From b47f1f2fbae2436979d21cd1c4c2f1e28b3d7e94 Mon Sep 17 00:00:00 2001
From: Peter Gerwinski <peter.gerwinski@hs-bochum.de>
Date: Thu, 17 Dec 2020 13:09:05 +0100
Subject: [PATCH] Vorbereitungen 17.12.2020, Praktikumsversuch 2

---
 20201112/hp-2020ws-p1.pdf                     |  Bin 106224 -> 106336 bytes
 20201112/hp-2020ws-p1.tex                     |    8 +-
 20201210/hp-20201210.tex                      |    2 +-
 20201217/aufgabe-2.c                          |   62 +
 20201217/gtk-10.c                             |   60 +
 20201217/gtk-11.c                             |   60 +
 20201217/gtk-12.c                             |   60 +
 20201217/gtk-13.c                             |   60 +
 20201217/gtk-16.c                             |   63 +
 20201217/gtk-9.c                              |   60 +
 20201217/hp-20201217.pdf                      |  Bin 0 -> 168561 bytes
 20201217/hp-20201217.tex                      |  930 ++++++++++++
 20201217/hp-2020ws-p2.pdf                     |  Bin 0 -> 144128 bytes
 20201217/hp-2020ws-p2.tex                     |  201 +++
 20201217/hp-musterloesung-20201217.pdf        |  Bin 0 -> 177405 bytes
 20201217/hp-musterloesung-20201217.tex        |  326 ++++
 20201217/hp-uebung-20201217.pdf               |  Bin 0 -> 98374 bytes
 20201217/hp-uebung-20201217.tex               |  193 +++
 20201217/loesung-1a.c                         |   22 +
 20201217/loesung-1b.c                         |   22 +
 20201217/loesung-1c.c                         |   22 +
 20201217/loesung-1c.dat                       | 1324 +++++++++++++++++
 20201217/loesung-1c.tikz                      |  521 +++++++
 .../logo-hochschule-bochum-cvh-text-v2.pdf    |    1 +
 20201217/logo-hochschule-bochum.pdf           |    1 +
 20201217/pendulum.pdf                         |    1 +
 20201217/pgscript.sty                         |    1 +
 20201217/pgslides.sty                         |    1 +
 README.md                                     |    6 +-
 hp-slides-2020ws.pdf                          |  Bin 1216427 -> 1388849 bytes
 hp-slides-2020ws.tex                          |    2 +
 31 files changed, 4004 insertions(+), 5 deletions(-)
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 create mode 100644 20201217/gtk-10.c
 create mode 100644 20201217/gtk-11.c
 create mode 100644 20201217/gtk-12.c
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 create mode 100644 20201217/gtk-16.c
 create mode 100644 20201217/gtk-9.c
 create mode 100644 20201217/hp-20201217.pdf
 create mode 100644 20201217/hp-20201217.tex
 create mode 100644 20201217/hp-2020ws-p2.pdf
 create mode 100644 20201217/hp-2020ws-p2.tex
 create mode 100644 20201217/hp-musterloesung-20201217.pdf
 create mode 100644 20201217/hp-musterloesung-20201217.tex
 create mode 100644 20201217/hp-uebung-20201217.pdf
 create mode 100644 20201217/hp-uebung-20201217.tex
 create mode 100644 20201217/loesung-1a.c
 create mode 100644 20201217/loesung-1b.c
 create mode 100644 20201217/loesung-1c.c
 create mode 100644 20201217/loesung-1c.dat
 create mode 100644 20201217/loesung-1c.tikz
 create mode 120000 20201217/logo-hochschule-bochum-cvh-text-v2.pdf
 create mode 120000 20201217/logo-hochschule-bochum.pdf
 create mode 120000 20201217/pendulum.pdf
 create mode 120000 20201217/pgscript.sty
 create mode 120000 20201217/pgslides.sty

diff --git a/20201112/hp-2020ws-p1.pdf b/20201112/hp-2020ws-p1.pdf
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diff --git a/20201112/hp-2020ws-p1.tex b/20201112/hp-2020ws-p1.tex
index 7eff7a2..46566d8 100644
--- a/20201112/hp-2020ws-p1.tex
+++ b/20201112/hp-2020ws-p1.tex
@@ -160,10 +160,12 @@
         die Dicke eines Blatts Papier messen. Beides ist jedoch möglich.
 
       \item
-        \textbf{Abgabe}
+        \textbf{Abgabe:}
         Ihre Quelltexte mit den Lösungen der Praktikumsaufgabe schicken Sie bitte
         per E-Mail an \file{peter.gerwinski@hs-bochum.de}
-        mit dem \textbf{Betreff:} \lstinline[style=terminal]{fi2niNoh}.
+        mit dem \textbf{Betreff:} \lstinline[style=terminal]{fi2niNoh}
+        unter Angabe von Name, Matrikel-Nummer,
+        Studiengang (MI/MP/TI) und Studienmodell (KIA/KIS/GS).
 
     \end{itemize}
 
@@ -181,7 +183,7 @@
 
     \setlength{\leftskip}{3cm}
 
-    Stand: 26.\ November 2020
+    Stand: 17.\ Dezember 2020
 
 %    Soweit nicht anders angegeben:\\
     Copyright \copyright\ 2014, 2015, 2016, 2017, 2018, 2019, 2020\quad Peter Gerwinski\\
diff --git a/20201210/hp-20201210.tex b/20201210/hp-20201210.tex
index f0a92cd..9e84077 100644
--- a/20201210/hp-20201210.tex
+++ b/20201210/hp-20201210.tex
@@ -20,7 +20,7 @@
 % Attribution-ShareAlike 3.0 Unported License along with this
 % document.  If not, see <http://creativecommons.org/licenses/>.
 
-% README: Parameter des Hauptprogramms, String-Operationen
+% README: Präprozessor, Bibliotheken einbinden und verwenden
 
