Mehr Folien und einige Typos.

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diff --git a/vorlesungen/slides/10/vektorfelder.mp b/vorlesungen/slides/10/vektorfelder.mp
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+%
+% Stroemungsfelder linearer Differentialgleichungen
+%
+% (c) 2015 Prof Dr Andreas Mueller, Hochschule Rapperswil
+% 2021-04-14, Roy Seitz, Copied for SeminarMatrizen
+%
+verbatimtex
+\documentclass{book}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{amsfonts}
+\usepackage{txfonts}
+\begin{document}
+etex;
+
+input TEX;
+
+TEXPRE("%&latex" & char(10) &
+"\documentclass{book}" &
+"\usepackage{times}" &
+"\usepackage{amsmath}" &
+"\usepackage{amssymb}" &
+"\usepackage{amsfonts}" &
+"\usepackage{txfonts}" &
+"\begin{document}");
+TEXPOST("\end{document}");
+
+%
+% Vektorfeld in der Ebene mit Lösungskurve
+% so(2)
+%
+beginfig(1)
+
+% Scaling parameter
+numeric unit;
+unit := 150;
+
+% Some points
+z1 = (-1.5,    0) * unit;
+z2 = ( 1.5,    0) * unit;
+z3 = (   0, -1.5) * unit;
+z4 = (   0,  1.5) * unit;
+
+pickup pencircle scaled 1pt;
+drawarrow (z1 shifted (-10,0))--(z2 shifted (10,0));
+drawarrow (z3 shifted (0,-10))--(z4 shifted (0,10));
+label.top(btex $x_1$ etex, z2 shifted (10,0));
+label.rt(btex $x_2$ etex, z4 shifted (0,10));
+
+% Draw circles
+for x = 0.2 step 0.2 until 1.4:
+  path p;
+  p = (x,0);
+  for a = 5 step 5 until 355:
+    p := p--(x*cosd(a), x*sind(a));
+  endfor;
+  p := p--cycle;
+  pickup pencircle scaled 1pt;
+  draw p scaled unit withcolor red;
+endfor;
+
+% Define DGL
+def dglField(expr x, y) =
+  %(-0.5 * (x + y), -0.5 * (y - x))
+  (-y, x)
+enddef;
+
+% Draw arrows for each grid point
+pickup pencircle scaled 0.5pt;
+for x = -1.5 step 0.1 until 1.55:
+  for y = -1.5 step 0.1 until 1.55:
+    drawarrow ((x, y) * unit)
+      --(((x,y) * unit) shifted (8 * dglField(x,y)))
+        withcolor blue;
+  endfor;
+endfor;
+
+endfig;
+
+
+
+%
+% Vektorfeld in der Ebene mit Lösungskurve
+% X \in sl(2, R)
+%
+beginfig(2)
+
+numeric unit;
+unit := 150;
+
+z0 = (   0,    0);
+z1 = (-1.5,    0) * unit;
+z2 = ( 1.5,    0) * unit;
+z3 = (   0, -1.5) * unit;
+z4 = (   0,  1.5) * unit;
+
+pickup pencircle scaled 1pt;
+drawarrow (z1 shifted (-10,0))--(z2 shifted (10,0));
+drawarrow (z3 shifted (0,-10))--(z4 shifted (0,10));
+label.top(btex $x_1$ etex, z2 shifted (10,0));
+label.rt(btex $x_2$ etex, z4 shifted (0,10));
+
+% Draw flow lines
+for y = -1.4 step 0.2 until 1.4:
+  path p;
+  p = (-1.5,y) -- (1.5, y);
+  pickup pencircle scaled 1pt;
+  draw p scaled unit withcolor red;
+endfor;
+
+def dglField(expr x, y) =
+  (y, 0)
+enddef;
+
+% Draw arrows for each grid point
+pickup pencircle scaled 0.5pt;
+for x = -1.5 step 0.1 until 1.55:
+  for y = -1.5 step 0.1 until 1.55:
+    drawarrow ((x, y) * unit)
+      --(((x,y) * unit) shifted (8 * dglField(x,y)))
+        withcolor blue;
+  endfor;
+endfor;
+
+endfig;
+
+
+
+
+%
+% Vektorfeld in der Ebene mit Lösungskurve
