Interessante Plots 2D und 3D

2D

D[ArcSin[Cos[x]], x]

Plot[-Sin[x]/Sqrt[1-Cos[x]^2],{x,-10,10},AspectRatio->Automatic];

Plot[ArcSin[Cos[x]], {x, -10, 10}, 
        AspectRatio -> Automatic];

Plot[Evaluate[D[ArcSin[Cos[x]], x]], {x, -10, 10}, 
        AspectRatio -> Automatic];

Plot[ArcCos[Cos[x]], {x, -10, 10}, 
        AspectRatio -> Automatic];

Plot[Evaluate[D[ArcCos[Cos[x]], x]], {x, -10, 10}, 
        AspectRatio -> Automatic];

Plot[Evaluate[D[ArcSin[Sin[x]], x]], {x, -10, 10}, 
        AspectRatio -> Automatic];

Plot[ ArcSin[Sin[x]], {x, -10, 10}, 
        AspectRatio -> Automatic];

Plot[ ArcTan[Tan[x]], {x, -10, 10}, 
        AspectRatio -> Automatic];

Plot[ ArcTan[Cot[x]], {x, -10, 10}, 
        AspectRatio -> Automatic];

Plot[{ ({{ArcTan[Cot[x]],  ArcTan[Tan[x]]}})},{x, -10, 10},AspectRatio -> Automatic,Axes -> False];

Plot[{ArcTan[Cot[x]], ArcTan[Tan[x]]}, {x, -10, 10}, 
        AspectRatio -> Automatic, Axes -> False];

Plot[{ArcTan[Cot[x]], ArcTan[Tan[x]], 
          Sin[x]/Sqrt[1 - Cos[x]^2]}, {x, -10, 10}, 
        AspectRatio -> Automatic, Axes -> False];

Plot[ArcTan[Sin[x]], {x, -10, 10}];

Plot[
        2  ArcSin[E^(-x^2)] * 
          Sign[Floor[  ArcSin[E^(-x^2)] ]], {x, -1, 1}, 
        PlotRange -> {-Pi, Pi}];

Plot[
        2  ArcSin[E^(-x^2)] * 
          Sign[Floor[ 2 ArcSin[E^(-x^2)] ]], {x, -1, 1}, 
        PlotRange -> {0, Pi}];

Plot[
        2  ArcSin[E^(-x^2)] * 
          Sign[Floor[ 
              2 ArcSin[E^(-(x - 0.5)^2)] ]], {x, -1, 1}, 
        PlotRange -> {-Pi, 2  Pi}];

Plot[
        2  ArcSin[E^(-x^2)] * 
            Sign[Floor[  ArcSin[E^(-x^2)] ]]  +  
          ArcSin[Cos[x]], {x, -1, 1}, 
        PlotRange -> {-Pi, 2  Pi}];

3D

p0=Plot3D[ ArcTan[Tan[x]] ArcSin[Sin[y]],{x,-5,5},{y,-5,5}];

p0=Plot3D[ ArcTan[Tan[x]]+ArcSin[Sin[y]],{x,-5,5},{y,-5,5}];

p0=Plot3D[-Sin[x]/Sqrt[1.0001-Cos[x]^2]+ArcSin[Sin[y]],{x,-5,5},{y,-5,5}];

p0=Plot3D[-Sin[x]/Sqrt[1.0001-Cos[x]^2] ArcSin[Sin[y]],{x,-5,5},{y,-5,5}];

p0=Plot3D[ Sin[x] Cos[y],{x,-5,5},{y,-5,5}];

p0=Plot3D[ Sin[x]+Cos[y],{x,-5,5},{y,-5,5}];

p1 = Plot3D[x^2 + y^2, {x, -2, 2}, {y, -2, 2}];

p2 = Plot3D[x y, {x, -2, 2}, {y, -2, 2}];

p3 = Plot3D[0, {x, -2, 2}, {y, -2, 2}];

Show[p2, p3];