 \documentclass[10pt,t]{beamer}
 
diff --git a/20201217/aufgabe-2.c b/20201217/aufgabe-2.c
new file mode 100644
index 0000000..5b0cb23
--- /dev/null
+++ b/20201217/aufgabe-2.c
@@ -0,0 +1,62 @@
+#include <gtk/gtk.h>
+
+#define WIDTH 320
+#define HEIGHT 240
+
+double t = 0.0;
+double dt = 0.2;
+
+int r = 5;
+
+double x = 10;
+double y = 200;
+double vx = 20;
+double vy = -60;
+double g = 9.81;
+
+gboolean draw (GtkWidget *widget, cairo_t *c, gpointer data)
+{
+  GdkRGBA blue = { 0.0, 0.5, 1.0, 1.0 };
+
+  gdk_cairo_set_source_rgba (c, &blue);
+  cairo_arc (c, x, y, r, 0, 2 * G_PI);
+  cairo_fill (c);
+
+  return FALSE;
+}
+
+gboolean timer (GtkWidget *widget)
+{
+  t += dt;
+  x += vx * dt;
+  y += vy * dt;
+  vx = vx;
+  vy = 0.5 * g * (t * t);
+  if (y + r >= HEIGHT)
+    vy = -vy * 0.9;
+  if (x + r >= WIDTH)
+    vx = -vx * 0.9;
+  if (x - r <= 0)
+    vx = -vx * 0.9;
+  gtk_widget_queue_draw_area (widget, 0, 0, WIDTH, HEIGHT);
+  g_timeout_add (50, (GSourceFunc) timer, widget);
+  return FALSE;
+}
+
+int main (int argc, char **argv)
+{
+  gtk_init (&argc, &argv);
+
+  GtkWidget *window = gtk_window_new (GTK_WINDOW_TOPLEVEL);
+  gtk_widget_show (window);
+  gtk_window_set_title (GTK_WINDOW (window), "Hello");
+  g_signal_connect (window, "destroy", G_CALLBACK (gtk_main_quit), NULL);
+
+  GtkWidget *drawing_area = gtk_drawing_area_new ();
+  gtk_widget_show (drawing_area);
+  gtk_container_add (GTK_CONTAINER (window), drawing_area);
+  gtk_widget_set_size_request (drawing_area, WIDTH, HEIGHT);
+
+  gtk_main ();
+  return 0;
+}
diff --git a/20201217/gtk-10.c b/20201217/gtk-10.c
new file mode 100644
index 0000000..f7fb2d5
--- /dev/null
+++ b/20201217/gtk-10.c
@@ -0,0 +1,60 @@
+#include <gtk/gtk.h>
+
+#define WIDTH 320
+#define HEIGHT 240
+
+double x = 5;
+double y = 95;
+double vx = 0.5;
+double vy = 0.7;
+double dt = 0.05;
+double g = 9.81;
+
+gboolean draw (GtkWidget *widget, cairo_t *c, gpointer data)
+{
+  GdkRGBA blue = { 0.0, 0.5, 1.0, 1.0 };
+  gdk_cairo_set_source_rgba (c, &blue);
+  cairo_arc (c, x, HEIGHT - y, 5, 0, 2 * G_PI);
+  cairo_fill (c);
+  return FALSE;
+}
+
+gboolean timer (GtkWidget *widget)
+{
+  x += vx * dt;
+  y += vy * dt;
+  vx += 0.0 * dt;
+  vy += (-g) * dt;
+  gtk_widget_queue_draw_area (widget, 0, 0, WIDTH, HEIGHT);
+  g_timeout_add (50, (GSourceFunc) timer, widget);
+  return FALSE;
+}
+
+int main (int argc, char **argv)
+{
+  gtk_init (&argc, &argv);
+  GtkWidget *window = gtk_window_new (GTK_WINDOW_TOPLEVEL);
+  gtk_window_set_title (GTK_WINDOW (window), "Hello");
+  g_signal_connect (window, "destroy", G_CALLBACK (gtk_main_quit), NULL);
+
+  GtkWidget *vbox = gtk_box_new (GTK_ORIENTATION_VERTICAL, 5);
+  gtk_container_add (GTK_CONTAINER (window), vbox);
+
+  GtkWidget *button = gtk_button_new_with_label ("Quit");
+  g_signal_connect (button, "clicked", G_CALLBACK (gtk_main_quit), NULL);
+  gtk_container_add (GTK_CONTAINER (vbox), button);
+
+  GtkWidget *drawing_area = gtk_drawing_area_new ();
+  gtk_container_add (GTK_CONTAINER (vbox), drawing_area);
+  g_signal_connect (drawing_area, "draw", G_CALLBACK (draw), NULL);
+  gtk_widget_set_size_request (drawing_area, WIDTH, HEIGHT);
+
+  g_timeout_add (50, (GSourceFunc) timer, drawing_area);
+
+  gtk_widget_show (drawing_area);
+  gtk_widget_show (button);
+  gtk_widget_show (vbox);
+  gtk_widget_show (window);
+  gtk_main ();
+  return 0;
+}
diff --git a/20201217/gtk-11.c b/20201217/gtk-11.c
new file mode 100644
index 0000000..1fa3d71
--- /dev/null
+++ b/20201217/gtk-11.c
@@ -0,0 +1,60 @@
+#include <gtk/gtk.h>
+
+#define WIDTH 640
+#define HEIGHT 480
+
+double x = 5;
+double y = 95;
+double vx = 0.5;
+double vy = 0.7;
+double dt = 0.05;
+double g = 9.81;
+
+gboolean draw (GtkWidget *widget, cairo_t *c, gpointer data)
+{
+  GdkRGBA blue = { 0.0, 0.5, 1.0, 1.0 };
+  gdk_cairo_set_source_rgba (c, &blue);
+  cairo_arc (c, x, HEIGHT - y, 5, 0, 2 * G_PI);
+  cairo_fill (c);
+  return FALSE;
+}
+
+gboolean timer (GtkWidget *widget)
+{
+  x += vx * dt;
+  y += vy * dt;
+  vx += 0.0 * dt;
+  vy += (-g) * dt;
+  gtk_widget_queue_draw_area (widget, 0, 0, WIDTH, HEIGHT);
+  g_timeout_add (50, (GSourceFunc) timer, widget);
+  return FALSE;
+}
+
+int main (int argc, char **argv)
+{
+  gtk_init (&argc, &argv);
+  GtkWidget *window = gtk_window_new (GTK_WINDOW_TOPLEVEL);
+  gtk_window_set_title (GTK_WINDOW (window), "Hello");
+  g_signal_connect (window, "destroy", G_CALLBACK (gtk_main_quit), NULL);
+
+  GtkWidget *vbox = gtk_box_new (GTK_ORIENTATION_VERTICAL, 5);
+  gtk_container_add (GTK_CONTAINER (window), vbox);
+
+  GtkWidget *button = gtk_button_new_with_label ("Quit");
+  g_signal_connect (button, "clicked", G_CALLBACK (gtk_main_quit), NULL);
+  gtk_container_add (GTK_CONTAINER (vbox), button);
+
+  GtkWidget *drawing_area = gtk_drawing_area_new ();
+  gtk_container_add (GTK_CONTAINER (vbox), drawing_area);
+  g_signal_connect (drawing_area, "draw", G_CALLBACK (draw), NULL);
+  gtk_widget_set_size_request (drawing_area, WIDTH, HEIGHT);
+
+  g_timeout_add (50, (GSourceFunc) timer, drawing_area);
+
+  gtk_widget_show (drawing_area);
+  gtk_widget_show (button);
+  gtk_widget_show (vbox);
+  gtk_widget_show (window);
+  gtk_main ();
+  return 0;
+}
diff --git a/20201217/gtk-12.c b/20201217/gtk-12.c
new file mode 100644
index 0000000..e0c2743
--- /dev/null
+++ b/20201217/gtk-12.c
@@ -0,0 +1,60 @@
+#include <gtk/gtk.h>
+
+#define WIDTH 640
+#define HEIGHT 480
+
+double x = 5;
+double y = 95;
+double vx = 5.0;
+double vy = 0.7;
+double dt = 0.05;
+double g = 9.81;
+
+gboolean draw (GtkWidget *widget, cairo_t *c, gpointer data)
+{
+  GdkRGBA blue = { 0.0, 0.5, 1.0, 1.0 };
+  gdk_cairo_set_source_rgba (c, &blue);
+  cairo_arc (c, x, HEIGHT - y, 5, 0, 2 * G_PI);
+  cairo_fill (c);
+  return FALSE;
+}
+
+gboolean timer (GtkWidget *widget)
+{
+  x += vx * dt;
+  y += vy * dt;
+  vx += 0.0 * dt;
+  vy += (-g) * dt;
+  gtk_widget_queue_draw_area (widget, 0, 0, WIDTH, HEIGHT);
+  g_timeout_add (50, (GSourceFunc) timer, widget);
+  return FALSE;
+}
+
+int main (int argc, char **argv)
+{
+  gtk_init (&argc, &argv);
+  GtkWidget *window = gtk_window_new (GTK_WINDOW_TOPLEVEL);
+  gtk_window_set_title (GTK_WINDOW (window), "Hello");
+  g_signal_connect (window, "destroy", G_CALLBACK (gtk_main_quit), NULL);
+
+  GtkWidget *vbox = gtk_box_new (GTK_ORIENTATION_VERTICAL, 5);
+  gtk_container_add (GTK_CONTAINER (window), vbox);
+
+  GtkWidget *button = gtk_button_new_with_label ("Quit");
+  g_signal_connect (button, "clicked", G_CALLBACK (gtk_main_quit), NULL);
+  gtk_container_add (GTK_CONTAINER (vbox), button);
+
+  GtkWidget *drawing_area = gtk_drawing_area_new ();
+  gtk_container_add (GTK_CONTAINER (vbox), drawing_area);
+  g_signal_connect (drawing_area, "draw", G_CALLBACK (draw), NULL);
+  gtk_widget_set_size_request (drawing_area, WIDTH, HEIGHT);
+
+  g_timeout_add (50, (GSourceFunc) timer, drawing_area);
+
+  gtk_widget_show (drawing_area);
+  gtk_widget_show (button);
+  gtk_widget_show (vbox);
+  gtk_widget_show (window);
+  gtk_main ();
+  return 0;
+}
diff --git a/20201217/gtk-13.c b/20201217/gtk-13.c
new file mode 100644
index 0000000..a91d9ab
--- /dev/null
+++ b/20201217/gtk-13.c
@@ -0,0 +1,60 @@
+#include <gtk/gtk.h>
+
+#define WIDTH 640
+#define HEIGHT 480
+
+double x = 5;
+double y = 95;
+double vx = 50.0;
+double vy = 0.7;
+double dt = 0.05;
+double g = 9.81;
+
+gboolean draw (GtkWidget *widget, cairo_t *c, gpointer data)
+{
+  GdkRGBA blue = { 0.0, 0.5, 1.0, 1.0 };
+  gdk_cairo_set_source_rgba (c, &blue);
+  cairo_arc (c, x, HEIGHT - y, 5, 0, 2 * G_PI);
+  cairo_fill (c);
+  return FALSE;
+}
+
+gboolean timer (GtkWidget *widget)
+{
+  x += vx * dt;
+  y += vy * dt;
+  vx += 0.0 * dt;
+  vy += (-g) * dt;
+  gtk_widget_queue_draw_area (widget, 0, 0, WIDTH, HEIGHT);
+  g_timeout_add (50, (GSourceFunc) timer, widget);
+  return FALSE;
+}
+
+int main (int argc, char **argv)
+{
+  gtk_init (&argc, &argv);
+  GtkWidget *window = gtk_window_new (GTK_WINDOW_TOPLEVEL);
+  gtk_window_set_title (GTK_WINDOW (window), "Hello");
+  g_signal_connect (window, "destroy", G_CALLBACK (gtk_main_quit), NULL);
+
+  GtkWidget *vbox = gtk_box_new (GTK_ORIENTATION_VERTICAL, 5);
+  gtk_container_add (GTK_CONTAINER (window), vbox);
+
+  GtkWidget *button = gtk_button_new_with_label ("Quit");
+  g_signal_connect (button, "clicked", G_CALLBACK (gtk_main_quit), NULL);
+  gtk_container_add (GTK_CONTAINER (vbox), button);
+
+  GtkWidget *drawing_area = gtk_drawing_area_new ();
+  gtk_container_add (GTK_CONTAINER (vbox), drawing_area);
+  g_signal_connect (drawing_area, "draw", G_CALLBACK (draw), NULL);
+  gtk_widget_set_size_request (drawing_area, WIDTH, HEIGHT);
+
+  g_timeout_add (50, (GSourceFunc) timer, drawing_area);
+
+  gtk_widget_show (drawing_area);
+  gtk_widget_show (button);
+  gtk_widget_show (vbox);
+  gtk_widget_show (window);
+  gtk_main ();
+  return 0;
+}
diff --git a/20201217/gtk-16.c b/20201217/gtk-16.c
new file mode 100644
index 0000000..0901dd7
--- /dev/null
+++ b/20201217/gtk-16.c
@@ -0,0 +1,63 @@
+#include <gtk/gtk.h>
+
+#define WIDTH 640
+#define HEIGHT 480
+#define RADIUS 5
+
+double x = 5;
+double y = 95;
+double vx = 50.0;
+double vy = 70.0;
+double dt = 0.05;
+double g = 9.81;
+
+gboolean draw (GtkWidget *widget, cairo_t *c, gpointer data)
+{
+  GdkRGBA blue = { 0.0, 0.5, 1.0, 1.0 };
+  gdk_cairo_set_source_rgba (c, &blue);
+  cairo_arc (c, x, HEIGHT - y, RADIUS, 0, 2 * G_PI);
+  cairo_fill (c);
+  return FALSE;
+}
+
+gboolean timer (GtkWidget *widget)
+{
+  x += vx * dt;
+  y += vy * dt;
+  vx += 0.0 * dt;
+  vy += (-g) * dt;
+  if (x + RADIUS >= WIDTH)
+    vx = -vx;
+  gtk_widget_queue_draw_area (widget, 0, 0, WIDTH, HEIGHT);
+  g_timeout_add (50, (GSourceFunc) timer, widget);
+  return FALSE;
+}
+
+int main (int argc, char **argv)
+{
+  gtk_init (&argc, &argv);
+  GtkWidget *window = gtk_window_new (GTK_WINDOW_TOPLEVEL);
+  gtk_window_set_title (GTK_WINDOW (window), "Hello");
+  g_signal_connect (window, "destroy", G_CALLBACK (gtk_main_quit), NULL);
+
+  GtkWidget *vbox = gtk_box_new (GTK_ORIENTATION_VERTICAL, 5);
+  gtk_container_add (GTK_CONTAINER (window), vbox);
+
+  GtkWidget *button = gtk_button_new_with_label ("Quit");
+  g_signal_connect (button, "clicked", G_CALLBACK (gtk_main_quit), NULL);
+  gtk_container_add (GTK_CONTAINER (vbox), button);
+
+  GtkWidget *drawing_area = gtk_drawing_area_new ();
+  gtk_container_add (GTK_CONTAINER (vbox), drawing_area);
+  g_signal_connect (drawing_area, "draw", G_CALLBACK (draw), NULL);
+  gtk_widget_set_size_request (drawing_area, WIDTH, HEIGHT);
+
+  g_timeout_add (50, (GSourceFunc) timer, drawing_area);
+
+  gtk_widget_show (drawing_area);
+  gtk_widget_show (button);
+  gtk_widget_show (vbox);
+  gtk_widget_show (window);
+  gtk_main ();
+  return 0;
+}
diff --git a/20201217/gtk-9.c b/20201217/gtk-9.c
new file mode 100644
index 0000000..7beb24c
--- /dev/null
+++ b/20201217/gtk-9.c
@@ -0,0 +1,60 @@
+#include <gtk/gtk.h>
+
+#define WIDTH 320
+#define HEIGHT 240
+
+double x = 5;
+double y = 95;
+double vx = 0.5;
+double vy = 0.7;
+double dt = 0.05;
+double g = 9.81;
+
+gboolean draw (GtkWidget *widget, cairo_t *c, gpointer data)
+{
+  GdkRGBA blue = { 0.0, 0.5, 1.0, 1.0 };
+  gdk_cairo_set_source_rgba (c, &blue);
+  cairo_arc (c, x, y, 5, 0, 2 * G_PI);
+  cairo_fill (c);
+  return FALSE;
+}
+
+gboolean timer (GtkWidget *widget)
+{
+  x += vx * dt;
+  y += vy * dt;
+  vx += 0.0 * dt;
+  vy += (-g) * dt;
+  gtk_widget_queue_draw_area (widget, 0, 0, WIDTH, HEIGHT);
+  g_timeout_add (50, (GSourceFunc) timer, widget);
+  return FALSE;
+}
+
+int main (int argc, char **argv)
+{
+  gtk_init (&argc, &argv);
+  GtkWidget *window = gtk_window_new (GTK_WINDOW_TOPLEVEL);
+  gtk_window_set_title (GTK_WINDOW (window), "Hello");
+  g_signal_connect (window, "destroy", G_CALLBACK (gtk_main_quit), NULL);
+
+  GtkWidget *vbox = gtk_box_new (GTK_ORIENTATION_VERTICAL, 5);
+  gtk_container_add (GTK_CONTAINER (window), vbox);
+
+  GtkWidget *button = gtk_button_new_with_label ("Quit");
+  g_signal_connect (button, "clicked", G_CALLBACK (gtk_main_quit), NULL);
+  gtk_container_add (GTK_CONTAINER (vbox), button);
+
+  GtkWidget *drawing_area = gtk_drawing_area_new ();
+  gtk_container_add (GTK_CONTAINER (vbox), drawing_area);
+  g_signal_connect (drawing_area, "draw", G_CALLBACK (draw), NULL);
+  gtk_widget_set_size_request (drawing_area, 100, 100);
+
+  g_timeout_add (50, (GSourceFunc) timer, drawing_area);
+
+  gtk_widget_show (drawing_area);
+  gtk_widget_show (button);
+  gtk_widget_show (vbox);
+  gtk_widget_show (window);
+  gtk_main ();
+  return 0;
+}
diff --git a/20201217/hp-20201217.pdf b/20201217/hp-20201217.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..173a2277de52dffc99c4e949574ebe3797c9d641
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diff --git a/20201217/hp-20201217.tex b/20201217/hp-20201217.tex
new file mode 100644
index 0000000..be44ed7
--- /dev/null
+++ b/20201217/hp-20201217.tex
@@ -0,0 +1,930 @@
+% hp-20201217.pdf - Lecture Slides on Low-Level Programming
+% Copyright (C) 2012, 2013, 2015, 2016, 2017, 2018, 2019, 2020  Peter Gerwinski
+%
+% This document is free software: you can redistribute it and/or
+% modify it either under the terms of the Creative Commons
+% Attribution-ShareAlike 3.0 License, or under the terms of the
+% GNU General Public License as published by the Free Software
+% Foundation, either version 3 of the License, or (at your option)
+% any later version.
+%
+% This document is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this document.  If not, see <http://www.gnu.org/licenses/>.
+%
+% You should have received a copy of the Creative Commons
+% Attribution-ShareAlike 3.0 Unported License along with this
+% document.  If not, see <http://creativecommons.org/licenses/>.
+
+% README: make, Differentialgleichungen
+
+\documentclass[10pt,t]{beamer}
+
+\usepackage{pgslides}
+\usepackage{pdftricks}
+\usepackage{tikz}
+
+\begin{psinputs}
+  \usepackage[utf8]{inputenc}
+  \usepackage[german]{babel}
+  \usepackage[T1]{fontenc}
+  \usepackage{helvet}
+  \renewcommand*\familydefault{\sfdefault}
+  \usepackage{pstricks,pst-grad}
+\end{psinputs}
+
+\title{Hardwarenahe Programmierung}
+\author{Prof.\ Dr.\ rer.\ nat.\ Peter Gerwinski}
+\date{17.\ Dezember 2020}
+
+\begin{document}
+
+\maketitleframe
+
+\nosectionnonumber{\inserttitle}
+
+\begin{frame}
+
+  \shownosectionnonumber
+
+  \begin{itemize}
+    \item[\textbf{1}] \textbf{Einführung}
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/hp}}}
+    \item[\textbf{2}] \textbf{Einführung in C}
+    \item[\textbf{3}] \textbf{Bibliotheken}
+      \begin{itemize}
+        \color{medgreen}
+        \item[3.1] Der Präprozessor
+        \item[3.2] Bibliotheken einbinden
+        \item[3.3] Bibliotheken verwenden
+        \color{red}
+        \item[3.4] Projekt organisieren: make
+        \vspace*{-\smallskipamount}
+        \item[\dots]
+      \end{itemize}
+    \item[\textbf{4}] \textbf{Hardwarenahe Programmierung}
+    \item[\textbf{5}] \textbf{Algorithmen}
+    \vspace*{-\smallskipamount}
+    \item[\textbf{\dots}]
+  \end{itemize}
+
+\end{frame}
+
+\setcounter{section}{2}
+\section{Bibliotheken}
+\subsection{Der Präprozessor}
+
+\begin{frame}[fragile]
+
+  \showsection
+  \showsubsection
+
+  \lstinline{#include}: %\pause:
+  Text einbinden
+  \begin{itemize}
+%    \pause
+    \item
+      \lstinline{#include <stdio.h>}: Standard-Verzeichnisse -- Standard-Header
+%    \pause
+    \item
+      \lstinline{#include "answer.h"}: auch aktuelles Verzeichnis -- eigene Header
+  \end{itemize}
+
+%  \pause
+  \bigskip
+
+  \lstinline{#define VIER 4}: Text ersetzen lassen -- Konstante definieren
+  \begin{itemize}
+%    \pause
+    \item
+      Kein Semikolon!
+%    \pause
+    \item
+      Berechnungen in Klammern setzen:\\
+      \lstinline{#define VIER (2 + 2)}
+%    \pause
+    \item
+      Konvention: Großbuchstaben
+  \end{itemize}
+
+\end{frame}
+
+\subsection{Bibliotheken einbinden}
+
+\begin{frame}[fragile]
+
+  \showsection
+  \showsubsection
+
+  Inhalt der Header-Datei: externe Deklarationen
+
+%  \pause
+  \smallskip
+  \lstinline{extern int answer (void);}
+
+%  \pause
+  \smallskip
+  \lstinline{extern int printf (__const char *__restrict __format, ...);}
+
+%  \pause
+  \bigskip
+  Funktion wird "`anderswo"' definiert
+  \begin{itemize}
+%    \pause
+    \item
+      separater C-Quelltext: mit an \lstinline[style=terminal]{gcc} übergeben
+%    \pause
+    \item
+      Zusammenfügen zu ausführbarem Programm durch den \newterm{Linker}
+%    \pause
+    \item
+      vorcompilierte Bibliothek: \lstinline[style=terminal]{-lfoo}\\
+%      \pause
+      = Datei \file{libfoo.a} in Standard-Verzeichnis
+  \end{itemize}
+
+\end{frame}
+
+\subsection{Bibliothek verwenden (Beispiel: GTK+)}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  \begin{itemize}
+    \item
+      \lstinline{#include <gtk/gtk.h>}
+%    \pause
+    \smallskip
+    \item
+      Mit \lstinline[style=cmd]{pkg-config --cflags --libs} erfährt man,\\
+      welche Optionen und Bibliotheken man an \lstinline[style=cmd]{gcc}
+      übergeben muß\alt<1->{.}{:}
+%      \pause
+      \begin{onlyenv}<1>
+        \begin{lstlisting}[style=terminal,gobble=10]
+          $ ¡pkg-config --cflags --libs gtk+-3.0¿
+          -pthread -I/usr/include/gtk-3.0 -I/usr/include/at-spi2-
+          atk/2.0 -I/usr/include/at-spi-2.0 -I/usr/include/dbus-1
+          .0 -I/usr/lib/x86_64-linux-gnu/dbus-1.0/include -I/usr/
+          include/gtk-3.0 -I/usr/include/gio-unix-2.0/ -I/usr/inc
+          lude/cairo -I/usr/include/pango-1.0 -I/usr/include/harf
+          buzz -I/usr/include/pango-1.0 -I/usr/include/atk-1.0 -I
+          /usr/include/cairo -I/usr/include/pixman-1 -I/usr/inclu
+          de/freetype2 -I/usr/include/libpng16 -I/usr/include/gdk
+          -pixbuf-2.0 -I/usr/include/libpng16 -I/usr/include/glib
+          -2.0 -I/usr/lib/x86_64-linux-gnu/glib-2.0/include -lgtk
+          -3 -lgdk-3 -lpangocairo-1.0 -lpango-1.0 -latk-1.0 -lcai
+          ro-gobject -lcairo -lgdk_pixbuf-2.0 -lgio-2.0 -lgobject
+          -2.0 -lglib-2.0
+        \end{lstlisting}
+        \vspace*{-3cm}
+      \end{onlyenv}
+    \pause
+    \arrowitem
+      Compiler-Aufruf:
+      \begin{onlyenv}<2>
+        \begin{lstlisting}[style=terminal,gobble=10]
+          $ ¡gcc -Wall -O hello-gtk.c -pthread -I/usr/include/gtk-
+          3.0 -I/usr/include/at-spi2-atk/2.0 -I/usr/include/at-sp
+          i-2.0 -I/usr/include/dbus-1.0 -I/usr/lib/x86_64-linux-g
+          nu/dbus-1.0/include -I/usr/include/gtk-3.0 -I/usr/inclu
+          de/gio-unix-2.0/ -I/usr/include/cairo -I/usr/include/pa
+          ngo-1.0 -I/usr/include/harfbuzz -I/usr/include/pango-1.
+          0 -I/usr/include/atk-1.0 -I/usr/include/cairo -I/usr/in
+          clude/pixman-1 -I/usr/include/freetype2 -I/usr/include/
+          libpng16 -I/usr/include/gdk-pixbuf-2.0 -I/usr/include/l
+          ibpng16 -I/usr/include/glib-2.0 -I/usr/lib/x86_64-linux
+          -gnu/glib-2.0/include -lgtk-3 -lgdk-3 -lpangocairo-1.0
+          -lpango-1.0 -latk-1.0 -lcairo-gobject -lcairo -lgdk_pix
+          buf-2.0 -lgio-2.0 -lgobject-2.0 -lglib-2.0 -o hello-gtk¿
+        \end{lstlisting}
+        \vspace*{-2cm}
+      \end{onlyenv}
+      \begin{onlyenv}<3->
+        \begin{lstlisting}[style=terminal,gobble=10]
+          $ ¡gcc -Wall -O hello-gtk.c $(pkg-config --cflags --libs
+                 gtk+-3.0 -o hello-gtk¿
+        \end{lstlisting}
+      \end{onlyenv}
+      \begin{onlyenv}<3>
+        \begin{picture}(0,0)(0.3,0.3)
+          \color{red}
+          \put(6.6,-0.6){\makebox(0,0)[bl]{\tikz{\draw[-latex](0,0)--(3,1.5);}}}
+          \put(6.3,-0.7){\makebox(0,0)[t]{\shortstack{\strut Optionen:\\
+                           \strut u.\,a.\ viele Include-Verzeichnisse:\\
+                           \lstinline[style=cmd]{-I/usr/include/gtk-3.0}}}}
+          \put(10.0,-2.1){\makebox(0,0)[bl]{\tikz{\draw[-latex](0,0)--(1.5,3);}}}
+          \put(10.3,-2.2){\makebox(0,0)[t]{\shortstack{\strut Bibliotheken:\\
