Reine Funktionen und Mapping

Remove["Global`*"]

Eine Funktion auf die Elementen einer  Mengen anwenden

Range[10]

r = Range[10] Pi/5

Sin[r]

f[x_] := E^x - Tan[x]

f[r]

Map[Plus, r + Pi/17]

Apply[Plus, r + Pi/17]

Map[Sin, r + Pi/17]

Map[Sin, r]

Map[Sin, r] // N

Reine Funktion

Function[argument1, Cos[argument1]/Sin[argument1 - 1]]

Function[Cos[#]/Sin[# - 1]]

Function[argument1, Cos[argument1]/Sin[argument1 - 1]][
      Pi/17]

Function[argument1, Cos[argument1]/Sin[argument1 - 1]][
      t]

Function[Cos[#]/Sin[# - 1]][Pi/17]

Function[argument1, Cos[argument1]/Sin[argument1 - 1]][
      0.142]

Function[Cos[#]/Sin[# - 1]][0.142]

Function[argument1, Cos[argument1]/Sin[argument1 - 1]][
      Pi]

Function[Cos[#]/Sin[# - 1]][Pi]

Function[{argument1, argument2}, Cos[argument1]/Sin[argument2]][
      Pi/17, Pi/19]

Function[,Cos[#1]/Sin[#2]][Pi/17, Pi/19]

Wählbare Funktion und Variable in einem Modul

ser1[f_, s_, ss_] := 
        Module[{}, 
Print[f]; 
Print[
            f /. t -> s]; 
Print[
            f /. x -> s]; 
Print[
            u[x]]; 
w[m_] := Function[u[#]][m];  
          Print[w[ss]];
];
u[t_] := Sin[t]; ser1[u[t], j, k]

ser2[f_, s_] := 
        Module[{}, 
w[m_] := Function[u[#]][m];  
          Print[w[s]];
];
ser2[u[t], xX]

Reine Funktion mappen

Map[
      Function[argument1, Cos[argument1]/Sin[argument1 - 1]], {Pi/11, Pi/13, 
        Pi/17, Pi/19}]

N[%]

Map[
      Function[argument1, Cos[argument1]/Sin[argument1 - 1]], {Pi/11, Pi/13, 
        Pi/17, Pi/19}]

Map[
      Function[Cos[#1]/Sin[#1 - 1]], {Pi/11, Pi/13, Pi/17, Pi/19}]

Map[
      Function[Cos[#1]/Sin[#1 - 1]] &, {Pi/11, Pi/13, Pi/17, 
        Pi/19}]

Map[Cos[#1]/Sin[#1 - 1] &, {Pi/11, Pi/13, Pi/17, Pi/19}]

Map[Cos[#1]/Sin[#1 - 1] &, {Pi/11, Pi/13, Pi/17, Pi/19}]

Cos[#1]/Sin[#1 - 1] /@ {Pi/11, Pi/13, Pi/17, Pi/19}

Cos[#1]/Sin[#1 - 1] & /@ {Pi/11, Pi/13, Pi/17, Pi/19}

(Cos[#1]/Sin[#1 - 1] &) /@ {Pi/11, Pi/13, Pi/17, Pi/19}

(Cos[#1]/Sin[#1 - 1] // N &) /@ {Pi/11, Pi/13, Pi/17, 
        Pi/19}

Eine Figur rotieren

fig1 = {{0, 0}, {1, 1}, {2, 3}, {1, 6}, {-1, 7}, {-2, 
            4}, {-1, 1}};
ListPlot[fig1, AspectRatio -> Automatic, 
        PlotStyle -> PointSize[0.04]];

φ = -3 Pi/11;
matrixRot = {{Cos[φ], -Sin[φ]}, {Sin[φ], Cos[φ]}};  matrixRot // MatrixForm

fig2 = Map[0.6*2.3 # &, fig1]

ListPlot[fig2, AspectRatio -> Automatic, 
        PlotStyle -> PointSize[0.04]];

fig3 = Map[matrixRot . # &, fig2]

ListPlot[fig3, AspectRatio -> Automatic, 
        PlotStyle -> PointSize[0.04]];

fig3 = matrixRot . # & /@ fig2

ListPlot[fig3, AspectRatio -> Automatic, 
        PlotStyle -> PointSize[0.04]];

fig4 = matrixRot . # & /@ fig3;
ListPlot[fig4, AspectRatio -> Automatic, 
        PlotStyle -> PointSize[0.04]];

fig[1] = fig1;
fig[k_] := (matrixRot // N) . # & /@ 
          fig[k - 1];

Flatten[Table[fig[k], {k, 1, 5}], 1]

Flatten[Table[fig[k], {k, 1, 5}], 1] // TableForm

fig[k_] := matrixRot . # & /@ 
          fig[k - 1];
ListPlot[Evaluate[Flatten[Table[fig[k], {k, 1, 5}], 1]], 
        AspectRatio -> Automatic, 
        PlotStyle -> PointSize[0.04]];