?PlotPoints

p4 = 
        Plot3D[x y/(x^2 + y^2)^2, {x, -2, 2}, {y, -2, 2}, 
          PlotRange -> {-5, 5}, PlotPoints -> 50];

p4 = 
        Plot3D[x y/(x^2 + y^2)^2, {x, -0.2, 0.2}, {y, -0.2, 
            0.2}, PlotRange -> {-1, 1}, 
          PlotPoints -> 50];

p4 = 
        Plot3D[x y/(x^2 + y^2)^2, {x, -0.02, 0.02}, {y, -0.02, 
            0.02}, PlotRange -> {-15000, 15000}, 
          PlotPoints -> 50];

ContourPlot[
        x y/(x^2 + y^2)^2, {x, -0.02, 0.02}, {y, -0.02, 0.02}, 
        PlotRange -> {-15000, 15000}, 
        PlotPoints -> 50];

p5 = 
        Plot3D[50/(10 + 3 (x - 1)^2 + 5 (y + 1)^2) + 
            70/(10 + 2 (x + 1)^2 + 10 (y - 2)^2), {x, -5, 
            5}, {y, -5, 5}, PlotPoints -> 50];

ContourPlot[
        50/(10 + 3 (x - 1)^2 + 5 (y + 1)^2) + 
          70/(10 + 2 (x + 1)^2 + 10 (y - 2)^2), {x, -5, 
          5}, {y, -5, 5}, PlotPoints -> 50];

Animate!

Table[Plot3D[(1+Sin[k Pi/20]) 50/(10+3(x-1)^2+5(y+1)^2)+ (1+Cos[k Pi/20]) 70/(10+2(x+1)^2+10(y-2)^2),{x,-5,5},{y,-5,5},PlotPoints->50,PlotRange->{0,20},Boxed->False,Axes->None],{k,0,40}];

Landschaft

f[x_, y_] := 1/E^x^2 Cos[x/5] (1 - y^2/5)

Plot[f[x, 0], {x, -5, 5}, PlotRange -> {0, 1}];

Remove[f];
f[x_, y_] := 
        1/E^x^2 Cos[
            x/5] (2 - (y - 3)^2 /2);
g[x_, y_] := 1 - 1/E^(x^2) Cos[x/5]; 
    Plot3D[-f[x, 0] (1 + Cos[x + y]) (Cos[y] + f[y/2, 0]) +  
        4  g[(x - 0.3), 0] + (x/4)^2, {x, -5, 5}, {y, -5, 5}, 
      PlotRange -> {6, -6}];

Uebungen

Plot3D[x^2 + y^2, {x, -2, 2}, {y, -2, 2}];

ContourPlot[x^2 + y^2, {x, -2, 2}, {y, -2, 2}];

Plot3D[x y, {x, -2, 2}, {y, -2, 2}, 
        AspectRatio -> 2];

ContourPlot[x y, {x, -2, 2}, {y, -2, 2}];

Plot3D[x y, {x, -2, 2}, {y, -2, 2}, AspectRatio -> 2, 
        ViewPoint -> {1.606,  -2.976,  -0.120}];

Plot3D[x y/(x^2 + y^2)^2, {x, -2, 2}, {y, -2, 2}, 
        PlotPoints -> 50, PlotRange -> {-5, 5}];

ContourPlot[
        x y/(x^2 + y^2)^2, {x, -2, 2}, {y, -2, 2}];

Plot3D[x y/(x^2 + y^2)^2, {x, -2, 2}, {y, -2, 2}, 
        PlotPoints -> 50, PlotRange -> {-5, 5}, 
        AspectRatio -> 2, 
        ViewPoint -> {1.606,  -2.976,  -0.120}];

Plot3D[Sin[x y], {x, -2, 2}, {y, -2, 2}];

ContourPlot[Sin[x y], {x, -2, 2}, {y, -2, 2}];

Plot3D[Sin[x + y], {x, -2, 2}, {y, -2, 2}];

Plot3D[Sin[x y^2 - 1/(x^2 + 1)], {x, -5, 5}, {y, -5, 5}, 
        PlotPoints -> 200];

p2 = Plot3D[x y, {x, -2, 2}, {y, -2, 2}];

p3 = Plot3D[0, {x, -2, 2}, {y, -2, 2}];