+                            \strut u.\,a.\ \lstinline[style=cmd]{-lgtk-3 -lcairo}\qquad\strut}}}
+        \end{picture}
+      \end{onlyenv}
+    \pause
+    \pause
+    \item
+      Auf manchen Plattformen kommt es auf die Reihenfolge an:
+      \begin{lstlisting}[style=terminal,gobble=8]
+        $ ¡gcc -Wall -O $(pkg-config --cflags gtk+-3.0) \
+               hello-gtk.c $(pkg-config --libs gtk+-3.0) \
+               -o hello-gtk¿
+      \end{lstlisting}
+      (Backslash = "`Es geht in der nächsten Zeile weiter."')
+  \end{itemize}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Selbst geschriebene Funktion übergeben: \newterm{Callback}
+
+  \bigskip
+
+  \begin{lstlisting}[xleftmargin=1em]
+    gboolean draw (GtkWidget *widget, cairo_t *c, gpointer data)
+    {
+      /* Zeichenbefehle */
+      ...
+
+      return FALSE;
+    }
+  
+    ...
+
+    g_signal_connect (drawing_area, "draw", G_CALLBACK (draw), NULL);
+  \end{lstlisting}
+
+  \medskip
+
+  \begin{itemize}
+    \arrowitem 
+      GTK+ ruft immer dann, wenn es etwas zu zeichnen gibt,\\
+      die Funktion \lstinline{draw} auf.
+  \end{itemize}
+
+%  \pause
+  \begin{picture}(0,0)(-0.07,0.2)
+    \color{red}
+    \put(5.3,4.8){\makebox(0,0)[bl]{\tikz{\draw[-latex](0,0)--(1.90,1.15);}}}
+    \put(5.0,4.7){\makebox(0,0)[t]{\shortstack{\strut repräsentiert den\\
+                    \strut Bildschirm, auf den\\
+                    \strut gezeichnet werden soll}}}
+%    \pause
+    \put(9.7,5.1){\makebox(0,0)[br]{\tikz{\draw[-latex](0,0)--(-0.2,0.85);}}}
+    \put(9.7,5.0){\makebox(0,0)[t]{\shortstack{\strut optionale Zusatzinformationen\\
+                    \strut für draw(), typischerweise\\
+                    \strut ein Zeiger auf ein struct}}}
+    \put(10.0,3.5){\makebox(0,0)[tl]{\tikz{\draw[-latex](0,0)--(0.6,-1.25);}}}
+  \end{picture}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Selbst geschriebene Funktion übergeben: \newterm{Callback}
+
+  \bigskip
+
+  \begin{lstlisting}[xleftmargin=1em]
+    gboolean timer (GtkWidget *widget)
+    {
+      /* Rechenbefehle */
+      ...
+
+      gtk_widget_queue_draw_area (widget, 0, 0, WIDTH, HEIGHT);
+      g_timeout_add (50, (GSourceFunc) timer, widget);
+      return FALSE;
+    }
+  
+    ...
+
+    g_timeout_add (50, (GSourceFunc) timer, drawing_area);
+  \end{lstlisting}
+
+  \medskip
+
+  \begin{itemize}
+    \arrowitem 
+      GTK+ ruft nach 50 Millisekunden
+      die Funktion \lstinline{timer} auf.
+  \end{itemize}
+
+%  \pause
+  \begin{picture}(0,0)(-0.07,0.2)
+    \color{red}
+    \put(9.7,6.7){\makebox(0,0)[t]{\shortstack{\strut Dieser Bereich soll\\
+                    \strut neu gezeichnet werden.}}}
+    \put(9.7,5.7){\makebox(0,0)[tr]{\tikz{\draw[-latex](0,0)--(-0.6,-0.8);}}}
+%    \pause
+    \put(4.3,3.2){\makebox(0,0)[br]{\tikz{\draw[-latex](0,0)--(-0.7,0.6);}}}
+    \put(4.3,3.1){\makebox(0,0)[t]{\shortstack{\strut In weiteren 50 Millisekunden soll\\
+                    \strut die Funktion erneut aufgerufen werden.}}}
+%    \pause
+    \put(9.3,2.9){\makebox(0,0)[br]{\tikz{\draw[-latex](0,0)--(-3.3,0.9);}}}
+    \put(9.8,2.8){\makebox(0,0)[t]{\shortstack{\strut Explizite Typumwandlung\\
+                    \strut eines Zeigers (später)}}}
+  \end{picture}
+
+\end{frame}
+
+\subsection{Projekt organisieren: make}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+  \begin{itemize}
+    \item
+      \only<4->{explizite und implizite} Regeln
+      \begin{onlyenv}<2>
+        \smallskip
+        \begin{lstlisting}[language=make,gobble=10]
+          philosophy: philosophy.o answer.o
+                  gcc philosophy.o answer.o -o philosophy
+
+          answer.o: answer.c answer.h
+                  gcc -Wall -O answer.c -c
+
+          philosophy.o: philosophy.c answer.h
+                  gcc -Wall -O philosophy.c -c
+        \end{lstlisting}
+      \end{onlyenv}
+      \begin{onlyenv}<4>
+        \smallskip
+        \begin{lstlisting}[language=make,gobble=10]
+          TARGET = philosophy
+          OBJECTS = philosophy.o answer.o
+          HEADERS = answer.h
+          CFLAGS = -Wall -O
+
+          $(TARGET): $(OBJECTS)
+                  gcc $(OBJECTS) -o $(TARGET)
+
+          %.o: %.c $(HEADERS)
+                  gcc $(CFLAGS) $< -c
+
+          clean:
+                  rm -f $(OBJECTS) $(TARGET)
+        \end{lstlisting}
+      \end{onlyenv}
+    \item
+      Makros
+      \begin{onlyenv}<3>
+        \smallskip
+        \begin{lstlisting}[language=make,gobble=10]
+          TARGET = philosophy
+          OBJECTS = philosophy.o answer.o
+          HEADERS = answer.h
+          CFLAGS = -Wall -O
+
+          $(TARGET): $(OBJECTS)
+                  gcc $(OBJECTS) -o $(TARGET)
+
+          answer.o: answer.c $(HEADERS)
+                  gcc $(CFLAGS) answer.c -c
+
+          philosophy.o: philosophy.c $(HEADERS)
+                  gcc $(CFLAGS) philosophy.c -c
+
+          clean:
+                  rm -f $(OBJECTS) $(TARGET)
+        \end{lstlisting}
+        \vspace*{-1cm}
+      \end{onlyenv}
+    \begin{onlyenv}<5->
+      \smallskip
+      \arrowitem
+        3 Sprachen: C, Präprozessor, make
+    \end{onlyenv}
+  \end{itemize}
+
+\end{frame}
+
+\section{Algorithmen}
+\subsection{Differentialgleichungen}
+
+\begin{frame}[fragile]
+
+  \showsection
+  \showsubsection
+
+  \textbf{Beispiel 1: Gleichmäßig beschleunigte Bewegung}
+
+  \strut\hfill
+  \begin{minipage}{2.5cm}
+    \vspace*{0.6cm}
+    \begin{align*}
+      x'(t) &= v_x(t) \\[0.65cm]
+      y'(t) &= v_y(t) \\[0.75cm]
+      v_x'(t) &= 0 \\[0.65cm]
+      v_y'(t) &= -g
+    \end{align*}
+    \vspace*{0.0cm}
+  \end{minipage}%
+  \only<1>{\hspace*{9.49cm}}\strut
+  \only<2->{\hfill$\Rightarrow$\hfill}%
+  \begin{onlyenv}<2-8>
+    \begin{minipage}{8.3cm}
+      \begin{align*}
+        x(t) &= \int v_x(t)\,dt
+          \visible<4->{= \int v_{0x}\,dt}
+          \visible<5->{= x_0 + v_{0x}\cdot t}\\[\medskipamount]
+        y(t) &= \int v_y(t)\,dt
+          \visible<7->{= \int v_{0y} - g\cdot t\,dt}
+          \visible<8->{= y_0 + v_{0y}\cdot t
+                         - {\textstyle\frac12}gt^2}\\[\bigskipamount]
+        v_x(t) &= \int 0\,dt
+          \visible<3->{= v_{0x}} \\[\medskipamount]
+        v_y(t) &= \int -g\,dt
+          \visible<6->{= v_{0y} - g\cdot t}
+      \end{align*}
+    \end{minipage}%
+  \end{onlyenv}%
+  \begin{onlyenv}<9->
+    \begin{minipage}{3.5cm}
+      \vspace*{0.5cm}
+      \begin{lstlisting}[gobble=8,xleftmargin=0.5em]
+        ¡x += vx * dt;¿
+      \end{lstlisting}
+      \vspace{0.75cm}
+      \begin{lstlisting}[gobble=8,xleftmargin=0.5em]
+        ¡y += vy * dt;¿
+      \end{lstlisting}
+      \vspace{0.90cm}
+      \begin{lstlisting}[gobble=8,xleftmargin=0.5em]
+        ¡vx += 0 * dt;¿
+      \end{lstlisting}
+      \vspace{0.75cm}
+      \begin{lstlisting}[gobble=8,xleftmargin=0.5em]
+        ¡vy += -g * dt;¿
+      \end{lstlisting}
+    \end{minipage}%
+    \begin{minipage}{5.13cm}
+      Siehe: \file{gtk-13.c}
+    \end{minipage}
+  \end{onlyenv}%
+  \hfill\strut
+
+\end{frame}
+
+\begin{frame}[fragile]
+  \showsection
+  \showsubsection
+
+  \textbf{Beispiel 1: Gleichmäßig beschleunigte Bewegung}
+
+  \medskip
+
+  \textbf{Beispiel 2: Mathematisches Pendel}
+
+  \vspace*{-2\bigskipamount}
+
+  \begin{picture}(0,0)
+    \put(8,-6.5){\includegraphics{pendulum.pdf}}
+  \end{picture}
+
+  \begin{eqnarray*}
+    \varphi'(t) &=& \omega(t) \\[\smallskipamount]
+    \omega'(t) &=& -\frac{g}{l}\cdot\sin\varphi(t)\hspace*{7.1cm}
+  \end{eqnarray*}
+  \vspace*{-1.5\medskipamount}
+  \begin{itemize}
+    \item
+      Von Hand (analytisch):\\
+      Lösung raten (Ansatz), Parameter berechnen
+    \item
+      Mit Computer (numerisch):\\
+      Eulersches Polygonzugverfahren
+  \end{itemize}
+  \smallskip
+  \begin{lstlisting}[gobble=0]
+    phi += dt * omega;
+    omega += - dt * g / l * sin (phi);
+  \end{lstlisting}
+
+  \pause
+  \bigskip
+
+  \textbf{Beispiel 3: Weltraum-Simulation}
+
+  Praktikumsaufgabe
+  \vspace*{-1cm}
+
+\end{frame}
+
+\nosectionnonumber{\inserttitle}
+
+\begin{frame}
+
+  \shownosectionnonumber
+
+  \begin{itemize}
+    \item[\textbf{1}] \textbf{Einführung}
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/hp.git}}}
+    \item[\textbf{2}] \textbf{Einführung in C}
+    \item[\textbf{3}] \textbf{Bibliotheken}
+      \begin{itemize}
+        \item[3.1] Der Präprozessor
+        \item[3.2] Bibliotheken einbinden
+        \item[3.3] Bibliotheken verwenden
+        \color{medgreen}
+        \item[3.4] Projekt organisieren: make
+      \end{itemize}
+    \item[\textbf{4}] \textbf{Hardwarenahe Programmierung}
+      \begin{itemize}
+        \color{red}
+        \item[4.1] Bit-Operationen
+        \item[4.2] I/O-Ports
+        \item[4.3] Interrupts
+        \vspace*{-0.1cm}
+        \item[\dots]
+      \end{itemize}
+    \item[\textbf{5}] \textbf{Algorithmen}
+      \begin{itemize}
+        \color{medgreen}
+        \item[5.1] Differentialgleichungen
+        \color{black}
+        \vspace*{-0.1cm}
+        \item[\dots]
+      \end{itemize}
+    \item[\textbf{\dots}]
+%    \item[\textbf{4}] \textbf{Hardwarenahe Programmierung}
+%    \item[\textbf{5}] \textbf{Algorithmen}
+%    \item[\textbf{6}] \textbf{Ergänzungen und Ausblicke}
+  \end{itemize}
+  \vspace*{-1cm}
+
+\end{frame}
+
+\iffalse
+
+\begin{frame}
+
+  \shownosectionnonumber
+
+  \begin{itemize}
+    \item[\textbf{1}] \textbf{Einführung}
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/hp}}}
+    \item[\textbf{2}] \textbf{Einführung in C}
+      \begin{itemize}
+        \vspace*{-\smallskipamount}
+        \item[\dots]
+        \item[2.10] Zeiger
+        \color{medgreen}
+        \item[2.11] Arrays und Strings
+        \item[2.12] Strukturen
+        \item[2.13] Dateien und Fehlerbehandlung
+        \color{red}
+        \item[2.14] Parameter des Hauptprogramms
+        \item[2.15] String-Operationen
+      \end{itemize}
+    \item[\textbf{3}] \textbf{Bibliotheken}
+%      \begin{itemize}
+%        \color{red}
+%        \item[3.1] Der Präprozessor
+%        \item[3.2] Bibliotheken einbinden
+%        \item[3.3] Bibliotheken verwenden
+%        \vspace*{-\smallskipamount}
+%        \item[\dots]
+%%        \item[3.4] Projekt organisieren: make
+%      \end{itemize}
+%    \vspace*{-\smallskipamount}
+    \item[\textbf{4}] \textbf{Hardwarenahe Programmierung}
+      \begin{itemize}
+        \color{red}
+        \item[4.1] Bit-Operationen
+        \item[4.2] I/O-Ports
+        \color{black}
+        \item[4.3] Interrupts
+        \vspace*{-0.1cm}
+        \item[\dots]
+      \end{itemize}
+    \item[\textbf{5}] \textbf{Algorithmen}
+    \item[\textbf{\dots}]
+  \end{itemize}
+
+\end{frame}
+
+\setcounter{section}{3}
+\section{Hardwarenahe Programmierung}
+\subsection{Bit-Operationen}
+\subsubsection{Zahlensysteme}
+
+\begin{frame}[fragile]
+
+  \showsection
+  \vspace*{-\smallskipamount}
+  \showsubsection
+  \vspace*{-\medskipamount}
+  \showsubsubsection
+
+  \begin{tabular}{rlrl}
+    Basis & Name & Beispiel & Anwendung \\[\smallskipamount]
+      2 & Binärsystem & 1\,0000\,0011 & Bit-Operationen \\
+      8 & Oktalsystem & \lstinline,0403, & Dateizugriffsrechte (Unix) \\
+     10 & Dezimalsystem & \lstinline,259, & Alltag \\
+     16 & Hexadezimalsystem & \lstinline,0x103, & Bit-Operationen \\
+    256 & (keiner gebräuchlich) & 0.0.1.3 & IP-Adressen (IPv4)
+  \end{tabular}
+
+  \bigskip
+
+  \begin{itemize}
+    \item
+      Computer rechnen im Binärsystem.
+    \item
+      Für viele Anwendungen (z.\,B.\ I/O-Ports, Grafik, \dots) ist es notwendig,\\
+      Bits in Zahlen einzeln ansprechen zu können.
+  \end{itemize}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsubsection
+
+  \begin{tabular}{rlrlrc}
+    \qquad 000 & \bf 0 \hspace*{1.5cm} & 0000 & \bf 0 & \quad 1000 & \bf 8\\
+           001 & \bf 1                 & 0001 & \bf 1 &       1001 & \bf 9\\
+           010 & \bf 2                 & 0010 & \bf 2 &       1010 & \bf A\\
+           011 & \bf 3                 & 0011 & \bf 3 &       1011 & \bf B\\[\smallskipamount]
+           100 & \bf 4                 & 0100 & \bf 4 &       1100 & \bf C\\
+           101 & \bf 5                 & 0101 & \bf 5 &       1101 & \bf D\\
+           110 & \bf 6                 & 0110 & \bf 6 &       1110 & \bf E\\
+           111 & \bf 7                 & 0111 & \bf 7 &       1111 & \bf F\\
+  \end{tabular}
+
+  \medskip
+
+  \begin{itemize}
+    \item
+      Oktal- und Hexadezimalzahlen lassen sich ziffernweise\\
+      in Binär-Zahlen umrechnen.
+    \item
+      Hexadezimalzahlen sind eine Kurzschreibweise für Binärzahlen,\\
+      gruppiert zu jeweils 4 Bits.
+    \item
+      Oktalzahlen sind eine Kurzschreibweise für Binärzahlen,\\
+      gruppiert zu jeweils 3 Bits.
+    \item
+      Trotz Taschenrechner u.\,ä.\ lohnt es sich,\\
+      die o.\,a.\ Umrechnungstabelle \textbf{auswendig} zu kennen.
+  \end{itemize}
+
+\end{frame}
+
+\subsubsection{Bit-Operationen in C}
+
+\begin{frame}[fragile]
+
+  \showsubsubsection
+
+  \begin{tabular}{lll}
+    C-Operator     & Verknüpfung              & Anwendung                \\[\smallskipamount]
+    \lstinline,&,  & Und                      & Bits gezielt löschen     \\
+    \lstinline,|,  & Oder                     & Bits gezielt setzen      \\
+    \lstinline,^,  & Exklusiv-Oder            & Bits gezielt invertieren \\
+    \lstinline,~,  & Nicht                    & Alle Bits invertieren    \\[\smallskipamount]
+    \lstinline,<<, & Verschiebung nach links  & Maske generieren         \\
+    \lstinline,>>, & Verschiebung nach rechts & Bits isolieren
+  \end{tabular}
+
+  \bigskip
+
+  Numerierung der Bits: von rechts ab 0
+
+  \medskip
+
+  \begin{tabular}{ll}
+    Bit Nr.\ 3 auf 1 setzen: &
+    \lstinline,a |= 1 << 3;, \\
+    Bit Nr.\ 4 auf 0 setzen: &
+    \lstinline,a &= ~(1 << 4);, \\
+    Bit Nr.\ 0 invertieren: &
+    \lstinline,a ^= 1 << 0;,
+  \end{tabular}
+
+  \smallskip
+
+  ~~Abfrage, ob Bit Nr.\ 1 gesetzt ist:\quad
+  \lstinline{if (a & (1 << 1))}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsubsection
+
+  C-Datentypen für Bit-Operationen:
+  \smallskip\par
+  \lstinline{#include <stdint.h>}
+  \medskip\par
+  \begin{tabular}{lllll}
+                    & 8 Bit & 16 Bit & 32 Bit & 64 Bit \\
+    mit Vorzeichen  & \lstinline,int8_t,
+                    & \lstinline,int16_t,
+                    & \lstinline,int32_t,
+                    & \lstinline,int64_t, \\
+    ohne Vorzeichen & \lstinline,uint8_t,
+                    & \lstinline,uint16_t,
+                    & \lstinline,uint32_t,
+                    & \lstinline,uint64_t,
+  \end{tabular}
+
+  \bigskip
+  \bigskip
+
+  Ausgabe:
+  \smallskip\par
+  \begin{lstlisting}
+    #include <stdio.h>
+    #include <stdint.h>
+    #include <inttypes.h>
+    ...
+    uint64_t x = 42;
+    printf ("Die Antwort lautet: %" PRIu64 "\n", x);
+  \end{lstlisting}
+
+  \bigskip
+
+  Aufgabe: Schreiben Sie C-Funktionen, die ein "`Array von Bits"' realisieren, z.\,B.
+
+  \smallskip
+
+  \begin{tabular}[t]{ll}
+    \lstinline|void set_bit (int i);|   & Bei Index $i$ auf 1 setzen \\
+    \lstinline|void clear_bit (int i);| & Bei Index $i$ auf 0 setzen \\
+    \lstinline|int get_bit (int i);|    & Bei Index $i$ lesen
+  \end{tabular}
+
+  \medskip
+
+  Hinweise:
+  \begin{itemize}
+    \item
+      Die Größe des Bit-"`Arrays"' (z.\,B.\ 1000) dürfen Sie als \emph{vorher bekannt\/} voraussetzen.
+    \item
+      Sie benötigen ein Array, z.\,B.\ von \lstinline|char|- oder \lstinline|int|-Variablen.
+    \item
+      Sie benötigen eine Division (\lstinline|/|) sowie den Divisionsrest (Modulo: \lstinline|%|).
+  \end{itemize}
+
+\end{frame}
+
+\subsection{I/O-Ports}
+
+\begin{frame}[fragile]
+
+%  \showsection
+  \showsubsection
+  \vspace*{-1.5\medskipamount}
+  {\large\textbf{\color{structure}4.3\quad Interrupts}}
+
+  \bigskip
+
+  Kommunikation mit externen Geräten
+
+  \bigskip
+
+  \begin{center}
+    \includegraphics{io-ports-and-interrupts.pdf}
+  \end{center}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  In Output-Port schreiben = Aktoren ansteuern
+
+  Beispiel: LED
+
+  \medskip
+
+  \begin{lstlisting}
+    #include <avr/io.h>
+    ...
+    DDRC = 0x70;
+    PORTC = 0x40;
+  \end{lstlisting}
+  \begin{picture}(0,0)
+    \put(3,0.67){\begin{minipage}{3cm}
+                \color{red}%
+                binär: 0111\,0000\\
+                binär: 0100\,0000
+              \end{minipage}}
+    \put(10,0.67){\makebox(0,0)[r]{\color{red}Herstellerspezifisch!}}
+  \end{picture}
+
+  \bigskip
+
+  \lstinline{DDR} = Data Direction Register\\
+  Bit = 1 für Output-Port\\
+  Bit = 0 für Input-Port
+
+  \bigskip
+
+  \emph{Details: siehe Datenblatt und Schaltplan}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Aus Input-Port lesen = Sensoren abfragen
+
+  Beispiel: Taster
+
+  \medskip
+
+  \begin{lstlisting}
+    #include <avr/io.h>
+    ...
+    DDRC = 0xfd;
+    while ((PINC & 0x02) == 0)
+      ; /* just wait */
+  \end{lstlisting}
+  \begin{picture}(0,0)(-1.5,-0.42)
+    \put(3,0.67){\begin{minipage}{3cm}
+                \color{red}%
+                binär: 1111\,1101\\
+                binär: 0000\,0010
+              \end{minipage}}
+    \put(10,0.67){\makebox(0,0)[r]{\color{red}Herstellerspezifisch!}}
+  \end{picture}
+
+  \bigskip
+
+  \lstinline{DDR} = Data Direction Register\\
+  Bit = 1 für Output-Port\\
+  Bit = 0 für Input-Port
+
+  \bigskip
+
+  \emph{Details: siehe Datenblatt und Schaltplan}
+  
+  \bigskip
+
+  Praktikumsaufgabe: Druckknopfampel
+
+\end{frame}
+
+\nosectionnonumber{\inserttitle}
+
+\begin{frame}
+
+  \shownosectionnonumber
+
+  \begin{itemize}
+    \item[\textbf{1}] \textbf{Einführung}
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/hp}}}
+    \item[\textbf{2}] \textbf{Einführung in C}
+      \begin{itemize}
+        \vspace*{-\smallskipamount}
+        \item[\dots]
+        \item[2.10] Zeiger
+        \item[2.11] Arrays und Strings
+        \item[2.12] Strukturen
+        \item[2.13] Dateien und Fehlerbehandlung
+        \color{medgreen}
+        \item[2.14] Parameter des Hauptprogramms
+        \item[2.15] String-Operationen
+      \end{itemize}
+    \item[\textbf{3}] \textbf{Bibliotheken}
+%      \begin{itemize}
+%        \color{red}
+%        \item[3.1] Der Präprozessor
+%        \item[3.2] Bibliotheken einbinden
+%        \item[3.3] Bibliotheken verwenden
+%        \vspace*{-\smallskipamount}
+%        \item[\dots]
+%%        \item[3.4] Projekt organisieren: make
+%      \end{itemize}
+%    \vspace*{-\smallskipamount}
+    \item[\textbf{4}] \textbf{Hardwarenahe Programmierung}
+      \begin{itemize}
+        \color{medgreen}
+        \item[4.1] Bit-Operationen
+        \item[4.2] I/O-Ports
+        \color{red}
+        \item[4.3] Interrupts
+        \vspace*{-0.1cm}
+        \item[\dots]
+      \end{itemize}
+    \item[\textbf{5}] \textbf{Algorithmen}
+    \item[\textbf{\dots}]
+  \end{itemize}
+
+\end{frame}
+
+\fi
+
+\end{document}
diff --git a/20201217/hp-2020ws-p2.pdf b/20201217/hp-2020ws-p2.pdf
new file mode 100644
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diff --git a/20201217/hp-2020ws-p2.tex b/20201217/hp-2020ws-p2.tex
new file mode 100644
index 0000000..38bdde2
--- /dev/null
+++ b/20201217/hp-2020ws-p2.tex
@@ -0,0 +1,201 @@
+% hp-2020ws-p2.pdf - Labor Notes on Low-Level Programming
+% Copyright (C) 2014, 2015, 2018, 2019, 2020  Peter Gerwinski
+%
+% This document is free software: you can redistribute it and/or
+% modify it either under the terms of the Creative Commons
+% Attribution-ShareAlike 3.0 License, or under the terms of the
+% GNU General Public License as published by the Free Software
+% Foundation, either version 3 of the License, or (at your option)
+% any later version.
+%
+% This document is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this document.  If not, see <http://www.gnu.org/licenses/>.
+%
+% You should have received a copy of the Creative Commons
+% Attribution-ShareAlike 3.0 Unported License along with this
