+\end{slide}}
+
+\overlays{3}{
+\begin{slide}{motivation}
+\FromSlide{1}{
+ \begin{center}
+ \begin{figure}[h]
+ \includegraphics[width=8cm]{cp_appl_field.eps}
+ \end{figure}
+ \end{center}
+}
+\FromSlide{2}{
+challenge:
+\begin{itemize}
+ \item precise mathematical theory
+ \item often: solving theory's equations ab-initio is not realistic
+ \item only a few models can be solved exactly
+\end{itemize}}
+\FromSlide{3}{
+$\Rightarrow$ study and implementation of numerical algorithms
+}
+\end{slide}}
+
+\overlays{5}{
+\begin{slide}{history of computing hardware}
+ \begin{minipage}[t]{10cm}
+ \onlySlide*{1}{\begin{center} \includegraphics[height=3cm]{abacus.eps} \end{center}}
+ \onlySlide*{2}{\begin{center} \includegraphics[height=3cm]{eniac.eps} \hspace{1cm} \includegraphics[height=3cm]{tube.eps} \end{center}}
+ \onlySlide*{3}{\begin{center} \includegraphics[height=3cm]{z1.eps} \end{center}}
+ \onlySlide*{4}{\begin{center} \includegraphics[height=3cm]{pdp1.eps} \hspace{1pt} \includegraphics[height=3cm]{transistor.eps} \end{center}}
+ \onlySlide*{5}{\begin{center} \includegraphics[height=3cm]{pdp8.eps} \hspace{1cm} \includegraphics[height=3cm]{ic.eps} \end{center}}
+ %\FromSlide{6}{\begin{center} \includegraphics[height=3cm]{} \end{center}}
+ \end{minipage}
+ \begin{minipage}[b]{10cm}
+ \begin{itemstep}
+ \item $3000 \, bc$: abacus - first calculating device
+ \item $1945$: eniac - electrical digital computer
+ \item $1938/41$: z1/3 - featuring memory and programmability
+ \item $1960$: pdp-1 - transistor based computers
+ \item $1964$: pdp-8 - integrated circuit computers
+ \end{itemstep}
+ \end{minipage}
+\end{slide}}
+
+\overlays{6}{
+\begin{slide}{history of computing hardware}
+ \begin{minipage}[t]{10cm}
+ \onlySlide*{1}{\begin{center} \includegraphics[height=3cm]{4004.eps} \end{center}}
+ \onlySlide*{2}{\begin{center} \includegraphics[height=3cm]{cray2.eps} \hspace{1pt} \includegraphics[height=3cm]{cray2_i.eps} \end{center}}
+ \onlySlide*{3}{\begin{center} \includegraphics[height=3cm]{apple2.eps} \includegraphics[height=3cm]{c64.eps} \end{center}}
+ \onlySlide*{4}{\begin{center} \includegraphics[height=3cm]{intel1.eps} \includegraphics[height=3cm]{intel2.eps} \end{center}}
+ \onlySlide*{5}{\begin{center} \includegraphics[height=3cm]{mips.eps} \hspace{1pt} \includegraphics[height=3cm]{ppc.eps} \end{center}}
+ \onlySlide*{6}{\begin{center} \includegraphics[height=3cm]{cluster1.eps} \hspace{1cm} \includegraphics[height=3cm]{cluster2.eps} \end{center}}
+ \end{minipage}
+ \begin{minipage}[b]{10cm}
+ \begin{itemstep}
+ \item $1970$: intel 4004 - first single chip $\mu$-processor
+ \item $1977/85$: cray1/2 - vector supercomputer
+ \item $1977/82/85$: 6502/6510/m68k - first pc
+ \item $1978/82/85 $: 8086/80286/80386
+ \item $1985$: mips - first risc design
+ \item $1990/2000$: massive parallel computing
+ \end{itemstep}
+ \end{minipage}
+\end{slide}}
+
+\overlays{11}{
+\begin{slide}{history of computing software}
+ \begin{itemstep}
+ \item $1946$: plankalk"ul - high-level programming language
+ \item $1950$: assembler - translating instruction mnemonics
+ \item $1954$: fortran - {\scriptsize formula translation}
+ \item $1963$: basic - {\scriptsize beginner's all purpose symbolic instruction code}
+ \item $1964$: os/360 - batch processing operating system
+ \item $1969$: unix - multics port to pdp-8, pdp-11/20
+ \item $1972$: c programming language - thompson, ritchie
+ \item $1978/84/85$: apple os/atari, amiga os/mac os
+ \item $1981/85/92/95$: ms-dos/windows 1.0/3.x/95
+ \item $1983$: gnu project - unix-like free software development
+ \item $1991$: linux - open-source kernel
+ \end{itemstep}
+\end{slide}}
+
+\overlays{7}{
+\begin{slide}{warning - numerical errors}
+ \begin{itemstep}
+ \item machine accuracy $\epsilon_m$
+ \begin{itemize}
+ \item ieee 64-bit floating point format: $v = -1^s 2^{-e} m$ \\
+ \begin{tabular}{lll}
+ $s$: & signe & 1 bit \\
+ $m$: & mantissa & 52 bit \\
+ $e$: & exponent & 11 bit \\
+ \end{tabular}
+ \item $\epsilon_m$: smallest floating point with $1 + \epsilon_m \neq 1$ \\
+ $\epsilon_m \approx 2.22 \times 10^{-16}$ \hspace{2pt} (roundoff error)
+ \end{itemize}
+ \item truncation error $\epsilon_t$
+ \begin{itemize}
+ \item discrete approximation of continuous quantity
+ \item persists even on hypothetical perfect computer ($\epsilon_m = 0$)
+ \item machine independent, characteristic of used algorithm
+ \end{itemize}
+ \end{itemstep}
+\end{slide}}
+
+\overlays{4}{
+\begin{slide}{warning - recursive functions}
+ \begin{itemstep}
+ \item avoid recursive functions!
+ \verbatiminput{fak1.c}
+ \item better:
+ \verbatiminput{fak2.c}
+ \end{itemstep}
+\end{slide}}
+
+\begin{slide}{computational techniques}
+ \begin{minipage}{5.5cm}
+ \begin{itemize}
+ \item rough discretization
+ \item solution of linear algebraic equations
+ \item interpolation and extrapolation
+ \item integration of functions
+ \item evaluation of (special) functions
+ \item monte carlo methods
+ \end{itemize}
+ \end{minipage}
+ \begin{minipage}{5.5cm}
+ \begin{itemize}
+ \item eigensystems
+ \item spectral applications
+ \item modeling of data
+ \item ordinary differential equations
+ \item two point boundary value problems
+ \item partial differential \\
+ equations
+ \end{itemize}
+ \end{minipage}
+\footnote{http://www.nr.com/}