.41176470588235292,0.88235294117647056}
  	\definecolor{burntorange}{rgb}{0.8,0.3333333333333333,0}
  	\setbeamercolor{frametitle}{fg=blue!80!black}
    	\setbeamertemplate{frametitle} {
	\begin{centering}
    		\vspace{-1.5cm}\textbf{\insertframetitle} \par
	\end{centering}
}
  }
  \usepackage[english]{babel}
  \usepackage[latin1]{inputenc}
  \usepackage{amsmath,amsthm, amssymb, latexsym}
  %\usepackage{times}\usefonttheme{professionalfonts}  % times is obsolete
  \usefonttheme[onlymath]{serif}
  \boldmath
  %\usepackage[orientation=portrait,size=a0,scale=1.4,debug]{beamerposter}                       % e.g. for DIN-A0 poster
  %\usepackage[orientation=portrait,size=a1,scale=1.4,grid,debug]{beamerposter}                  % e.g. for DIN-A1 poster, with optional grid and debug output
  \usepackage[size=custom,width=45.72,height=60.96,scale=1.8,debug]{beamerposter}                     % e.g. for custom size poster (18in x 24in w/ printable 17in x 23in)
  %\usepackage[orientation=portrait,size=a0,scale=1.0,printer=rwth-glossy-uv.df]{beamerposter}   % e.g. for DIN-A0 poster with rwth-glossy-uv printer check
  % ...
  %
  \geometry{margin=.5in}
  \usepackage{array}
  \usepackage{booktabs}
  \newcolumntype{P}[1]{>{\raggedright\large}p{#1}}
  \def\imagetop#1{\vtop{\vspace{-1.5cm}\null\hbox{#1}\vspace{-1.5cm}}}
  \usepackage{tikz}

  \newcommand{\xx}{\textcolor{variable}{x}}
  \newcommand{\yy}{\textcolor{variable}{y}}
  \newcommand{\versus}{vs\ }
  \newcommand{\plotscale}{1.5}
  \newcommand{\plotline}{6pt}
  \newcommand{\formatmm}[1]{\textcolor{royalblue}{\textbf{#1}}}
  \colorlet{plot}{burntorange}
  \colorlet{variable}{blue!80!black}

  \title[Graph Methods]{Graphical Methods Summary}
  \author[Vancil]{Brian Vancil}
  \institute[Sumner]{Sumner Academy of Arts & Sciences}
  \date{2012-04-07}

  \begin{document}
  \begin{frame}{Graphical Methods Summary}
    \defaultaddspace=.25em
    \vspace{-2cm}
    \begin{tabular}{P{.25\linewidth}P{.16\linewidth}P{.30\linewidth}@{\quad}>{\arraybackslash}P{.21\linewidth}} \toprule[.1em]
    \normalsize Mathematical model & \normalsize Graph shape & \normalsize Written relationship & \normalsize To linearize, graph\ldots \\ \midrule[.1em] \addlinespace

    \formatmm{constant}\ \ \  $\yy=b$ &
    \imagetop{\begin{tikzpicture}[scale=\plotscale,domain=0:4,line width=\plotline,smooth]
    \draw[color=plot] plot (\x,3);
    \draw[] (0,4) -- (0,0) -- (4,0);
    \end{tikzpicture}}
    & $\yy$ is constant. & \\ \addlinespace \midrule \addlinespace

    \formatmm{proportional} $\yy=m\xx$ &
    \imagetop{\begin{tikzpicture}[scale=\plotscale,domain=0:4,line width=\plotline,smooth]
    \draw[color=plot] plot (\x,.8*\x);
    \draw[] (0,4) -- (0,0) -- (4,0);
    \end{tikzpicture}}
    & $\yy$ is directly proportional to $\xx$.  & \\ \addlinespace  \midrule \addlinespace

    \formatmm{linear} $\yy=m\xx+b$ &
    \imagetop{\begin{tikzpicture}[scale=\plotscale,domain=0:4,line width=\plotline,smooth]
    \draw[color=plot] plot (\x,.6*\x+1);
    \draw[] (0,4) -- (0,0) -- (4,0);
    \end{tikzpicture}}
    & $\yy$ is linear in $\xx$.  & \\ \addlinespace \midrule \addlinespace

    \formatmm{inversely proportional} $\yy=\frac{a}{\xx}$ &
    \imagetop{\begin{tikzpicture}[scale=\plotscale,domain=.1:4,line width=\plotline,smooth,samples=40]
    \draw[color=plot] plot (\x,.4/\x);
    \draw[] (0,4) -- (0,0) -- (4,0);
    \end{tikzpicture}}
    & $\yy$ is inversely proportional to $\xx$.  & $\yy$ \versus $\frac{1}{\xx}$ \\ \addlinespace \midrule \addlinespace

    \formatmm{power law} $\yy=a\xx^{n}$ &
    \imagetop{\begin{tikzpicture}[scale=\plotscale,domain=0:4,line width=\plotline,smooth,samples=40]
    \draw[color=plot] plot (\x,.25*\x*\x);
    \draw[] (0,4) -- (0,0) -- (4,0);
    \end{tikzpicture}}
    & $\yy$ is proportional to $\xx^{n}$.  & $\yy$ \versus $\xx^{n}$ \\ \addlinespace \midrule \addlinespace

    \formatmm{square root} $\yy=a\sqrt{\xx}$ &
    \imagetop{\begin{tikzpicture}[scale=\plotscale,domain=0:4,line width=\plotline,smooth,samples=40]
    \draw[color=plot] plot (.25*\x*\x,\x);
    \draw[] (0,4) -- (0,0) -- (4,0);
    \end{tikzpicture}}
    %& $\yy^{2}$ is proportional to $\xx$. & Graph $\yy^{2}$ \versus $\xx$ \\ \addlinespace \midrule \addlinespace
    & $\yy$ is proportional to the square root of $\xx$. & $\yy^{2}$ \versus $\xx$ \\ \addlinespace \midrule \addlinespace

    \formatmm{exponential} $\yy=ab^{\xx}$ &
    \imagetop{\begin{tikzpicture}[scale=\plotscale,domain=0:4,line width=\plotline,smooth,samples=40]
    \draw[color=plot] plot (\x,{pow(pow(4,.25),\x)});
    \draw[] (0,4) -- (0,0) -- (4,0);
    \end{tikzpicture}}
    & $\yy$ is exponential in $\xx$. & $\log \yy$ \versus $\xx$ \\  \addlinespace

    \bottomrule[.1em]
    \end{tabular}
  \end{frame}
  \end{document}
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2 thoughts on “Graphical Methods Summary

  1. Pingback: Basic Classes of Mathematical Models | Fock Physics

  2. Pingback: Rules of Ten: rules of thumb for data collection and processing | Fock Physics

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