+% document.  If not, see <http://creativecommons.org/licenses/>.
+
+% README: Versuch 2: Weltraum-Simulation
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+\usepackage{multicol}
+%\usepackage{sfmath}
+
+\sloppy
+\raggedcolumns
+\pagestyle{empty}
+\addtolength{\textheight}{1cm}
+\newcommand{\sep}{~$\cdot$~}
+\newcommand{\mylicense}{CC BY-SA (Version 4.0) oder GNU GPL (Version 3 oder höher)}
+
+\begin{document}
+
+  \makebox(0,0.005)[tl]{\includegraphics[scale=0.72]{logo-hochschule-bochum-cvh-text-v2.pdf}}\hfill
+  \makebox(0,0)[tr]{\includegraphics[scale=0.5]{logo-hochschule-bochum.pdf}}
+  \par\bigskip\bigskip
+  \begin{center}
+    \Large\textbf{Praktikumsversuch 2: Weltraum-Simulation}
+    \par\medskip
+    \normalsize Hardwarenahe Programmierung\sep
+    Wintersemester 2020/21\sep
+    Prof.~Dr.~Peter Gerwinski
+  \end{center}
+
+  Aufgabe: Schreiben Sie ein C-Programm,
+  das die Bahnen von beliebig vielen Massenpunkten unter Einfluß der Gravitation
+  simuliert und in bewegter Grafik darstellt.
+
+  \begin{multicols}{2}
+
+    \begin{itemize}
+      \item
+        Zwei Massenpunkte ("`Himmelskörper"') mit den Massen $m_i$ und $m_j$
+        an den Orten $\vec{r}_i$ und $\vec{r}_j$ ziehen einander an.
+        Diese Kraft heißt Gravitation. Sie hat den Betrag:
+        \begin{equation}
+          |\vec{F}_{ij}| = \frac{m_j\cdot m_i\cdot G}{|\vec{r}_j - \vec{r}_i|^2}
+        \end{equation}
+        Hierbei ist $G$ eine Konstante (Gravitationskonstante).
+
+      \item
+        Die auf einen Himmelskörper wirkende Gesamtkraft $\vec{F}_i$
+        ergibt sich als Summe der von allen anderen Himmelskörpern herrührenden
+        Gravitationskräfte:
+        \begin{equation}
+          \vec{F}_i = \sum_{j=0,\,j\ne i}^{N - 1} \vec{F}_{ij}
+        \end{equation}
+
+      \item
+        Die Gravitationskraft beschleunigt jeden Himmelskörper gemäß:
+        \begin{equation}
+          \vec{F_i} = m_i\cdot \vec{a_i}
+        \end{equation}
+
+      \item
+        Beispiel: Wir betrachten zwei Himmelskörper. Einer davon ("`Zentralgestirn"')
+        ruht im Zentrum ($\vec{r}_0 = 0$, $\vec{v}_0 = 0$)
+        und hat eine wesentlich größere Masse als der andere
+        ("`Satellit"', $m_1 \ll m_0$).  Mit geeignetem Anfangsort $\vec{r}_1$
+        und geeigneter Anfangsgeschwindigkeit $\vec{v}_1$ beschreibt dann
+        der Satellit eine elliptische Umlaufbahn um das Zentralgestirn.
+
+      \item
+        Wir rechnen in zwei Dimensionen $x$ und $y$.
+
+      \item
+        Für die Zerlegung einer Kraft $\vec{F}_{ij}$ in $x$- und $y$-Komponenten
+        benötigen Sie nur die Grundrechenarten und die Wurzelfunktion,
+        jedoch insbesondere \emph{keine} trigonometrischen Funktionen:
+        \begin{equation}
+          \vec{F}_{ij} = |\vec{F}_{ij}| \cdot \frac{\vec{r}_j - \vec{r}_i}{|\vec{r}_j - \vec{r}_i|}
+        \end{equation}
+
+      \item
+        Die Wurzelfunktion \lstinline{sqrt()} finden Sie
+        in der Mathematik-Bibliothek.
+        Um diese zu nutzen, verwenden Sie \lstinline{#include <math.h>} im Quelltext,
+        und geben Sie beim \lstinline[style=cmd]{gcc}-Aufruf
+        \lstinline[style=cmd]{-lm} mit an.
+
+      \columnbreak
+
+      \item
+        Für die Simulation betrachten wir das System in kurzen Zeitintervallen $dt$
+        und berechnen die Änderungen des Ortes $\vec{r}_i = (x_i,y_i)$
+        und der Geschwindigkeit $\vec{v}_i = (v_{xi},v_{yi})$ jedes Himmelskörpers
+        mit Hilfe des expliziten Eulerschen Polygonzugverfahrens.
+        \par
+        (Wer möchte, darf natürlich auch andere Verfahren anwenden,
+        beispielsweise das klassische Runge-Kutta-Verfahren 4.~Ordnung.)
+
+      \item
+        Für eine derartige Simulation
+        einschließlich ihrer Darstellung als bewegte Grafik
+        können Sie sich von dem Beispiel-Programm \gitfile{hp}{20201217}{gtk-16.c}
+        inspirieren lassen.
+%        (Compilieren mit:
+%        \lstinline[style=cmd]{gcc}
+%        \lstinline[style=cmd]{-Wall}
+%        \lstinline[style=cmd]{-O}
+%        \lstinline[style=cmd]{gtk-16.c}
+%        \lstinline[style=cmd]{$(pkg-config}
+%        \lstinline[style=cmd]{--cflags}
+%        \lstinline[style=cmd]{--libs}
+%        \lstinline[style=cmd]{gtk+-3.0)}
+%        \lstinline[style=cmd]{-o}
+%        \lstinline[style=cmd]{gtk-16})
+
+      \item
+        In einer \file{GTK+}-\lstinline{drawing_area}
+        liegt der Nullpunkt der Zeichnung oben links,
+        eine Längeneinheit entspricht einem Pixel,
+        und die $y$-Koordinate wächst nach unten.
+        Es empfiehlt sich, die Koordinaten so umzurechnen,
+        daß der Nullpunkt in der Mitte der Zeichnung liegt,
+        die Längeneinheit Ihrem persönlichen Geschmack entspricht
+        und die $y$-Koordinate nach oben wächst.
+
+      \item
+        Beispiel-Szenarien für 3 oder mehr Körper:
+        \vspace{-\smallskipamount}
+        \begin{itemize}\itemsep0pt
+          \item 
+            Planet mit Mond umkreist Sonne
+          \item
+            Sonne mit mehreren Planeten, die sich gegenseitig beeinflussen
+          \item
+            zwei Sonnen umkreisen sich gegenseitig, Planet kreist drumherum
+          \item
+            Raumsonde besucht nacheinander mehrere Planeten
+        \end{itemize}
+
+      \item
+        \textbf{Hinweis:}
+        Speichern Sie die verschiedenen Körper nicht als separate Variable,
+        sondern in einem Array. Ihr Programm wird dadurch nicht nur flexibler,
+        sondern auch übersichtlicher und weniger fehleranfällig.
+
+      \item
+        \textbf{Abgabe:}
+        Ihre Quelltexte mit den Lösungen der Praktikumsaufgabe schicken Sie bitte
+        per E-Mail an \file{peter.gerwinski@hs-bochum.de}
+        mit dem \textbf{Betreff:} \lstinline[style=terminal]{aezeev1C}
+        unter Angabe von Name, Matrikel-Nummer,
+        Studiengang (MI/MP/TI) und Studienmodell (KIA/KIS/GS).
+
+    \end{itemize}
+
+  \end{multicols}
+
+  \vspace*{-\bigskipamount}
+
+  \strut\hfill\emph{Viel Erfolg!}\qquad\qquad
+
+  \vfill
+
+  \begingroup
+
+    \small
+
+    \setlength{\leftskip}{3cm}
+
+    Stand: 17.\ Dezember 2020
+
+%    Soweit nicht anders angegeben:\\
+    Copyright \copyright\ 2014, 2015, 2018, 2019, 2020\quad Peter Gerwinski\\
+    Lizenz: \mylicense
+
+    Sie können diese Praktikumsunterlagen einschließlich \LaTeX-Quelltext
+    und Beispielprogramm herunterladen unter:
+    \url{https://gitlab.cvh-server.de/pgerwinski/hp}
+
+  \endgroup
+
+\end{document}
diff --git a/20201217/hp-musterloesung-20201217.pdf b/20201217/hp-musterloesung-20201217.pdf
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diff --git a/20201217/hp-musterloesung-20201217.tex b/20201217/hp-musterloesung-20201217.tex
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+% hp-musterloesung-20201217.pdf - Solutions to the Exercises on Low-Level Programming
+% Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019, 2020  Peter Gerwinski
+%
+% This document is free software: you can redistribute it and/or
+% modify it either under the terms of the Creative Commons
+% Attribution-ShareAlike 3.0 License, or under the terms of the
+% GNU General Public License as published by the Free Software
+% Foundation, either version 3 of the License, or (at your option)
+% any later version.
+%
+% This document is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this document.  If not, see <http://www.gnu.org/licenses/>.
+%
+% You should have received a copy of the Creative Commons
+% Attribution-ShareAlike 3.0 Unported License along with this
+% document.  If not, see <http://creativecommons.org/licenses/>.
+
+% README: Kondensator, hüpfender Ball
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+\usepackage{gnuplot-lua-tikz}
+
+\begin{document}
+
+  \section*{Hardwarenahe Programmierung\\
+            Musterlösung zu den Übungsaufgaben -- 17.\ Dezember 2020}
+
+  \exercise{Kondensator}
+
+  Ein Kondensator der Kapazität $C = 100\,\mu{\rm F}$
+  ist auf die Spannung $U_0 = 5\,{\rm V}$ aufgeladen
+  und wird über einen Widerstand $R = 33\,{\rm k}\Omega$ entladen.
+
+  \begin{enumerate}[(a)]
+    \item
+      Schreiben Sie ein C-Programm, das
+      den zeitlichen Spannungsverlauf in einer Tabelle darstellt.
+      \points{5}
+    \item
+      Schreiben Sie ein C-Programm, das ermittelt,
+      wie lange es dauert, bis die Spannung unter $0.1\,{\rm V}$ gefallen ist.
+      \points{4}
+    \item
+      Vergleichen Sie die berechneten Werte mit der exakten theoretischen Entladekurve:
+      \begin{math}
+        U(t) = U_0 \cdot e^{-\frac{t}{RC}}
+      \end{math}\\
+      \points{3}
+  \end{enumerate}
+
+  Hinweise:
+  \begin{itemize}
+    \item
+      Für die Simulation zerlegen wir den Entladevorgang in kurze Zeitintervalle $dt$.
+      Innerhalb jedes Zeitintervalls betrachten wir den Strom $I$ als konstant
+      und berechnen, wieviel Ladung $Q$ innerhalb des Zeitintervalls
+      aus dem Kondensator herausfließt.
+      Aus der neuen Ladung berechnen wir die Spannung am Ende des Zeitintervalls.
+    \item
+      Für den Vergleich mit der exakten theoretischen Entladekurve
+      benötigen Sie die Exponentialfunktion \lstinline{exp()}.
+      Diese finden Sie in der Mathematik-Bibliothek:
+      \lstinline{#include <math.h>} im Quelltext,
+      beim \lstinline[style=cmd]{gcc}-Aufruf \lstinline[style=cmd]{-lm} mit angeben.
+    \item
+      $Q = C \cdot U$,\quad $U = R \cdot I$,\quad $I = \frac{dQ}{dt}$
+  \end{itemize}
+
+  \solution
+
+  \begin{itemize}
+    \item
+      \textbf{Schreiben Sie ein C-Programm, das
+      den zeitlichen Spannungsverlauf in einer Tabelle darstellt.}
+
+      In dem Programm \gitfile{hp}{20201217}{loesung-1a.c}
+      arbeiten wir, dem ersten Hinweis folgend,
+      mit einem Zeitintervall von \lstinline{dt = 0.01}.
+      Mit dieser Schrittweite lassen wir uns eine Tabelle ausgeben,
+      die jeweils die Zeit und durch die Simulation berechnete Spannung ausgibt.
+
+      Wir simulieren, wie die Ladung $Q = C \cdot U$ des Kondensators
+      im Laufe der Zeit abfließt.
+      Dazu berechnen wir in jedem Zeitschritt zunächst den Strom $I = U / R$,
+      der aus dem Kondensator fließt.
+      Dieser Strom bewirkt, daß innerhalb des Zeitintervalls $dt$
+      die Ladung $dQ = I \cdot dt$ aus dem Kondensator abfließt.
+      Am Ende des Zeitintervalls berechnen wir die zur neuen Ladung $Q$
+      gehörende neue Spannung $U = Q / C$.
+
+      Für eine einfache Ausgabe der Tabelle
+      verwenden wir die Formatspezifikationen \lstinline{%10.3lf} für drei 
+      bzw.\ \lstinline{%15.8lf} für acht Nachkommastellen Genauigkeit.
+      Damit schreiben wir jeweils eine \emph{lange Fließkommazahl\/} (\lstinline{%lf})
+      rechtsbündig in ein Feld der Breite 10 bzw.\ 15
+      und lassen uns 3 bzw.\ 8 Nachkommastellen ausgeben. 
+
+      Wir compilieren das Programm mit:
+      \lstinline[style=cmd]{gcc -Wall -O loesung-1a.c -o loesung-1a}
+
+    \item
+      \textbf{Schreiben Sie ein C-Programm, das ermittelt,
+      wie lange es dauert, bis die Spannung unter \boldmath $0.1\,{\rm V}$ gefallen ist.}
+
+      Wir ändern das Programm \gitfile{hp}{20201217}{loesung-1a.c} so ab,
+      daß zum einen die Schleife abbricht, sobald die Spannung 
+      den Wert $0.1\,{\rm V}$ unterschreitet (\gitfile{hp}{20201217}{loesung-1b.c}),
+      und daß zum anderen nicht jedesmal eine Zeile für die Tabelle ausgegeben wird,
+      sondern erst am Ende die Zeit (und die Spannung).
+
+      Der Ausgabe entnehmen wir, daß die Spannung bei etwa $t = 12.90\,{\rm s}$
+      den Wert $0.1\,{\rm V}$ unterschreitet.
+
+    \item
+      \textbf{Vergleichen Sie die berechneten Werte
+      mit der exakten theoretischen Entladekurve:\\[0.5\smallskipamount]
+      \boldmath  
+      \begin{math}
+        U(t) = U_0 \cdot e^{-\frac{t}{RC}}
+      \end{math}}
+
+      Wir ändern das Programm \gitfile{hp}{20201217}{loesung-1a.c} so ab,
+      daß es zusätzlich zur Zeit und zur simulierten Spannung
+      die exakte Spannung $U_0 \cdot e^{-\frac{t}{RC}}$
+      gemäß der theoretischen Entladekurve ausgibt (\gitfile{hp}{20201217}{loesung-1c.c}),
+
+      Da dieses Programm die Exponentialfunktion verwendet, müssen wir nun
+      beim Compilieren zusätzlich \lstinline[style=cmd]{-lm}\hspace{1pt}
+      für das Einbinden der Mathematik-Bibliothek angeben.
+
+      Der erweiterten Tabelle können wir entnehmen,
+      daß die durch die Simulation berechnete Spannung
+      mit der Spannung $U_0 \cdot e^{-\frac{t}{RC}}$
+      gemäß der theoretischen Entladekurve
+      bis auf wenige Prozent übereinstimmt.
+      Dies ist für viele praktische Anwendungen ausreichend,
+      wenn auch nicht für Präzisionsmessungen.
+
+      Wenn Sie die Ausgabe des Programms, z.\,B.\ mit
+      \lstinline[style=cmd]{./loesung-1c > loesung-1c.dat},
+      in einer Datei \gitfile{hp}{20201217}{loesung-1c.dat} speichern,
+      können Sie sich die beiden Kurven graphisch darstellen lassen,
+      z.\,B.\ mit \file{gnuplot} und dem folgenden Befehl:
+      \begin{lstlisting}[style=cmd,gobble=8]
+        plot "loesung-1c.dat" using 1:2 with lines title "Simulation",
+             "loesung-1c.dat" using 1:3 with lines title "Theorie"
+      \end{lstlisting}
+      \begin{center}
+        \input{loesung-1c.tikz}
+      \end{center}
+
+      Der Unterschied zwischen der simulierten und der theoretischen Entladungskurve
+      ist mit bloßem Auge nicht sichtbar.
+  \end{itemize}
+
+  \vfill
+
+  \exercise{Fehlerhaftes Programm: Hüpfender Ball}
+
+  Das auf der nächsten Seite abgedruckte GTK+-Programm
+  (Datei: \gitfile{hp}{20201217}{aufgabe-2.c}) soll einen
+  hüpfenden Ball darstellen, ist jedoch fehlerhaft.
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      Warum sieht man lediglich ein leeres Fenster?
+      Welchen Befehl muß man ergänzen, um diesen Fehler zu beheben?
+      \points{3}
+    \item
+      Nach der Fehlerbehebung in Aufgabenteil (a)
+      zeigt das Programm einen unbeweglichen Ball.
+      Welchen Befehl muß man ergänzen, um diesen Fehler zu beheben, und warum?
+      \points{2}
+    \item
+      Erklären Sie das merkwürdige Hüpfverhalten des Balls.
+      Wie kommt es zustande?
+      Was an diesem Verhalten ist korrekt, und was ist fehlerhaft? \points{5}
+    \item
+      Welche Befehle muß man in welcher Weise ändern,
+      um ein realistischeres Hüpf-Verhalten zu bekommen? \points{2}
+  \end{enumerate}
+
+  Hinweis: Das Hinzuziehen von Beispiel-Programmen aus der Vorlesung
+  ist ausdrücklich erlaubt -- auch in der Klausur.
+
+  Allgemeiner Hinweis:
+  Wenn Sie die Übungsaufgaben zu dieser Lehrveranstaltung
+  als PDF-Datei betrachten und darin auf die Dateinamen klicken,
+  können Sie die Beispiel-Programme direkt herunterladen.
+  Dadurch vermeiden Sie Übertragungsfehler.
+
+  \clearpage
+
+  \vbox to \textheight{\vspace*{-0.5cm}\begin{lstlisting}
+    #include <gtk/gtk.h>
+
+    #define WIDTH 320
+    #define HEIGHT 240
+
+    double t = 0.0;
+    double dt = 0.2;
+
+    int r = 5;
+
+    double x = 10;
+    double y = 200;
+    double vx = 20;
+    double vy = -60;
+    double g = 9.81;
+
+    gboolean draw (GtkWidget *widget, cairo_t *c, gpointer data)
+    {
+      GdkRGBA blue = { 0.0, 0.5, 1.0, 1.0 };
+
+      gdk_cairo_set_source_rgba (c, &blue);
+      cairo_arc (c, x, y, r, 0, 2 * G_PI);
+      cairo_fill (c);
+
+      return FALSE;
+    }
+
+    gboolean timer (GtkWidget *widget)
+    {
+      t += dt;
+      x += vx * dt;
+      y += vy * dt;
+      vx = vx;
+      vy = 0.5 * g * (t * t);
+      if (y + r >= HEIGHT)
+        vy = -vy * 0.9;
+      if (x + r >= WIDTH)
+        vx = -vx * 0.9;
+      if (x - r <= 0)
+        vx = -vx * 0.9;
+      gtk_widget_queue_draw_area (widget, 0, 0, WIDTH, HEIGHT);
+      g_timeout_add (50, (GSourceFunc) timer, widget);
+      return FALSE;
+    }
+
+    int main (int argc, char **argv)
+    {
+      gtk_init (&argc, &argv);
+
+      GtkWidget *window = gtk_window_new (GTK_WINDOW_TOPLEVEL);
+      gtk_widget_show (window);
+      gtk_window_set_title (GTK_WINDOW (window), "Hello");
+      g_signal_connect (window, "destroy", G_CALLBACK (gtk_main_quit), NULL);
+
+      GtkWidget *drawing_area = gtk_drawing_area_new ();
+      gtk_widget_show (drawing_area);
+      gtk_container_add (GTK_CONTAINER (window), drawing_area);
+      gtk_widget_set_size_request (drawing_area, WIDTH, HEIGHT);
+
+      gtk_main ();
+      return 0;
+    }
+  \end{lstlisting}\vss}
+
+  \solution
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      \textbf{Warum sieht man lediglich ein leeres Fenster?
+      Welchen Befehl muß man ergänzen, um diesen Fehler zu beheben?}
+
+      Die für das Zeichnen zuständige Callback-Funktion wurde zwar geschrieben,
+      aber nicht installiert.
+      Um dies zu beheben, ergänze man den folgenden Befehl im Hauptprogramm:
+
+      \lstinline{g_signal_connect (drawing_area, "draw", G_CALLBACK (draw), NULL);}
+
+      Dies erkennt man sehr schnell durch Vergleich mit dem Beispiel-Programm
+      \gitfile{hp}{20201217}{gtk-16.c}.
+
+    \item
+      \textbf{Nach der Fehlerbehebung in Aufgabenteil (a)
+      zeigt das Programm einen unbeweglichen Ball.
+      Welchen Befehl muß man ergänzen, um diesen Fehler zu beheben, und warum?}
+
+      Die Timer-Callback-Funktion wurde zwar geschrieben, aber nicht installiert.
+      Um dies zu beheben, ergänze man den folgenden Befehl im Hauptprogramm:
+
+      \lstinline{g_timeout_add (50, (GSourceFunc) timer, drawing_area);}
+
+      Auch dies erkennt man sehr schnell durch Vergleich mit dem Beispiel-Programm
+      \gitfile{hp}{20201217}{gtk-16.c}.
+
+    \item
+      \textbf{Erklären Sie das merkwürdige Hüpfverhalten des Balls.
+      Wie kommt es zustande?
+      Was an diesem Verhalten ist korrekt, und was ist fehlerhaft?}
+
+      Die Geschwindigkeit in $y$-Richtung wächst immer weiter.
+      Der Grund dafür ist, daß die $y$-Komponente der Geschwindigkeit
+      nicht auf physikalisch sinnvolle Weise berechnet wird.
+      In der dafür zuständigen Zeile
+      \lstinline{vy = 0.5 * g * (t * t);}
+      wird stattdessen der Weg in $y$-Richtung bei einer gleichmäßig
+      beschleunigten Bewegung berechnet und als Geschwindigkeit verwendet.
+
+    \item
+      \textbf{Welche Befehle muß man in welcher Weise ändern,
+      um ein realistischeres Hüpf-Verhalten zu bekommen?}
+
+      Da der Ball am Boden abprallen soll, ist es \emph{nicht\/} sinnvoll,
+      die $y$-Komponente der Geschwindigkeit über die bekannte physikalische
+      Formel $v_y = -g\cdot t$ für die Geschwindigkeit in einer
+      gleichmäßig beschleunigten Bewegung zu berechnen.
+
+      Stattdessen ist es sinnvoll, die \emph{Geschwindigkeitsänderung\/}
+      innerhalb des Zeitintervalls \lstinline{dt}
+      zur Geschwindigkeitskomponente zu addieren:
+      \lstinline{vy += g * dt;}
+
+      Auch dies erkennt man sehr schnell durch Vergleich mit dem Beispiel-Programm
+      \gitfile{hp}{20201217}{gtk-16.c}.
+  \end{enumerate}
+
+\end{document}
diff --git a/20201217/hp-uebung-20201217.pdf b/20201217/hp-uebung-20201217.pdf
new file mode 100644
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diff --git a/20201217/hp-uebung-20201217.tex b/20201217/hp-uebung-20201217.tex
new file mode 100644
index 0000000..c751465
--- /dev/null
+++ b/20201217/hp-uebung-20201217.tex
@@ -0,0 +1,193 @@
+% hp-uebung-20201217.pdf - Exercises on Low-Level Programming
+% Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019, 2020  Peter Gerwinski
+%
+% This document is free software: you can redistribute it and/or
+% modify it either under the terms of the Creative Commons
+% Attribution-ShareAlike 3.0 License, or under the terms of the
+% GNU General Public License as published by the Free Software
+% Foundation, either version 3 of the License, or (at your option)
+% any later version.
+%
+% This document is distributed in the hope that it will be useful,
+% but WITHOUT ANY WARRANTY; without even the implied warranty of
+% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+% GNU General Public License for more details.
+%
+% You should have received a copy of the GNU General Public License
+% along with this document.  If not, see <http://www.gnu.org/licenses/>.
+%
+% You should have received a copy of the Creative Commons
+% Attribution-ShareAlike 3.0 Unported License along with this
+% document.  If not, see <http://creativecommons.org/licenses/>.
+
+% README: Kondensator, hüpfender Ball
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+
+\begin{document}
+
+%  \thispagestyle{empty}
+
+  \section*{Hardwarenahe Programmierung\\
+            Übungsaufgaben -- 17.\ Dezember 2020}
+
+  Diese Übung enthält Punkteangaben wie in einer Klausur.
+  Um zu "`bestehen"', müssen Sie innerhalb von 70 Minuten
+  unter Verwendung ausschließlich zugelassener Hilfsmittel
+  12 Punkte (von insgesamt \totalpoints) erreichen.
+
+  \exercise{Kondensator}
+
+  Ein Kondensator der Kapazität $C = 100\,\mu{\rm F}$
+  ist auf die Spannung $U_0 = 5\,{\rm V}$ aufgeladen
+  und wird über einen Widerstand $R = 33\,{\rm k}\Omega$ entladen.
+
+  \begin{enumerate}[(a)]
+    \item
+      Schreiben Sie ein C-Programm, das
+      den zeitlichen Spannungsverlauf in einer Tabelle darstellt.
+      \points{5}
+    \item
+      Schreiben Sie ein C-Programm, das ermittelt,
+      wie lange es dauert, bis die Spannung unter $0.1\,{\rm V}$ gefallen ist.
+      \points{4}
+    \item
+      Vergleichen Sie die berechneten Werte mit der exakten theoretischen Entladekurve:
+      \begin{math}
+        U(t) = U_0 \cdot e^{-\frac{t}{RC}}
+      \end{math}\\
+      \points{3}
+  \end{enumerate}
+
+  Hinweise:
+  \begin{itemize}
+    \item
+      Für die Simulation zerlegen wir den Entladevorgang in kurze Zeitintervalle $dt$.
+      Innerhalb jedes Zeitintervalls betrachten wir den Strom $I$ als konstant
+      und berechnen, wieviel Ladung $Q$ innerhalb des Zeitintervalls
+      aus dem Kondensator herausfließt.
+      Aus der neuen Ladung berechnen wir die Spannung am Ende des Zeitintervalls.
+    \item
+      Für den Vergleich mit der exakten theoretischen Entladekurve
+      benötigen Sie die Exponentialfunktion \lstinline{exp()}.
+      Diese finden Sie in der Mathematik-Bibliothek:
+      \lstinline{#include <math.h>} im Quelltext,
+      beim \lstinline[style=cmd]{gcc}-Aufruf \lstinline[style=cmd]{-lm} mit angeben.
+    \item
+      $Q = C \cdot U$,\quad $U = R \cdot I$,\quad $I = \frac{dQ}{dt}$
+  \end{itemize}
+
+  \exercise{Fehlerhaftes Programm: Hüpfender Ball}
+
+  Das auf der nächsten Seite abgedruckte GTK+-Programm
+  (Datei: \gitfile{hp}{20201217}{aufgabe-2.c}) soll einen
+  hüpfenden Ball darstellen, ist jedoch fehlerhaft.
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      Warum sieht man lediglich ein leeres Fenster?
+      Welchen Befehl muß man ergänzen, um diesen Fehler zu beheben?
+      \points{3}
+    \item
+      Nach der Fehlerbehebung in Aufgabenteil (a)
+      zeigt das Programm einen unbeweglichen Ball.
+      Welchen Befehl muß man ergänzen, um diesen Fehler zu beheben, und warum?
+      \points{2}
+    \item
+      Erklären Sie das merkwürdige Hüpfverhalten des Balls.
+      Wie kommt es zustande?
+      Was an diesem Verhalten ist korrekt, und was ist fehlerhaft? \points{5}
+    \item
+      Welche Befehle muß man in welcher Weise ändern,
+      um ein realistischeres Hüpf-Verhalten zu bekommen? \points{2}
+  \end{enumerate}
+
+  Hinweis: Das Hinzuziehen von Beispiel-Programmen aus der Vorlesung
+  ist ausdrücklich erlaubt -- auch in der Klausur.
+
+  Allgemeiner Hinweis:
+  Wenn Sie die Übungsaufgaben zu dieser Lehrveranstaltung
+  als PDF-Datei betrachten und darin auf die Dateinamen klicken,
+  können Sie die Beispiel-Programme direkt herunterladen.
+  Dadurch vermeiden Sie Übertragungsfehler.
+
+  \bigskip
+
+  \begin{flushright}
+    \textit{Viel Erfolg!}
+  \end{flushright}
+
+  \clearpage
+
+  \vbox to \textheight{\vspace*{-0.5cm}\begin{lstlisting}
+    #include <gtk/gtk.h>
+
+    #define WIDTH 320
+    #define HEIGHT 240
+
+    double t = 0.0;
+    double dt = 0.2;
+
+    int r = 5;
+
+    double x = 10;
+    double y = 200;
+    double vx = 20;
+    double vy = -60;
+    double g = 9.81;
+
+    gboolean draw (GtkWidget *widget, cairo_t *c, gpointer data)
+    {
+      GdkRGBA blue = { 0.0, 0.5, 1.0, 1.0 };
+
+      gdk_cairo_set_source_rgba (c, &blue);
+      cairo_arc (c, x, y, r, 0, 2 * G_PI);
+      cairo_fill (c);
+
+      return FALSE;
+    }
+
+    gboolean timer (GtkWidget *widget)
+    {
+      t += dt;
+      x += vx * dt;
+      y += vy * dt;
+      vx = vx;
+      vy = 0.5 * g * (t * t);
+      if (y + r >= HEIGHT)
+        vy = -vy * 0.9;
+      if (x + r >= WIDTH)
+        vx = -vx * 0.9;
+      if (x - r <= 0)
+        vx = -vx * 0.9;
+      gtk_widget_queue_draw_area (widget, 0, 0, WIDTH, HEIGHT);
+      g_timeout_add (50, (GSourceFunc) timer, widget);
+      return FALSE;
+    }
+
+    int main (int argc, char **argv)
+    {
+      gtk_init (&argc, &argv);
+
+      GtkWidget *window = gtk_window_new (GTK_WINDOW_TOPLEVEL);
+      gtk_widget_show (window);
+      gtk_window_set_title (GTK_WINDOW (window), "Hello");
+      g_signal_connect (window, "destroy", G_CALLBACK (gtk_main_quit), NULL);
+
+      GtkWidget *drawing_area = gtk_drawing_area_new ();
+      gtk_widget_show (drawing_area);
+      gtk_container_add (GTK_CONTAINER (window), drawing_area);
+      gtk_widget_set_size_request (drawing_area, WIDTH, HEIGHT);
+
+      gtk_main ();
+      return 0;
+    }
+  \end{lstlisting}\vss}
+
+  \makeatletter
+    \immediate\write\@mainaux{\string\gdef\string\totalpoints{\arabic{points}}}
+  \makeatother
+
+\end{document}
diff --git a/20201217/loesung-1a.c b/20201217/loesung-1a.c
new file mode 100644
index 0000000..f355706
--- /dev/null
+++ b/20201217/loesung-1a.c
@@ -0,0 +1,22 @@
+#include <stdio.h>
+#include <math.h>
+
+int main (void)
+{
+  double C = 0.0001;
+  double U0 = 5.0;
+  double U = U0;
+  double R = 33000.0;
+  double t = 0.0;
+  double dt = 0.01;
+  double Q = C * U;
+  while (U > 0.09)
+    {
+      printf ("%10.3lf%15.8lf\n", t, U);
+      double I = U / R;
+      Q -= I * dt;
+      U = Q / C;
+      t += dt;
+    }
+  return 0;
+}
diff --git a/20201217/loesung-1b.c b/20201217/loesung-1b.c
new file mode 100644
index 0000000..f5fc220
--- /dev/null
+++ b/20201217/loesung-1b.c
@@ -0,0 +1,22 @@
+#include <stdio.h>
+#include <math.h>
+
+int main (void)
+{
+  double C = 0.0001;
+  double U0 = 5.0;
+  double U = U0;
+  double R = 33000.0;
+  double t = 0.0;
+  double dt = 0.01;
+  double Q = C * U;
+  while (U >= 0.1)
+    {
+      double I = U / R;
+      Q -= I * dt;
+      U = Q / C;
+      t += dt;
+    }
+  printf ("%10.3lf%15.8lf\n", t, U);
+  return 0;
+}
diff --git a/20201217/loesung-1c.c b/20201217/loesung-1c.c
new file mode 100644
index 0000000..71802e0
--- /dev/null
+++ b/20201217/loesung-1c.c
@@ -0,0 +1,22 @@
+#include <stdio.h>
+#include <math.h>
+
+int main (void)
+{
+  double C = 0.0001;
+  double U0 = 5.0;
+  double U = U0;
+  double R = 33000.0;
+  double t = 0.0;
+  double dt = 0.01;
+  double Q = C * U;
+  while (U > 0.09)
+    {
+      printf ("%10.3lf%15.8lf%15.8lf\n", t, U, U0 * exp (-t / (R * C)));
+      double I = U / R;
+      Q -= I * dt;
+      U = Q / C;
+      t += dt;
+    }
+  return 0;
+}
diff --git a/20201217/loesung-1c.dat b/20201217/loesung-1c.dat
new file mode 100644
index 0000000..4df7062
--- /dev/null
+++ b/20201217/loesung-1c.dat
@@ -0,0 +1,1324 @@
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+  --(1.285,7.598)--(1.293,7.578)--(1.301,7.556)--(1.309,7.535)--(1.317,7.514)--(1.324,7.493)%
+  --(1.332,7.472)--(1.340,7.452)--(1.348,7.431)--(1.356,7.410)--(1.363,7.390)--(1.371,7.370)%
+  --(1.379,7.348)--(1.387,7.328)--(1.395,7.308)--(1.403,7.288)--(1.410,7.267)--(1.418,7.247)%
+  --(1.426,7.227)--(1.434,7.207)--(1.442,7.187)--(1.449,7.168)--(1.457,7.148)--(1.465,7.128)%
+  --(1.473,7.108)--(1.481,7.089)--(1.488,7.069)--(1.496,7.049)--(1.504,7.030)--(1.512,7.010)%
+  --(1.520,6.991)--(1.528,6.971)--(1.535,6.952)--(1.543,6.934)--(1.551,6.913)--(1.559,6.895)%
+  --(1.567,6.876)--(1.574,6.858)--(1.582,6.837)--(1.590,6.819)--(1.598,6.800)--(1.606,6.781)%
+  --(1.613,6.763)--(1.621,6.744)--(1.629,6.726)--(1.637,6.707)--(1.645,6.688)--(1.652,6.670)%
+  --(1.660,6.653)--(1.668,6.634)--(1.676,6.615)--(1.684,6.597)--(1.692,6.580)--(1.699,6.561)%
+  --(1.707,6.542)--(1.715,6.525)--(1.723,6.507)--(1.731,6.489)--(1.738,6.471)--(1.746,6.454)%
+  --(1.754,6.437)--(1.762,6.418)--(1.770,6.401)--(1.777,6.384)--(1.785,6.365)--(1.793,6.348)%
+  --(1.801,6.331)--(1.809,6.314)--(1.817,6.297)--(1.824,6.280)--(1.832,6.263)--(1.840,6.246)%
+  --(1.848,6.229)--(1.856,6.211)--(1.863,6.194)--(1.871,6.177)--(1.879,6.160)--(1.887,6.143)%
+  --(1.895,6.126)--(1.902,6.111)--(1.910,6.093)--(1.918,6.076)--(1.926,6.061)--(1.934,6.044)%
+  --(1.941,6.027)--(1.949,6.011)--(1.957,5.994)--(1.965,5.979)--(1.973,5.961)--(1.981,5.946)%
+  --(1.988,5.929)--(1.996,5.913)--(2.004,5.898)--(2.012,5.881)--(2.020,5.865)--(2.027,5.850)%
+  --(2.035,5.834)--(2.043,5.819)--(2.051,5.801)--(2.059,5.786)--(2.066,5.770)--(2.074,5.755)%
+  --(2.082,5.739)--(2.090,5.724)--(2.098,5.708)--(2.106,5.693)--(2.113,5.677)--(2.121,5.662)%
+  --(2.129,5.648)--(2.137,5.632)--(2.145,5.617)--(2.152,5.601)--(2.160,5.587)--(2.168,5.572)%
+  --(2.176,5.556)--(2.184,5.541)--(2.191,5.527)--(2.199,5.511)--(2.207,5.497)--(2.215,5.482)%
+  --(2.223,5.468)--(2.230,5.452)--(2.238,5.438)--(2.246,5.423)--(2.254,5.409)--(2.262,5.395)%
+  --(2.270,5.379)--(2.277,5.365)--(2.285,5.351)--(2.293,5.337)--(2.301,5.322)--(2.309,5.308)%
+  --(2.316,5.294)--(2.324,5.280)--(2.332,5.266)--(2.340,5.252)--(2.348,5.238)--(2.355,5.224)%
+  --(2.363,5.210)--(2.371,5.196)--(2.379,5.182)--(2.387,5.168)--(2.394,5.154)--(2.402,5.140)%
+  --(2.410,5.126)--(2.418,5.112)--(2.426,5.100)--(2.434,5.086)--(2.441,5.072)--(2.449,5.059)%
+  --(2.457,5.045)--(2.465,5.031)--(2.473,5.019)--(2.480,5.005)--(2.488,4.991)--(2.496,4.978)%
+  --(2.504,4.964)--(2.512,4.952)--(2.519,4.938)--(2.527,4.926)--(2.535,4.913)--(2.543,4.899)%
+  --(2.551,4.887)--(2.559,4.874)--(2.566,4.860)--(2.574,4.848)--(2.582,4.836)--(2.590,4.822)%
+  --(2.598,4.809)--(2.605,4.797)--(2.613,4.784)--(2.621,4.772)--(2.629,4.759)--(2.637,4.747)%
+  --(2.644,4.735)--(2.652,4.722)--(2.660,4.710)--(2.668,4.697)--(2.676,4.685)--(2.683,4.672)%
+  --(2.691,4.660)--(2.699,4.648)--(2.707,4.635)--(2.715,4.623)--(2.723,4.610)--(2.730,4.598)%
+  --(2.738,4.587)--(2.746,4.575)--(2.754,4.562)--(2.762,4.551)--(2.769,4.539)--(2.777,4.526)%
+  --(2.785,4.516)--(2.793,4.503)--(2.801,4.491)--(2.808,4.480)--(2.816,4.467)--(2.824,4.457)%
+  --(2.832,4.444)--(2.840,4.433)--(2.848,4.421)--(2.855,4.410)--(2.863,4.399)--(2.871,4.387)%
+  --(2.879,4.376)--(2.887,4.363)--(2.894,4.353)--(2.902,4.342)--(2.910,4.331)--(2.918,4.318)%
+  --(2.926,4.307)--(2.933,4.297)--(2.941,4.286)--(2.949,4.275)--(2.957,4.262)--(2.965,4.252)%
+  --(2.972,4.241)--(2.980,4.230)--(2.988,4.219)--(2.996,4.208)--(3.004,4.197)--(3.012,4.186)%
+  --(3.019,4.175)--(3.027,4.165)--(3.035,4.154)--(3.043,4.143)--(3.051,4.132)--(3.058,4.123)%
+  --(3.066,4.112)--(3.074,4.101)--(3.082,4.090)--(3.090,4.079)--(3.097,4.070)--(3.105,4.059)%
+  --(3.113,4.048)--(3.121,4.037)--(3.129,4.028)--(3.137,4.017)--(3.144,4.006)--(3.152,3.997)%
+  --(3.160,3.986)--(3.168,3.977)--(3.176,3.966)--(3.183,3.957)--(3.191,3.946)--(3.199,3.936)%
+  --(3.207,3.925)--(3.215,3.916)--(3.222,3.905)--(3.230,3.896)--(3.238,3.885)--(3.246,3.876)%
+  --(3.254,3.866)--(3.261,3.856)--(3.269,3.846)--(3.277,3.837)--(3.285,3.826)--(3.293,3.817)%
+  --(3.301,3.807)--(3.308,3.798)--(3.316,3.787)--(3.324,3.778)--(3.332,3.769)--(3.340,3.759)%
+  --(3.347,3.750)--(3.355,3.741)--(3.363,3.731)--(3.371,3.720)--(3.379,3.711)--(3.386,3.702)%
+  --(3.394,3.692)--(3.402,3.683)--(3.410,3.674)--(3.418,3.665)--(3.426,3.655)--(3.433,3.647)%
+  --(3.441,3.638)--(3.449,3.629)--(3.457,3.620)--(3.465,3.610)--(3.472,3.601)--(3.480,3.592)%
+  --(3.488,3.584)--(3.496,3.574)--(3.504,3.565)--(3.511,3.556)--(3.519,3.547)--(3.527,3.539)%
+  --(3.535,3.529)--(3.543,3.520)--(3.550,3.512)--(3.558,3.503)--(3.566,3.494)--(3.574,3.486)%
+  --(3.582,3.477)--(3.590,3.469)--(3.597,3.460)--(3.605,3.450)--(3.613,3.442)--(3.621,3.433)%
+  --(3.629,3.425)--(3.636,3.416)--(3.644,3.408)--(3.652,3.401)--(3.660,3.391)--(3.668,3.383)%
+  --(3.675,3.374)--(3.683,3.366)--(3.691,3.359)--(3.699,3.349)--(3.707,3.342)--(3.715,3.334)%
+  --(3.722,3.324)--(3.730,3.317)--(3.738,3.309)--(3.746,3.300)--(3.754,3.292)--(3.761,3.284)%
+  --(3.769,3.276)--(3.777,3.269)--(3.785,3.259)--(3.793,3.251)--(3.800,3.244)--(3.808,3.236)%
+  --(3.816,3.228)--(3.824,3.220)--(3.832,3.213)--(3.839,3.205)--(3.847,3.197)--(3.855,3.189)%
+  --(3.863,3.182)--(3.871,3.174)--(3.879,3.166)--(3.886,3.158)--(3.894,3.150)--(3.902,3.143)%
+  --(3.910,3.135)--(3.918,3.127)--(3.925,3.119)--(3.933,3.112)--(3.941,3.104)--(3.949,3.096)%
+  --(3.957,3.088)--(3.964,3.082)--(3.972,3.074)--(3.980,3.067)--(3.988,3.059)--(3.996,3.051)%
+  --(4.004,3.045)--(4.011,3.037)--(4.019,3.029)--(4.027,3.023)--(4.035,3.015)--(4.043,3.008)%
+  --(4.050,3.001)--(4.058,2.994)--(4.066,2.986)--(4.074,2.980)--(4.082,2.972)--(4.089,2.964)%
+  --(4.097,2.958)--(4.105,2.950)--(4.113,2.944)--(4.121,2.936)--(4.128,2.930)--(4.136,2.922)%
+  --(4.144,2.916)--(4.152,2.908)--(4.160,2.902)--(4.168,2.894)--(4.175,2.888)--(4.183,2.880)%
+  --(4.191,2.874)--(4.199,2.866)--(4.207,2.860)--(4.214,2.854)--(4.222,2.846)--(4.230,2.840)%
+  --(4.238,2.834)--(4.246,2.826)--(4.253,2.820)--(4.261,2.813)--(4.269,2.806)--(4.277,2.800)%
+  --(4.285,2.793)--(4.293,2.787)--(4.300,2.779)--(4.308,2.773)--(4.316,2.767)--(4.324,2.761)%
+  --(4.332,2.754)--(4.339,2.747)--(4.347,2.741)--(4.355,2.734)--(4.363,2.728)--(4.371,2.722)%
+  --(4.378,2.716)--(4.386,2.709)--(4.394,2.703)--(4.402,2.695)--(4.410,2.689)--(4.417,2.683)%
+  --(4.425,2.677)--(4.433,2.671)--(4.441,2.664)--(4.449,2.658)--(4.457,2.652)--(4.464,2.646)%
+  --(4.472,2.640)--(4.480,2.633)--(4.488,2.629)--(4.496,2.622)--(4.503,2.616)--(4.511,2.610)%
+  --(4.519,2.604)--(4.527,2.598)--(4.535,2.591)--(4.542,2.585)--(4.550,2.579)--(4.558,2.574)%
+  --(4.566,2.568)--(4.574,2.562)--(4.581,2.556)--(4.589,2.549)--(4.597,2.545)--(4.605,2.539)%
+  --(4.613,2.532)--(4.621,2.526)--(4.628,2.522)--(4.636,2.515)--(4.644,2.509)--(4.652,2.504)%
+  --(4.660,2.498)--(4.667,2.492)--(4.675,2.487)--(4.683,2.481)--(4.691,2.475)--(4.699,2.470)%
+  --(4.706,2.464)--(4.714,2.458)--(4.722,2.453)--(4.730,2.447)--(4.738,2.442)--(4.746,2.436)%
+  --(4.753,2.430)--(4.761,2.425)--(4.769,2.419)--(4.777,2.414)--(4.785,2.408)--(4.792,2.404)%
+  --(4.800,2.397)--(4.808,2.393)--(4.816,2.386)--(4.824,2.382)--(4.831,2.377)--(4.839,2.371)%
+  --(4.847,2.366)--(4.855,2.360)--(4.863,2.355)--(4.870,2.349)--(4.878,2.344)--(4.886,2.340)%
+  --(4.894,2.334)--(4.902,2.329)--(4.910,2.324)--(4.917,2.318)--(4.925,2.313)--(4.933,2.309)%
+  --(4.941,2.303)--(4.949,2.298)--(4.956,2.293)--(4.964,2.289)--(4.972,2.282)--(4.980,2.278)%
+  --(4.988,2.273)--(4.995,2.268)--(5.003,2.262)--(5.011,2.258)--(5.019,2.253)--(5.027,2.248)%
+  --(5.035,2.244)--(5.042,2.237)--(5.050,2.233)--(5.058,2.228)--(5.066,2.223)--(5.074,2.219)%
+  --(5.081,2.214)--(5.089,2.209)--(5.097,2.203)--(5.105,2.199)--(5.113,2.194)--(5.120,2.189)%
+  --(5.128,2.185)--(5.136,2.180)--(5.144,2.175)--(5.152,2.171)--(5.159,2.166)--(5.167,2.161)%
+  --(5.175,2.157)--(5.183,2.152)--(5.191,2.147)--(5.199,2.143)--(5.206,2.138)--(5.214,2.133)%
+  --(5.222,2.129)--(5.230,2.124)--(5.238,2.119)--(5.245,2.115)--(5.253,2.110)--(5.261,2.105)%
+  --(5.269,2.101)--(5.277,2.096)--(5.284,2.093)--(5.292,2.088)--(5.300,2.084)--(5.308,2.079)%
+  --(5.316,2.074)--(5.324,2.070)--(5.331,2.065)--(5.339,2.062)--(5.347,2.057)--(5.355,2.053)%
+  --(5.363,2.048)--(5.370,2.043)--(5.378,2.040)--(5.386,2.035)--(5.394,2.031)--(5.402,2.026)%
+  --(5.409,2.023)--(5.417,2.018)--(5.425,2.014)--(5.433,2.009)--(5.441,2.006)--(5.448,2.001)%
+  --(5.456,1.997)--(5.464,1.994)--(5.472,1.989)--(5.480,1.984)--(5.488,1.980)--(5.495,1.976)%
+  --(5.503,1.972)--(5.511,1.969)--(5.519,1.964)--(5.527,1.959)--(5.534,1.956)--(5.542,1.952)%
+  --(5.550,1.947)--(5.558,1.944)--(5.566,1.939)--(5.573,1.936)--(5.581,1.931)--(5.589,1.927)%
+  --(5.597,1.924)--(5.605,1.919)--(5.613,1.916)--(5.620,1.911)--(5.628,1.908)--(5.636,1.903)%
+  --(5.644,1.900)--(5.652,1.896)--(5.659,1.893)--(5.667,1.888)--(5.675,1.885)--(5.683,1.880)%
+  --(5.691,1.877)--(5.698,1.872)--(5.706,1.869)--(5.714,1.865)--(5.722,1.862)--(5.730,1.858)%
+  --(5.737,1.854)--(5.745,1.851)--(5.753,1.846)--(5.761,1.843)--(5.769,1.840)--(5.777,1.835)%
+  --(5.784,1.832)--(5.792,1.827)--(5.800,1.824)--(5.808,1.821)--(5.816,1.816)--(5.823,1.813)%
+  --(5.831,1.810)--(5.839,1.806)--(5.847,1.802)--(5.855,1.799)--(5.862,1.795)--(5.870,1.792)%
+  --(5.878,1.789)--(5.886,1.785)--(5.894,1.781)--(5.902,1.778)--(5.909,1.775)--(5.917,1.770)%
+  --(5.925,1.767)--(5.933,1.764)--(5.941,1.761)--(5.948,1.756)--(5.956,1.753)--(5.964,1.750)%
+  --(5.972,1.747)--(5.980,1.743)--(5.987,1.739)--(5.995,1.736)--(6.003,1.733)--(6.011,1.730)%
+  --(6.019,1.726)--(6.026,1.723)--(6.034,1.719)--(6.042,1.716)--(6.050,1.712)--(6.058,1.709)%
+  --(6.066,1.706)--(6.073,1.703)--(6.081,1.700)--(6.089,1.695)--(6.097,1.692)--(6.105,1.689)%
+  --(6.112,1.686)--(6.120,1.683)--(6.128,1.680)--(6.136,1.677)--(6.144,1.674)--(6.151,1.670)%
+  --(6.159,1.667)--(6.167,1.664)--(6.175,1.661)--(6.183,1.658)--(6.191,1.655)--(6.198,1.650)%
+  --(6.206,1.647)--(6.214,1.644)--(6.222,1.641)--(6.230,1.638)--(6.237,1.635)--(6.245,1.632)%
+  --(6.253,1.629)--(6.261,1.625)--(6.269,1.624)--(6.276,1.621)--(6.284,1.618)--(6.292,1.615)%
+  --(6.300,1.611)--(6.308,1.608)--(6.315,1.605)--(6.323,1.602)--(6.331,1.599)--(6.339,1.596)%
+  --(6.347,1.593)--(6.355,1.590)--(6.362,1.587)--(6.370,1.584)--(6.378,1.582)--(6.386,1.579)%
+  --(6.394,1.576)--(6.401,1.573)--(6.409,1.570)--(6.417,1.566)--(6.425,1.563)--(6.433,1.560)%
+  --(6.440,1.559)--(6.448,1.556)--(6.456,1.552)--(6.464,1.549)--(6.472,1.546)--(6.480,1.545)%
+  --(6.487,1.542)--(6.495,1.538)--(6.503,1.535)--(6.511,1.532)--(6.519,1.531)--(6.526,1.528)%
+  --(6.534,1.525)--(6.542,1.521)--(6.550,1.518)--(6.558,1.517)--(6.565,1.514)--(6.573,1.511)%
+  --(6.581,1.507)--(6.589,1.506)--(6.597,1.503)--(6.604,1.500)--(6.612,1.497)--(6.620,1.495)%
+  --(6.628,1.492)--(6.636,1.489)--(6.644,1.487)--(6.651,1.484)--(6.659,1.481)--(6.667,1.479)%
+  --(6.675,1.476)--(6.683,1.473)--(6.690,1.470)--(6.698,1.469)--(6.706,1.465)--(6.714,1.464)%
+  --(6.722,1.461)--(6.729,1.458)--(6.737,1.456)--(6.745,1.453)--(6.753,1.450)--(6.761,1.448)%
+  --(6.768,1.445)--(6.776,1.442)--(6.784,1.441)--(6.792,1.438)--(6.800,1.436)--(6.808,1.433)%
+  --(6.815,1.430)--(6.823,1.428)--(6.831,1.425)--(6.839,1.424)--(6.847,1.420)--(6.854,1.419)%
+  --(6.862,1.416)--(6.870,1.413)--(6.878,1.411)--(6.886,1.408)--(6.893,1.406)--(6.901,1.403)%
+  --(6.909,1.402)--(6.917,1.399)--(6.925,1.397)--(6.933,1.394)--(6.940,1.393)--(6.948,1.389)%
+  --(6.956,1.388)--(6.964,1.385)--(6.972,1.383)--(6.979,1.380)--(6.987,1.379)--(6.995,1.375)%
+  --(7.003,1.374)--(7.011,1.371)--(7.018,1.369)--(7.026,1.366)--(7.034,1.365)--(7.042,1.361)%
+  --(7.050,1.360)--(7.057,1.357)--(7.065,1.355)--(7.073,1.352)--(7.081,1.351)--(7.089,1.349)%
+  --(7.097,1.346)--(7.104,1.344)--(7.112,1.341)--(7.120,1.340)--(7.128,1.337)--(7.136,1.335)%
+  --(7.143,1.333)--(7.151,1.330)--(7.159,1.329)--(7.167,1.326)--(7.175,1.324)--(7.182,1.323)%
+  --(7.190,1.320)--(7.198,1.318)--(7.206,1.316)--(7.214,1.313)--(7.222,1.312)--(7.229,1.309)%
+  --(7.237,1.307)--(7.245,1.306)--(7.253,1.302)--(7.261,1.301)--(7.268,1.299)--(7.276,1.296)%
+  --(7.284,1.295)--(7.292,1.293)--(7.300,1.290)--(7.307,1.288)--(7.315,1.287)--(7.323,1.285)%
+  --(7.331,1.282)--(7.339,1.281)--(7.346,1.279)--(7.354,1.276)--(7.362,1.274)--(7.370,1.273)%
+  --(7.378,1.270)--(7.386,1.268)--(7.393,1.267)--(7.401,1.265)--(7.409,1.262)--(7.417,1.260)%