+% Y \in sl(2, R)
+%
+beginfig(3)
+
+numeric unit;
+unit := 150;
+
+z0 = (   0,    0);
+z1 = (-1.5,    0) * unit;
+z2 = ( 1.5,    0) * unit;
+z3 = (   0, -1.5) * unit;
+z4 = (   0,  1.5) * unit;
+
+pickup pencircle scaled 1pt;
+drawarrow (z1 shifted (-10,0))--(z2 shifted (10,0));
+drawarrow (z3 shifted (0,-10))--(z4 shifted (0,10));
+label.top(btex $x_1$ etex, z2 shifted (10,0));
+label.rt(btex $x_2$ etex, z4 shifted (0,10));
+
+% Draw flow lines
+for x = -1.4 step 0.2 until 1.4:
+  path p;
+  p = (x, -1.5) -- (x, 1.5);
+  pickup pencircle scaled 1pt;
+  draw p scaled unit withcolor red;
+endfor;
+
+def dglField(expr x, y) =
+  (0, x)
+enddef;
+
+% def dglFieldp(expr z) =
+%   dglField(xpart z, ypart z)
+% enddef;
+% 
+% def curve(expr z, l) =
+%   path p;
+%   p := z;
+%   for t = 0 step 1 until l:
+%     p := p--((point (length p) of p) shifted (0.01 * dglFieldp(point (length p) of p)));
+%   endfor;
+%   draw p scaled unit withcolor red;
+% enddef;
+%
+% numeric outerlength;
+% outerlength = 200;
+% curve(( 0.1, 0), outerlength);
+% curve(( 0.2, 0), outerlength);
+%
+% numeric innerlength;
+% innerlength = 500;
+% 
+% for a = 0 step 30 until 330:
+%   curve(0.05 * (cosd(a), sind(a)), innerlength);
+% endfor;
+
+% Draw arrows for each grid point
+pickup pencircle scaled 0.5pt;
+for x = -1.5 step 0.1 until 1.55:
+  for y = -1.5 step 0.1 until 1.55:
+    drawarrow ((x, y) * unit)
+      --(((x,y) * unit) shifted (8 * dglField(x,y)))
+        withcolor blue;
+  endfor;
+endfor;
+
+endfig;
+
+
+%
+% Vektorfeld in der Ebene mit Lösungskurve
+% H \in sl(2, R)
+%
+beginfig(4)
+
+numeric unit;
+unit := 150;
+
+z0 = (   0,    0);
+z1 = (-1.5,    0) * unit;
+z2 = ( 1.5,    0) * unit;
+z3 = (   0, -1.5) * unit;
+z4 = (   0,  1.5) * unit;
+
+pickup pencircle scaled 1pt;
+drawarrow (z1 shifted (-25,0))--(z2 shifted (25,0));
+drawarrow (z3 shifted (0,-10))--(z4 shifted (0,10));
+label.top(btex $x_1$ etex, z2 shifted (25,0));
+label.rt(btex $x_2$ etex, z4 shifted (0,10));
+
+def dglField(expr x, y) =
+  (x, -y)
+enddef;
+
+def dglFieldp(expr z) =
+  dglField(xpart z, ypart z)
+enddef;
+
+def curve(expr z, l) =
+  path p;
+  p := z;
+  for t = 0 step 1 until l:
+    p := p--((point (length p) of p) shifted (0.01 * dglFieldp(point (length p) of p)));
+  endfor;
+  draw p scaled unit withcolor red;
+enddef;
+
+for i = -1 step 2 until 1:
+  for k = -1 step 2 until 1:
+    curve((1.3 * i,  1.5 * k), 18);
+    curve((1.1 * i,  1.5 * k), 35);
+    curve((0.9 * i,  1.5 * k), 55);
+    curve((0.7 * i,  1.5 * k), 80);
+    curve((0.5 * i,  1.5 * k), 114);
+    curve((0.3 * i,  1.5 * k), 165);
+    curve((0.1 * i,  1.5 * k), 275);
+  endfor;
+endfor;
+
+% Draw arrows for each grid point
+pickup pencircle scaled 0.5pt;
+for x = -1.5 step 0.1 until 1.55:
+  for y = -1.5 step 0.1 until 1.55:
+    drawarrow ((x, y) * unit)
+      --(((x,y) * unit) shifted (8 * dglField(x,y)))
+        withcolor blue;
+  endfor;
+endfor;
+
+endfig;
+
+
+
+end;