\end{minipage}
\end{slide}}
-\overlays{5}{
+\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]{mips.eps} \hspace{1pt} \includegraphics[height=3cm]{ppc.eps} \end{center}}
- \onlySlide*{5}{\begin{center} \includegraphics[height=3cm]{cluster1.eps} \hspace{1cm} \includegraphics[height=3cm]{cluster2.eps} \end{center}}
- %\FromSlide{6}{\begin{center} \includegraphics[height=3cm]{} \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{8}{
-\begin{slide}{}
+\overlays{11}{
+\begin{slide}{history of computing software}
\begin{itemstep}
- \item
- \item
- \item
- \item
- \item
- \item
- \item
- \item
+ \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}}
-\begin{slide}{}
-
-\end{slide}
+\overlays{4}{
+\begin{slide}{warning - machine accuracy $\epsilon_m$}
+ \begin{itemstep}
+ \item numerical precision of 64-bit floating point \\
+ ieee floating point format: $v = -1^s 2^{-e} m$
+ \[
+ \begin{array}{lll}
+ s: & \textrm{signe} & \textrm{1 bit} \\
+ m: & \textrm{mantissa} & \textrm{52 bit} \\
+ e: & \textrm{exponent} & \textrm{11 bit} \\
+ \end{array}
+ \]
+ \item $\epsilon_m$: smallest floating point with $1 + \epsilon_m \neq 1$ \\
+ $\epsilon_m \approx 2 \times 10^{-18}$ \hspace{2pt} (roundoff error)
+ \item $N$ arithmetic operations $\Rightarrow$ error of order $N \epsilon_m$
+ \item subtraction of very nearly equal numbers\\
+ (difference in few significant low-order bits)
+ \end{itemstep}
+\end{slide}}
-\begin{slide}{}
+\overlays{6}{
+\begin{slide}{warning - truncation error}
+ \begin{itemstep}
+ \item discrete approximation of continuous quantity
+ \item truncation error $\equiv$ discrepancy between true answer and practical calculation
+ \item persists even on hypothetical perfect computer ($\epsilon_m = 0$)
+ \item machine independent, characteristic of used algorithm
+ \item numerical analysis: minimizing truncation error
+ \item unstable method: roundoff error interacting at early stage
+ \end{itemstep}
+\end{slide}}
-\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}
techniques discussed in the talk:
\end{slide}
\begin{slide}{computational techniques}
-techniques \textcolor{red}{not yet} discussed in the talk:\footnote{if time is available this will be completed. read more at http://www.nr.com}
+techniques \textcolor{red}{not yet} discussed in the talk:\footnote{if time is available this will be completed. updates at:\\http://www.physik.uni-augsburg.de/\~{}zirkelfr/download/cp/cp.pdf\\read more at: http://www.nr.com}
\begin{itemize}
%\item rough discretization
%\item solution of linear algebraic equations
\hspace{6cm}
\end{slide}
+\overlays{2}{
+\begin{slide}{rough discretization}
+ \begin{itemstep}
+ \item example: homogenous field of force $\vec{F} = (0,-mg)$ \\
+ \begin{tabular}{ll}
+ equation of motion: & $\vec{F} = m \vec{a} = m \frac{d^2 \vec{r}}{dt^2}$ \\
+ initial condition: & $\vec{r}(t=0) = \vec{r_0} = (x_0,y_0)$ \\
+ & $\frac{d \vec{r}}{dt}|_{t=0} = (v_{x_0},v_{y_0})$ \\
+ \end{tabular}
+ \item algorithm using discretized time ($T_{total} = N \tau$):
+ \begin{tabular}{lll}
+ $x^1 = x_0;$ & $y^1 = y_0;$ & \\
+ $v^1_x = v_{x_0};$ & $v^1_y = v_{y_0};$ & \\
+ loop: & $x^2 = x^1 + \tau v^1_x;$ & $y^2 = y^1 + \tau v^1_y;$ \\
+ & $v^2_x = v^1_x;$ & $v^2_y = v^1_y + (-mg) \tau;$ \\
+ & $x^1 = x^2;$ & $y^1 = y^2$ \\
+ & $v^1_x = v^2_x;$ & $v^1_y = v^2_y;$ \\
+ \end{tabular}
+ \end{itemstep}
+\end{slide}}
+
+%\overlays{3}{
+%\begin{slide}{}
+% \begin{itemstep}
+% \item
+% \item
+% \item
+% \end{itemstep}
+%\end{slide}}
+
+%\overlays{3}{
+%\begin{slide}{}
+% \begin{itemstep}
+% \item
+% \item
+% \item
+% \end{itemstep}
+%\end{slide}}
+
+%\overlays{3}{
+%\begin{slide}{}
+% \begin{itemstep}
+% \item
+% \item
+% \item
+% \end{itemstep}
+%\end{slide}}
+
+%\overlays{3}{
+%\begin{slide}{}
+% \begin{itemstep}
+% \item
+% \item
+% \item
+% \end{itemstep}
+%\end{slide}}
+
+%\overlays{3}{
+%\begin{slide}{}
+% \begin{itemstep}
+% \item
+% \item
+% \item
+% \end{itemstep}
+%\end{slide}}
+
+%\overlays{3}{
+%\begin{slide}{}
+% \begin{itemstep}
+% \item
+% \item
+% \item
+% \end{itemstep}
+%\end{slide}}
+
+%\overlays{3}{
+%\begin{slide}{}
+% \begin{itemstep}
+% \item
+% \item
+% \item
+% \end{itemstep}
+%\end{slide}}
+
+%\overlays{3}{
+%\begin{slide}{}
+% \begin{itemstep}
+% \item
+% \item
+% \item
+% \end{itemstep}
+%\end{slide}}
+
+%\overlays{3}{
+%\begin{slide}{}
+% \begin{itemstep}
+% \item
+% \item
+% \item
+% \end{itemstep}
+%\end{slide}}
+
+%\overlays{3}{
+%\begin{slide}{}
+% \begin{itemstep}
+% \item
+% \item
+% \item
+% \end{itemstep}
+%\end{slide}}
+
\end{document}
projects / lectures / latex.git / blobdiff