# Best way to typeset Euler's method

I need to typset my calculations for several iterations of Euler's method and I'm having trouble depicting it in a way that is easy to read. Here is what I have now:

\documentclass[11pt]{article}
\usepackage{booktabs}

\begin{document}
\begin{tabular}{ccccc}
\toprule
$n$ & $t_n$ & $y'(t_{n-1},y_{n-1})$                          & $y_n = y_{n-1} + (t_n - t_{n-1})y'(t_{n-1},y_{n-1})$  \\\midrule
1 & 0       & --                                             & 1 \\
2 & 0.2     & $-2\cdot1+1-e^0 = -2$                          & $1 + 0.2(-2) = 0.6$  \\
3 & 0.4     & $-2\cdot0.6+ 1 - e^{-4\cdot0.2} \approx -0.65$ &   $0.6 + 0.2(-0.65) = 0.47$\\
\bottomrule
\end{tabular}
\end{document}


I would appreciate any suggestions on how to make this table more readable.

In my opinion, the only thing that's making the above hard to read is spacing between rows and arrays. I think a little moderation should fix it (NOTE: I adjusted the size of your table with \scalebox so it fits, hence the graphicx package):

\documentclass[11pt]{article}
\usepackage{booktabs}
\usepackage{graphicx}

\begin{document}

\def\arraystretch{2}
\setlength\tabcolsep{23pt}

\begin{center}
\scalebox{0.7}{
\begin{tabular}{c c c c c}
\toprule
$n$ & $t_n$ & $y'(t_{n-1},y_{n-1})$                          & $y_n = y_{n-1} + (t_n - t_{n-1})y'(t_{n-1},y_{n-1})$  \\\midrule
1 & 0       & --                                             & 1 \\
2 & 0.2     & $-2\cdot1+1-e^0 = -2$                          & $1 + 0.2(-2) = 0.6$  \\
3 & 0.4     & $-2\cdot0.6+ 1 - e^{-4\cdot0.2} \approx -0.65$ &   $0.6 + 0.2(-0.65) = 0.47$\\
\bottomrule
\end{tabular}
}
\end{center}

\end{document}


I hope my post was helpful. Cheers.