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+  --(3.019,4.180)--(3.027,4.169)--(3.035,4.158)--(3.043,4.148)--(3.051,4.137)--(3.058,4.126)%
+  --(3.066,4.115)--(3.074,4.106)--(3.082,4.095)--(3.090,4.084)--(3.097,4.073)--(3.105,4.064)%
+  --(3.113,4.053)--(3.121,4.042)--(3.129,4.031)--(3.137,4.022)--(3.144,4.011)--(3.152,4.002)%
+  --(3.160,3.991)--(3.168,3.980)--(3.176,3.970)--(3.183,3.960)--(3.191,3.950)--(3.199,3.939)%
+  --(3.207,3.930)--(3.215,3.919)--(3.222,3.910)--(3.230,3.901)--(3.238,3.890)--(3.246,3.880)%
+  --(3.254,3.870)--(3.261,3.860)--(3.269,3.851)--(3.277,3.840)--(3.285,3.831)--(3.293,3.821)%
+  --(3.301,3.812)--(3.308,3.801)--(3.316,3.792)--(3.324,3.783)--(3.332,3.773)--(3.340,3.764)%
+  --(3.347,3.755)--(3.355,3.744)--(3.363,3.734)--(3.371,3.725)--(3.379,3.716)--(3.386,3.706)%
+  --(3.394,3.697)--(3.402,3.688)--(3.410,3.679)--(3.418,3.669)--(3.426,3.660)--(3.433,3.651)%
+  --(3.441,3.641)--(3.449,3.633)--(3.457,3.624)--(3.465,3.615)--(3.472,3.606)--(3.480,3.596)%
+  --(3.488,3.587)--(3.496,3.579)--(3.504,3.570)--(3.511,3.560)--(3.519,3.551)--(3.527,3.543)%
+  --(3.535,3.534)--(3.543,3.525)--(3.550,3.515)--(3.558,3.508)--(3.566,3.498)--(3.574,3.491)%
+  --(3.582,3.481)--(3.590,3.472)--(3.597,3.464)--(3.605,3.455)--(3.613,3.447)--(3.621,3.438)%
+  --(3.629,3.430)--(3.636,3.421)--(3.644,3.413)--(3.652,3.404)--(3.660,3.396)--(3.668,3.387)%
+  --(3.675,3.379)--(3.683,3.371)--(3.691,3.362)--(3.699,3.354)--(3.707,3.346)--(3.715,3.337)%
+  --(3.722,3.329)--(3.730,3.321)--(3.738,3.312)--(3.746,3.304)--(3.754,3.296)--(3.761,3.289)%
+  --(3.769,3.281)--(3.777,3.272)--(3.785,3.264)--(3.793,3.256)--(3.800,3.248)--(3.808,3.241)%
+  --(3.816,3.233)--(3.824,3.225)--(3.832,3.216)--(3.839,3.208)--(3.847,3.200)--(3.855,3.192)%
+  --(3.863,3.185)--(3.871,3.177)--(3.879,3.169)--(3.886,3.161)--(3.894,3.154)--(3.902,3.146)%
+  --(3.910,3.138)--(3.918,3.132)--(3.925,3.124)--(3.933,3.116)--(3.941,3.109)--(3.949,3.101)%
+  --(3.957,3.093)--(3.964,3.085)--(3.972,3.079)--(3.980,3.071)--(3.988,3.064)--(3.996,3.056)%
+  --(4.004,3.048)--(4.011,3.042)--(4.019,3.034)--(4.027,3.026)--(4.035,3.020)--(4.043,3.012)%
+  --(4.050,3.005)--(4.058,2.998)--(4.066,2.991)--(4.074,2.983)--(4.082,2.977)--(4.089,2.969)%
+  --(4.097,2.963)--(4.105,2.955)--(4.113,2.947)--(4.121,2.941)--(4.128,2.933)--(4.136,2.927)%
+  --(4.144,2.919)--(4.152,2.913)--(4.160,2.905)--(4.168,2.899)--(4.175,2.891)--(4.183,2.885)%
+  --(4.191,2.879)--(4.199,2.871)--(4.207,2.865)--(4.214,2.857)--(4.222,2.851)--(4.230,2.845)%
+  --(4.238,2.837)--(4.246,2.831)--(4.253,2.824)--(4.261,2.817)--(4.269,2.810)--(4.277,2.804)%
+  --(4.285,2.798)--(4.293,2.790)--(4.300,2.784)--(4.308,2.778)--(4.316,2.772)--(4.324,2.764)%
+  --(4.332,2.758)--(4.339,2.751)--(4.347,2.745)--(4.355,2.739)--(4.363,2.733)--(4.371,2.727)%
+  --(4.378,2.719)--(4.386,2.713)--(4.394,2.706)--(4.402,2.700)--(4.410,2.694)--(4.417,2.688)%
+  --(4.425,2.681)--(4.433,2.675)--(4.441,2.669)--(4.449,2.663)--(4.457,2.657)--(4.464,2.650)%
+  --(4.472,2.644)--(4.480,2.638)--(4.488,2.632)--(4.496,2.626)--(4.503,2.619)--(4.511,2.613)%
+  --(4.519,2.608)--(4.527,2.602)--(4.535,2.596)--(4.542,2.590)--(4.550,2.584)--(4.558,2.577)%
+  --(4.566,2.571)--(4.574,2.567)--(4.581,2.560)--(4.589,2.554)--(4.597,2.548)--(4.605,2.542)%
+  --(4.613,2.537)--(4.621,2.531)--(4.628,2.525)--(4.636,2.520)--(4.644,2.514)--(4.652,2.508)%
+  --(4.660,2.501)--(4.667,2.497)--(4.675,2.490)--(4.683,2.484)--(4.691,2.480)--(4.699,2.473)%
+  --(4.706,2.469)--(4.714,2.463)--(4.722,2.456)--(4.730,2.452)--(4.738,2.445)--(4.746,2.441)%
+  --(4.753,2.435)--(4.761,2.430)--(4.769,2.424)--(4.777,2.417)--(4.785,2.413)--(4.792,2.407)%
+  --(4.800,2.402)--(4.808,2.396)--(4.816,2.391)--(4.824,2.386)--(4.831,2.380)--(4.839,2.376)%
+  --(4.847,2.369)--(4.855,2.365)--(4.863,2.358)--(4.870,2.354)--(4.878,2.349)--(4.886,2.343)%
+  --(4.894,2.338)--(4.902,2.334)--(4.910,2.327)--(4.917,2.323)--(4.925,2.318)--(4.933,2.312)%
+  --(4.941,2.307)--(4.949,2.303)--(4.956,2.296)--(4.964,2.292)--(4.972,2.287)--(4.980,2.282)%
+  --(4.988,2.276)--(4.995,2.271)--(5.003,2.267)--(5.011,2.262)--(5.019,2.256)--(5.027,2.251)%
+  --(5.035,2.247)--(5.042,2.242)--(5.050,2.237)--(5.058,2.233)--(5.066,2.226)--(5.074,2.222)%
+  --(5.081,2.217)--(5.089,2.212)--(5.097,2.208)--(5.105,2.203)--(5.113,2.199)--(5.120,2.194)%
+  --(5.128,2.189)--(5.136,2.183)--(5.144,2.178)--(5.152,2.174)--(5.159,2.169)--(5.167,2.164)%
+  --(5.175,2.160)--(5.183,2.155)--(5.191,2.150)--(5.199,2.146)--(5.206,2.141)--(5.214,2.136)%
+  --(5.222,2.132)--(5.230,2.127)--(5.238,2.122)--(5.245,2.119)--(5.253,2.115)--(5.261,2.110)%
+  --(5.269,2.105)--(5.277,2.101)--(5.284,2.096)--(5.292,2.091)--(5.300,2.087)--(5.308,2.082)%
+  --(5.316,2.079)--(5.324,2.074)--(5.331,2.070)--(5.339,2.065)--(5.347,2.060)--(5.355,2.056)%
+  --(5.363,2.053)--(5.370,2.048)--(5.378,2.043)--(5.386,2.039)--(5.394,2.034)--(5.402,2.031)%
+  --(5.409,2.026)--(5.417,2.021)--(5.425,2.017)--(5.433,2.014)--(5.441,2.009)--(5.448,2.004)%
+  --(5.456,2.001)--(5.464,1.997)--(5.472,1.992)--(5.480,1.987)--(5.488,1.984)--(5.495,1.980)%
+  --(5.503,1.975)--(5.511,1.972)--(5.519,1.967)--(5.527,1.964)--(5.534,1.959)--(5.542,1.955)%
+  --(5.550,1.952)--(5.558,1.947)--(5.566,1.944)--(5.573,1.939)--(5.581,1.934)--(5.589,1.931)%
+  --(5.597,1.927)--(5.605,1.924)--(5.613,1.919)--(5.620,1.916)--(5.628,1.911)--(5.636,1.908)%
+  --(5.644,1.903)--(5.652,1.899)--(5.659,1.896)--(5.667,1.893)--(5.675,1.888)--(5.683,1.885)%
+  --(5.691,1.880)--(5.698,1.877)--(5.706,1.872)--(5.714,1.869)--(5.722,1.865)--(5.730,1.862)%
+  --(5.737,1.857)--(5.745,1.854)--(5.753,1.851)--(5.761,1.846)--(5.769,1.843)--(5.777,1.838)%
+  --(5.784,1.835)--(5.792,1.832)--(5.800,1.827)--(5.808,1.824)--(5.816,1.821)--(5.823,1.816)%
+  --(5.831,1.813)--(5.839,1.810)--(5.847,1.806)--(5.855,1.802)--(5.862,1.799)--(5.870,1.795)%
+  --(5.878,1.792)--(5.886,1.789)--(5.894,1.784)--(5.902,1.781)--(5.909,1.778)--(5.917,1.775)%
+  --(5.925,1.770)--(5.933,1.767)--(5.941,1.764)--(5.948,1.761)--(5.956,1.756)--(5.964,1.753)%
+  --(5.972,1.750)--(5.980,1.747)--(5.987,1.743)--(5.995,1.739)--(6.003,1.736)--(6.011,1.733)%
+  --(6.019,1.730)--(6.026,1.726)--(6.034,1.722)--(6.042,1.719)--(6.050,1.716)--(6.058,1.712)%
+  --(6.066,1.709)--(6.073,1.706)--(6.081,1.703)--(6.089,1.698)--(6.097,1.695)--(6.105,1.692)%
+  --(6.112,1.689)--(6.120,1.686)--(6.128,1.683)--(6.136,1.680)--(6.144,1.677)--(6.151,1.674)%
+  --(6.159,1.670)--(6.167,1.667)--(6.175,1.664)--(6.183,1.661)--(6.191,1.658)--(6.198,1.655)%
+  --(6.206,1.652)--(6.214,1.647)--(6.222,1.644)--(6.230,1.641)--(6.237,1.638)--(6.245,1.635)%
+  --(6.253,1.632)--(6.261,1.630)--(6.269,1.627)--(6.276,1.624)--(6.284,1.621)--(6.292,1.618)%
+  --(6.300,1.615)--(6.308,1.611)--(6.315,1.608)--(6.323,1.605)--(6.331,1.602)--(6.339,1.599)%
+  --(6.347,1.596)--(6.355,1.593)--(6.362,1.590)--(6.370,1.587)--(6.378,1.585)--(6.386,1.582)%
+  --(6.394,1.579)--(6.401,1.576)--(6.409,1.573)--(6.417,1.570)--(6.425,1.566)--(6.433,1.563)%
+  --(6.440,1.562)--(6.448,1.559)--(6.456,1.556)--(6.464,1.552)--(6.472,1.549)--(6.480,1.546)%
+  --(6.487,1.545)--(6.495,1.542)--(6.503,1.538)--(6.511,1.535)--(6.519,1.532)--(6.526,1.531)%
+  --(6.534,1.528)--(6.542,1.525)--(6.550,1.521)--(6.558,1.520)--(6.565,1.517)--(6.573,1.514)%
+  --(6.581,1.511)--(6.589,1.509)--(6.597,1.506)--(6.604,1.503)--(6.612,1.500)--(6.620,1.498)%
+  --(6.628,1.495)--(6.636,1.492)--(6.644,1.489)--(6.651,1.487)--(6.659,1.484)--(6.667,1.481)%
+  --(6.675,1.479)--(6.683,1.476)--(6.690,1.473)--(6.698,1.472)--(6.706,1.469)--(6.714,1.465)%
+  --(6.722,1.464)--(6.729,1.461)--(6.737,1.458)--(6.745,1.456)--(6.753,1.453)--(6.761,1.450)%
+  --(6.768,1.448)--(6.776,1.445)--(6.784,1.444)--(6.792,1.441)--(6.800,1.438)--(6.808,1.436)%
+  --(6.815,1.433)--(6.823,1.431)--(6.831,1.428)--(6.839,1.425)--(6.847,1.424)--(6.854,1.420)%
+  --(6.862,1.419)--(6.870,1.416)--(6.878,1.414)--(6.886,1.411)--(6.893,1.408)--(6.901,1.406)%
+  --(6.909,1.403)--(6.917,1.402)--(6.925,1.399)--(6.933,1.397)--(6.940,1.394)--(6.948,1.393)%
+  --(6.956,1.389)--(6.964,1.388)--(6.972,1.385)--(6.979,1.383)--(6.987,1.380)--(6.995,1.379)%
+  --(7.003,1.375)--(7.011,1.374)--(7.018,1.371)--(7.026,1.369)--(7.034,1.366)--(7.042,1.365)%
+  --(7.050,1.361)--(7.057,1.360)--(7.065,1.358)--(7.073,1.355)--(7.081,1.354)--(7.089,1.351)%
+  --(7.097,1.349)--(7.104,1.346)--(7.112,1.344)--(7.120,1.343)--(7.128,1.340)--(7.136,1.338)%
+  --(7.143,1.335)--(7.151,1.333)--(7.159,1.332)--(7.167,1.329)--(7.175,1.327)--(7.182,1.324)%
+  --(7.190,1.323)--(7.198,1.321)--(7.206,1.318)--(7.214,1.316)--(7.222,1.313)--(7.229,1.312)%
+  --(7.237,1.310)--(7.245,1.307)--(7.253,1.306)--(7.261,1.304)--(7.268,1.301)--(7.276,1.299)%
+  --(7.284,1.298)--(7.292,1.295)--(7.300,1.293)--(7.307,1.292)--(7.315,1.288)--(7.323,1.287)%
+  --(7.331,1.285)--(7.339,1.284)--(7.346,1.281)--(7.354,1.279)--(7.362,1.278)--(7.370,1.274)%
+  --(7.378,1.273)--(7.386,1.271)--(7.393,1.268)--(7.401,1.267)--(7.409,1.265)--(7.417,1.264)%
+  --(7.425,1.260)--(7.432,1.259)--(7.440,1.257)--(7.448,1.256)--(7.456,1.253)--(7.464,1.251)%
+  --(7.471,1.250)--(7.479,1.248)--(7.487,1.245)--(7.495,1.243)--(7.503,1.242)--(7.511,1.240)%
+  --(7.518,1.239)--(7.526,1.236)--(7.534,1.234)--(7.542,1.233)--(7.550,1.231)--(7.557,1.229)%
+  --(7.565,1.226)--(7.573,1.225)--(7.581,1.223)--(7.589,1.222)--(7.596,1.220)--(7.604,1.217)%
+  --(7.612,1.215)--(7.620,1.214)--(7.628,1.212)--(7.635,1.211)--(7.643,1.209)--(7.651,1.206)%
+  --(7.659,1.205)--(7.667,1.203)--(7.675,1.201)--(7.682,1.200)--(7.690,1.198)--(7.698,1.197)%
+  --(7.706,1.194)--(7.714,1.192)--(7.721,1.191)--(7.729,1.189)--(7.737,1.188)--(7.745,1.186)%
+  --(7.753,1.184)--(7.760,1.183)--(7.768,1.181)--(7.776,1.178)--(7.784,1.177)--(7.792,1.175)%
+  --(7.800,1.174)--(7.807,1.172)--(7.815,1.170)--(7.823,1.169)--(7.831,1.167)--(7.839,1.166)%
+  --(7.846,1.164)--(7.854,1.163)--(7.862,1.161)--(7.870,1.160)--(7.878,1.156)--(7.885,1.155)%
+  --(7.893,1.153)--(7.901,1.152)--(7.909,1.150)--(7.917,1.149)--(7.924,1.147)--(7.932,1.146)%
+  --(7.940,1.144)--(7.948,1.142)--(7.956,1.141)--(7.964,1.139)--(7.971,1.138)--(7.979,1.136)%
+  --(7.987,1.135)--(7.995,1.133)--(8.003,1.132)--(8.010,1.130)--(8.018,1.128)--(8.026,1.127)%
+  --(8.034,1.125)--(8.042,1.124)--(8.049,1.122)--(8.057,1.121)--(8.065,1.119)--(8.073,1.118)%
+  --(8.081,1.116)--(8.089,1.115)--(8.096,1.113)--(8.104,1.111)--(8.112,1.110)--(8.120,1.108)%
+  --(8.128,1.107)--(8.135,1.105)--(8.143,1.104)--(8.151,1.102)--(8.159,1.101)--(8.167,1.101)%
+  --(8.174,1.099)--(8.182,1.097)--(8.190,1.096)--(8.198,1.094)--(8.206,1.093)--(8.213,1.091)%
+  --(8.221,1.090)--(8.229,1.088)--(8.237,1.087)--(8.245,1.085)--(8.253,1.083)--(8.260,1.082)%
+  --(8.268,1.080)--(8.276,1.080)--(8.284,1.079)--(8.292,1.077)--(8.299,1.076)--(8.307,1.074)%
+  --(8.315,1.073)--(8.323,1.071)--(8.331,1.069)--(8.338,1.068)--(8.346,1.068)--(8.354,1.066)%
+  --(8.362,1.065)--(8.370,1.063)--(8.378,1.062)--(8.385,1.060)--(8.393,1.059)--(8.401,1.057)%
+  --(8.409,1.057)--(8.417,1.055)--(8.424,1.054)--(8.432,1.052)--(8.440,1.051)--(8.448,1.049)%
+  --(8.456,1.048)--(8.463,1.048)--(8.471,1.046)--(8.479,1.045)--(8.487,1.043)--(8.495,1.042)%
+  --(8.502,1.040)--(8.510,1.040)--(8.518,1.038)--(8.526,1.037)--(8.534,1.035)--(8.542,1.034)%
+  --(8.549,1.034)--(8.557,1.032)--(8.565,1.031)--(8.573,1.029)--(8.581,1.028)--(8.588,1.026)%
+  --(8.596,1.026)--(8.604,1.024)--(8.612,1.023)--(8.620,1.021)--(8.627,1.021)--(8.635,1.020)%
+  --(8.643,1.018)--(8.651,1.017)--(8.659,1.015)--(8.667,1.015)--(8.674,1.014)--(8.682,1.012)%
+  --(8.690,1.010)--(8.698,1.010)--(8.706,1.009)--(8.713,1.007)--(8.721,1.006)--(8.729,1.004)%
+  --(8.737,1.004)--(8.745,1.003)--(8.752,1.001)--(8.760,1.000)--(8.768,1.000)--(8.776,0.998)%
+  --(8.784,0.996)--(8.791,0.995)--(8.799,0.995)--(8.807,0.993)--(8.815,0.992)--(8.823,0.992)%
+  --(8.831,0.990)--(8.838,0.989)--(8.846,0.987)--(8.854,0.987)--(8.862,0.986)--(8.870,0.984)%
+  --(8.877,0.983)--(8.885,0.983)--(8.893,0.981)--(8.901,0.979)--(8.909,0.979)--(8.916,0.978)%
+  --(8.924,0.976)--(8.932,0.975)--(8.940,0.975)--(8.948,0.973)--(8.955,0.972)--(8.963,0.972)%
+  --(8.971,0.970)--(8.979,0.969)--(8.987,0.969)--(8.995,0.967)--(9.002,0.965)--(9.010,0.965)%
+  --(9.018,0.964)--(9.026,0.962)--(9.034,0.962)--(9.041,0.961)--(9.049,0.959)--(9.057,0.959)%
+  --(9.065,0.958)--(9.073,0.956)--(9.080,0.956)--(9.088,0.955)--(9.096,0.953)--(9.104,0.953)%
+  --(9.112,0.951)--(9.120,0.950)--(9.127,0.950)--(9.135,0.948)--(9.143,0.947)--(9.151,0.947)%
+  --(9.159,0.945)--(9.166,0.944)--(9.174,0.944)--(9.182,0.942)--(9.190,0.941)--(9.198,0.941)%
+  --(9.205,0.939)--(9.213,0.939)--(9.221,0.937)--(9.229,0.936)--(9.237,0.936)--(9.244,0.934)%
+  --(9.252,0.933)--(9.260,0.933)--(9.268,0.931)--(9.276,0.931)--(9.284,0.930)--(9.291,0.928)%
+  --(9.299,0.928)--(9.307,0.927)--(9.315,0.927)--(9.323,0.925)--(9.330,0.923)--(9.338,0.923)%
+  --(9.346,0.922)--(9.354,0.922)--(9.362,0.920)--(9.369,0.919)--(9.377,0.919)--(9.385,0.917)%
+  --(9.393,0.917)--(9.401,0.916)--(9.409,0.914)--(9.416,0.914)--(9.424,0.913)--(9.432,0.913)%
+  --(9.440,0.911)--(9.448,0.911)--(9.455,0.910)--(9.463,0.908)--(9.471,0.908)--(9.479,0.906)%
+  --(9.487,0.906)--(9.494,0.905)--(9.502,0.905)--(9.510,0.903)--(9.518,0.902)--(9.526,0.902)%
+  --(9.533,0.900)--(9.541,0.900)--(9.549,0.899)--(9.557,0.899)--(9.565,0.897)--(9.573,0.897)%
+  --(9.580,0.896)--(9.588,0.894)--(9.596,0.894)--(9.604,0.892)--(9.612,0.892)--(9.619,0.891)%
+  --(9.627,0.891)--(9.635,0.889)--(9.643,0.889)--(9.651,0.888)--(9.658,0.888)--(9.666,0.886)%
+  --(9.674,0.886)--(9.682,0.885)--(9.690,0.885)--(9.698,0.883)--(9.705,0.882)--(9.713,0.882)%
+  --(9.721,0.880)--(9.729,0.880)--(9.737,0.878)--(9.744,0.878)--(9.752,0.877)--(9.760,0.877)%
+  --(9.768,0.875)--(9.776,0.875)--(9.783,0.874)--(9.791,0.874)--(9.799,0.872)--(9.807,0.872)%
+  --(9.815,0.871)--(9.822,0.871)--(9.830,0.869)--(9.838,0.869)--(9.846,0.868)--(9.854,0.868)%
+  --(9.862,0.866)--(9.869,0.866)--(9.877,0.864)--(9.885,0.864)--(9.893,0.863)--(9.901,0.863)%
+  --(9.908,0.861)--(9.916,0.861)--(9.924,0.861)--(9.932,0.860)--(9.940,0.860)--(9.947,0.858)%
+  --(9.955,0.858)--(9.963,0.857)--(9.971,0.857)--(9.979,0.855)--(9.987,0.855)--(9.994,0.854)%
+  --(10.002,0.854)--(10.010,0.852)--(10.018,0.852)--(10.026,0.851)--(10.033,0.851)--(10.041,0.851)%
+  --(10.049,0.849)--(10.057,0.849)--(10.065,0.847)--(10.072,0.847)--(10.080,0.846)--(10.088,0.846)%
+  --(10.096,0.844)--(10.104,0.844)--(10.111,0.843)--(10.119,0.843)--(10.127,0.843)--(10.135,0.841)%
+  --(10.143,0.841)--(10.151,0.840)--(10.158,0.840)--(10.166,0.838)--(10.174,0.838)--(10.182,0.838)%
+  --(10.190,0.837)--(10.197,0.837)--(10.205,0.835)--(10.213,0.835)--(10.221,0.833)--(10.229,0.833)%
+  --(10.236,0.833)--(10.244,0.832)--(10.252,0.832)--(10.260,0.830)--(10.268,0.830)--(10.276,0.829)%
+  --(10.283,0.829)--(10.291,0.829)--(10.299,0.827)--(10.307,0.827)--(10.315,0.826)--(10.322,0.826)%
+  --(10.330,0.826)--(10.338,0.824)--(10.346,0.824)--(10.354,0.823)--(10.361,0.823)--(10.369,0.823)%
+  --(10.377,0.821)--(10.385,0.821)--(10.393,0.819)--(10.400,0.819)--(10.408,0.819)--(10.416,0.818)%
+  --(10.424,0.818)--(10.432,0.816)--(10.440,0.816)--(10.447,0.816)--(10.455,0.815)--(10.463,0.815)%
+  --(10.471,0.813)--(10.479,0.813)--(10.486,0.813)--(10.494,0.812)--(10.502,0.812)--(10.510,0.812)%
+  --(10.518,0.810)--(10.525,0.810)--(10.533,0.809)--(10.541,0.809)--(10.549,0.809)--(10.557,0.807)%
+  --(10.565,0.807)--(10.572,0.805)--(10.580,0.805)--(10.588,0.805)--(10.596,0.804)--(10.604,0.804)%
+  --(10.611,0.804)--(10.619,0.802)--(10.627,0.802)--(10.635,0.802)--(10.643,0.801)--(10.650,0.801)%
+  --(10.658,0.799)--(10.666,0.799)--(10.674,0.799)--(10.682,0.798)--(10.689,0.798)--(10.697,0.798)%
+  --(10.705,0.796)--(10.713,0.796)--(10.721,0.796)--(10.729,0.795)--(10.736,0.795)--(10.744,0.795)%
+  --(10.752,0.793)--(10.760,0.793)--(10.768,0.793)--(10.775,0.791)--(10.783,0.791)--(10.791,0.791)%
+  --(10.799,0.790)--(10.807,0.790)--(10.814,0.790)--(10.822,0.788)--(10.830,0.788)--(10.838,0.788)%
+  --(10.846,0.787)--(10.854,0.787)--(10.861,0.787)--(10.869,0.785)--(10.877,0.785)--(10.885,0.785)%
+  --(10.893,0.784)--(10.900,0.784)--(10.908,0.784)--(10.916,0.782)--(10.924,0.782)--(10.932,0.782)%
+  --(10.939,0.781)--(10.947,0.781)--(10.955,0.781)--(10.963,0.779)--(10.971,0.779)--(10.978,0.779)%
+  --(10.986,0.778)--(10.994,0.778)--(11.002,0.778)--(11.010,0.776)--(11.018,0.776)--(11.025,0.776)%
+  --(11.033,0.774)--(11.041,0.774)--(11.049,0.774)--(11.057,0.774)--(11.064,0.773)--(11.072,0.773)%
+  --(11.080,0.773)--(11.088,0.771)--(11.096,0.771)--(11.103,0.771)--(11.111,0.770)--(11.119,0.770)%
+  --(11.127,0.770)--(11.135,0.768)--(11.142,0.768)--(11.150,0.768)--(11.158,0.768)--(11.166,0.767)%
+  --(11.174,0.767)--(11.182,0.767)--(11.189,0.765)--(11.197,0.765)--(11.205,0.765)--(11.213,0.765)%
+  --(11.221,0.764)--(11.228,0.764)--(11.236,0.764)--(11.244,0.762)--(11.252,0.762)--(11.260,0.762)%
+  --(11.267,0.762)--(11.275,0.760)--(11.283,0.760)--(11.291,0.760)--(11.299,0.759)--(11.307,0.759)%
+  --(11.314,0.759)--(11.322,0.759)--(11.330,0.757)--(11.338,0.757)--(11.346,0.757);
+\gpcolor{color=gp lt color border}
+\draw[gp path] (1.012,8.381)--(1.012,0.616)--(11.947,0.616)--(11.947,8.381)--cycle;
+%% coordinates of the plot area
+\gpdefrectangularnode{gp plot 1}{\pgfpoint{1.012cm}{0.616cm}}{\pgfpoint{11.947cm}{8.381cm}}
+\end{tikzpicture}
+%% gnuplot variables
diff --git a/20201217/logo-hochschule-bochum-cvh-text-v2.pdf b/20201217/logo-hochschule-bochum-cvh-text-v2.pdf
new file mode 120000
index 0000000..4aa99b8
--- /dev/null
+++ b/20201217/logo-hochschule-bochum-cvh-text-v2.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum-cvh-text-v2.pdf
\ No newline at end of file
diff --git a/20201217/logo-hochschule-bochum.pdf b/20201217/logo-hochschule-bochum.pdf
new file mode 120000
index 0000000..b6b9491
--- /dev/null
+++ b/20201217/logo-hochschule-bochum.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum.pdf
\ No newline at end of file
diff --git a/20201217/pendulum.pdf b/20201217/pendulum.pdf
new file mode 120000
index 0000000..7d1d873
--- /dev/null
+++ b/20201217/pendulum.pdf
@@ -0,0 +1 @@
+../common/pendulum.pdf
\ No newline at end of file
diff --git a/20201217/pgscript.sty b/20201217/pgscript.sty
new file mode 120000
index 0000000..95c8884
--- /dev/null
+++ b/20201217/pgscript.sty
@@ -0,0 +1 @@
+../common/pgscript.sty
\ No newline at end of file
diff --git a/20201217/pgslides.sty b/20201217/pgslides.sty
new file mode 120000
index 0000000..5be1416
--- /dev/null
+++ b/20201217/pgslides.sty
@@ -0,0 +1 @@
+../common/pgslides.sty
\ No newline at end of file
diff --git a/README.md b/README.md
index 4995d1b..7a96786 100644
--- a/README.md
+++ b/README.md
@@ -22,7 +22,8 @@ Vortragsfolien und Beispiele:
  * [19.11.2020: Einführung in C: Zeiger, Arrays und Strings](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201119/hp-20201119.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master/20201119/)
  * [26.11.2020: Einführung in C: Arrays und Strings und Zeichen, Strukturen, Dateien und Fehlerbehandlung](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201126/hp-20201126.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master/20201126/)
  * [03.12.2020: Parameter des Hauptprogramms, String-Operationen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201203/hp-20201203.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master/20201203/)
- * [10.12.2020: Parameter des Hauptprogramms, String-Operationen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201210/hp-20201210.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master/20201210/)
+ * [10.12.2020: Präprozessor, Bibliotheken einbinden und verwenden](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201210/hp-20201210.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master/20201210/)
+ * [17.12.2020: make, Differentialgleichungen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201217/hp-20201217.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master/20201217/)
  * [alle in 1 Datei](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/hp-slides-2020ws.pdf)
 
