Uebungen in Mathematica

WIR93

Abbildung eines Parallelgitters in der
komplexen Ebene

"Putzmaschine" einsetzen

Remove["Global`*"];

Remove["Global`@*"]

Vorübung

Funktion w definieren

Clear[w]

w[s_, t_] := (1/(1 + s + I t))

Diverse Plots

ParametricPlot[{Re[w[s, 0]], Im[w[s, 0]]}, {s, -10, 10}];

ParametricPlot[{Re[w[0, s]], Im[w[0, s]]}, {s, -10, 10}];

ParametricPlot[{Re[w[Cos[t], Sin[t]]], Im[w[Cos[t], Sin[t]]]}, {t, 
        -10, 10}];

Alles in einem Schritt; das Gitter, das abgebildet wird

Remove["Global`*"];
Remove["Global`@*"];

w[s_, t_] := s + I t;
a = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[n, s]], Im[w[n, s]]}, {n, -10, 
                10}]], {s, -10, 10}];
b = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[s, n]], Im[w[s, n]]}, {n, -10, 
                10}]], {s, -10, 10}];
Show[a, b];

Alles in einem Schritt, 1., 1/(1+z)

Remove["Global`*"];
Remove["Global`@*"];

w[s_, t_] := (1/(1 + s + I t));
a = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[n, s]], Im[w[n, s]]}, {n, -5, 5}]], {s, -20, 
            20}];
b = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[s, n]], Im[w[s, n]]}, {n, -5, 5}]], {s, -20, 
            20}];
Show[a, b];

Alles in einem Schritt, 2., E^z

Remove["Global`*"];
Remove["Global`@*"];

w[s_, t_] := (E^(s + I t));
a = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[n, s]], Im[w[n, s]]}, {n, -10, 
                10}]], {s, -10, 10}];
b = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[s, n]], Im[w[s, n]]}, {n, -10, 
                10}]], {s, -10, 10}];
Show[a, b];

Show[{a, b}, AspectRatio -> GoldenRatio];

Alles in einem Schritt, 3., z^2

Remove["Global`*"];
Remove["Global`@*"];

w[s_, t_] := (((s + I t))^2);
a = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[n, s]], Im[w[n, s]]}, {n, -10, 
                10}]], {s, -10, 10}];
b = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[s, n]], Im[w[s, n]]}, {n, -10, 
                10}]], {s, -10, 10}];
Show[a, b];

Alles in einem Schritt, 4., z^3

Remove["Global`*"];
Remove["Global`@*"];

w[s_, t_] := (((s + I t))^3);
a = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[n, s]], Im[w[n, s]]}, {n, -10, 
                10}]], {s, -10, 10}];
b = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[s, n]], Im[w[s, n]]}, {n, -10, 
                10}]], {s, -10, 10}];
Show[a, b];

Alles in einem Schritt, 5., z^4

Remove["Global`*"];
Remove["Global`@*"];

w[s_, t_] := (((s + I t))^4);
a = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[n, s]], Im[w[n, s]]}, {n, -10, 
                10}]], {s, -10, 10}];
b = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[s, n]], Im[w[s, n]]}, {n, -10, 
                10}]], {s, -10, 10}];
Show[a, b];

Alles in einem Schritt, 6., z^5

Remove["Global`*"];
Remove["Global`@*"];

w[s_, t_] := (((s + I t))^5);
a = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[n, s]], Im[w[n, s]]}, {n, -10, 
                10}]], {s, -10, 10}];
b = 
        ParametricPlot[
          Evaluate[
            Table[{Re[w[s, n]], Im[w[s, n]]}, {n, -10, 
                10}]], {s, -10, 10}];
Show[a, b];

Alles in einem Schritt, 7., Sin[z]

Remove["Global`*"];
Remove["Global`@*"];

w[s_, t_] := Sin[s + I t];
a = 
        ParametricPlot[
          Evaluate[Table[{Re[w[n, s]], Im[w[n, s]]}, {n, 1, 10}]], {s, 1, 
            10}];
b = 
        ParametricPlot[
          Evaluate[Table[{Re[w[s, n]], Im[w[s, n]]}, {n, 1, 10}]], {s, 1, 
            10}];
Show[a, b];

Alles in einem Schritt, 8., 1/z

Remove["Global`*"];
Remove["Global`@*"];

w[s_, t_] := (1/(s + I t)); a = 
      ParametricPlot[
        Evaluate[Table[{Re[w[n, s]], Im[w[n, s]]}, {n, -10, 10}]], {s, 
          -10, 10}]; b = 
      ParametricPlot[
        Evaluate[Table[{Re[w[s, n]], Im[w[s, n]]}, {n, -10, 10}]], {s, 
          -10, 10}]; Show[a, b];

Alles in einem Schritt, 9., (z-1)/(z+1)

Remove["Global`*"];
Remove["Global`@*"];

w[s_, t_] := ((s + I t - 1)/(s + I t + 1)); a = 
      ParametricPlot[
        Evaluate[Table[{Re[w[n, s]], Im[w[n, s]]}, {n, -10, 10}]], {s, 
          -10, 10}]; b = 
      ParametricPlot[
        Evaluate[Table[{Re[w[s, n]], Im[w[s, n]]}, {n, -10, 10}]], {s, 
          -10, 10}]; Show[a, b];