\documentclass[pdf,azure,slideColor,nocolorBG]{prosper}
%\documentclass[ps,whitecross,slideBW,nocolorBG]{prosper}
%% use pdf and colorBG for powerpoint-like presentation, 
%% ps and colorBW to print slides
\DefaultTransition{Wipe}
%Other choices:Split,Blinds,Box,Wipe,Dissolve,Glitter,Replace(default)
%% The packages below are required for the second example, not the first.
\usepackage{pst-plot,pst-node,}
\usepackage{amsmath}
\begin{document}
\title{Sample Prosper file}
\subtitle{animated incremental math}
\author{\href{http://www.math.wisc.edu/~ynagel}{{\red Yvonne Nagel}}}
\institution{%
  UW Math Dept\\
    Madison, WI}
\maketitle

\overlays{2}{%
\begin{slide}{Math example (columns)}

\fromSlide{1}{
\begin{minipage}[t]{2.5in}
\begin{eqnarray*}
  \exp(x)  \approx   1  + &x   & + x^2/2! \\
  \sin(x)  \approx   x  - &x^3/3! & + x^5/5! 
\end{eqnarray*}
\end{minipage}
}
\fromSlide{2}{
\begin{minipage}[t]{1in}
\begin{eqnarray*}
   &+ x^3/3! +\cdots\\
   &+ x^7/7! + \cdots
\end{eqnarray*}
\end{minipage}
}
\end{slide}
}

%---------------------------------------------------------------------- 
%% Animated math SLIDE  from Fabian Waleffe
\overlays{2}{%
\begin{slide}{Math example (columns)}
\begin{equation*}
\begin{array}{rcccl}
   \exp(x)  \approx&   1 + & x  & + x^2/2! & \onlySlide{2}{+ x^3/3! + 
\cdots} \\
   \sin(x)   \approx&          & x  &                & \onlySlide{2}{- 
x^3/3! + \cdots}
\end{array}
\end{equation*}
\end{slide}
}

%---------------------------------------------------------------------- SLIDE -
%% from prosper-tour
\overlays{3}{%
\begin{slide}{Householder formula}
\small
The Householder formula below lets you compute $f^{-1}(x)$ for an arbitrary
$f$.
{\scriptsize
\begin{equation}\label{Householder}
x_{k+1}\mapsto \Phi_n(x_k)=x_k+(n-1)
\frac{\bigl(\frac{1}{f(x_k)}\bigr)^{n-2}}{\bigl(\frac{1}{f(x_k)}\bigr)^{n-1}}+
f(x_k)^{n+1}%
\fromSlide*{2}{\rnode{NA}{\pscirclebox[linecolor=red]{\psi}}}
\onlySlide*{1}{\rnode{NA}{\pscirclebox[linecolor=red,linestyle=none]{\psi}}}
\end{equation}}

\FromSlide{2}%
where $n\geq 2$ and \rnode{NB}{$\psi$} is an arbitrary function.
\fromSlide*{3}{\nccurve[linecolor=red,angleA=90,angleB=270]{->}{NB}{NA}}

\OnlySlide{3}%
Formula~\eqref{Householder} gives an iteration of order $n$ converging
towards $x_*$ such that: $f(x_*)=0$.
\end{slide}
}
%------------------------------------------------------------------------------
\end{document}