 Übungsaufgaben:
@@ -33,6 +34,7 @@ Vortragsfolien und Beispiele:
  * [26.11.2020: Strings, Programm analysieren, fehlerhaftes Primzahl-Programm](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201126/hp-uebung-20201126.pdf)
  * [03.12.2020: Arrays mit Zahlen, Datum-Bibliothek](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201203/hp-uebung-20201203.pdf)
  * [10.12.2020: Ausgabe von Hexadezimalzahlen, Einfügen in Strings, Länge von Strings](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201210/hp-uebung-20201210.pdf)
+ * [17.12.2020: Kondensator, hüpfender Ball](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201217/hp-uebung-20201217.pdf)
 
 Musterlösungen:
 ---------------
@@ -41,6 +43,7 @@ Musterlösungen:
  * [26.11.2020: Strings, Programm analysieren, fehlerhaftes Primzahl-Programm](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201126/hp-musterloesung-20201126.pdf)
  * [03.12.2020: Arrays mit Zahlen, Datum-Bibliothek](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201203/hp-musterloesung-20201203.pdf)
  * [10.12.2020: Ausgabe von Hexadezimalzahlen, Einfügen in Strings, Länge von Strings](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201210/hp-musterloesung-20201210.pdf)
+ * [17.12.2020: Kondensator, hüpfender Ball](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201217/hp-musterloesung-20201217.pdf)
 
 Tafelbilder:
 ------------
@@ -49,6 +52,7 @@ Tafelbilder:
 Praktikumsunterlagen:
 ---------------------
  * [Versuch 1: RSA-Verschlüsselung](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201112/hp-2020ws-p1.pdf)
+ * [Versuch 2: Weltraum-Simulation](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20201217/hp-2020ws-p2.pdf)
 
 Alte Klausuren:
 ---------------
diff --git a/hp-slides-2020ws.pdf b/hp-slides-2020ws.pdf
index a0f4265a16fba411e21cb081b541eac4c8d2fe15..4f36f89341d38beb155f7c1b2cf88ea449c8442c 100644
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diff --git a/hp-slides-2020ws.tex b/hp-slides-2020ws.tex
index 1e448e3..7d3efec 100644
--- a/hp-slides-2020ws.tex
+++ b/hp-slides-2020ws.tex
@@ -22,4 +22,6 @@
   \includepdf[pages=-]{20201203/hp-20201203.pdf}
   \pdfbookmark[1]{10.12.2020: Parameter des Hauptprogramms, String-Operationen}{20201210}
   \includepdf[pages=-]{20201210/hp-20201210.pdf}
+  \pdfbookmark[1]{17.12.2020: Parameter des Hauptprogramms, String-Operationen}{20201217}
+  \includepdf[pages=-]{20201217/hp-20201217.pdf}
 \end{document}
-- 
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