Show[p2, p3];

?PlotPoints

p3 = 
        Plot3D[x y/(x^2 + y^2)^2, {x, -2, 2}, {y, -2, 2}, 
          PlotRange -> {-5, 5}, PlotPoints -> 50];

p3 = 
        Plot3D[x y/(x^2 + y^2)^2, {x, -0.2, 0.2}, {y, -0.2, 
            0.2}, PlotRange -> {-1, 1}, 
          PlotPoints -> 50];

p3 = 
        Plot3D[x y/(x^2 + y^2)^2, {x, -0.02, 0.02}, {y, -0.02, 
            0.02}, PlotRange -> {-15000, 15000}, 
          PlotPoints -> 50];

ContourPlot[
        x y/(x^2 + y^2)^2, {x, -0.02, 0.02}, {y, -0.02, 0.02}, 
        PlotRange -> {-15000, 15000}, 
        PlotPoints -> 50];

50/(10 + 3 (x - 1)^2 + 5 (y + 1)^2) + 
      70/(10 + 2 (x + 1)^2 + 10 (y - 2)^2)

p3 = 
        Plot3D[50/(10 + 3 (x - 1)^2 + 5 (y + 1)^2) + 
            70/(10 + 2 (x + 1)^2 + 10 (y - 2)^2), {x, -5, 
            5}, {y, -5, 5}, PlotPoints -> 50];

ContourPlot[
        50/(10 + 3 (x - 1)^2 + 5 (y + 1)^2) + 
          70/(10 + 2 (x + 1)^2 + 10 (y - 2)^2), {x, -5, 
          5}, {y, -5, 5}, PlotPoints -> 50];

p4 = Plot3D[Floor[x]+Floor[y],{x,-3,3},{y,-3,3}];

p5 = Plot3D[Floor[x]-Floor[y],{x,-3,3},{y,-3,3}];

p6 = Plot3D[Floor[x] Floor[y],{x,-3,3},{y,-3,3}];

p7 = Plot3D[Floor[x] Floor[y]^2,{x,-3,3},{y,-3,3}];

p8 = Plot3D[Floor[5 Sin[x] Sin[y]],{x,-3,3},{y,-3,3}];

ParametricPlots

Remove["Global`*"]

v[t_] := {t,  1 - 0.25 t^2};
ParametricPlot[v[t], {t, -2, 2}, 
        AspectRatio -> Automatic];

v[t_] := {2 Sin[t]/(1 + Cos[t]), 
          2 Cos[t]/(1 + Cos[t])};
ParametricPlot[v[t], {t, -Pi/2, Pi/2}, 
        AspectRatio -> Automatic];

?PlotRange

v[t_] := {2  t - 3  t^2 + t^3, 
          1 - t^2 + 3  t^3 - 3.25  t^4 + 1.5  t^5 - 
            0.25  t^6};
ParametricPlot[v[t], {t, -0.52138, 2.52138}, 
        AspectRatio -> Automatic, 
        PlotRange -> {0, 1}];

v[t_] := { Sin[t], Cos[t], t};
ParametricPlot3D[v[t], {t, 0, 2  Pi}, 
        ViewPoint -> {0.891,  -1.387,  1.773}];

v[t_] := { Sin[t], Cos[t]};
ParametricPlot[v[t], {t, 0, 2  Pi}, 
        AspectRatio -> Automatic];

v[t_] := { Sin[t], t};
ParametricPlot[v[t], {t, 0, 10  Pi}];

v[t_] := { Sin[t], Cos[t], t};
ParametricPlot3D[v[t], {t, 0, 4  Pi}, 
        AspectRatio -> Automatic];

v[t_] := {t  Sin[t], Cos[t], Sin[t]};
ParametricPlot3D[v[t], {t, 0, 5  Pi}];

v[t_] := {t  Sin[t], Cos[t], Sin[t]};
ParametricPlot3D[v[t], {t, 0, 2  Pi}];

v[t_] := {t  Sin[t], Cos[t], Sin[t]};
ParametricPlot3D[v[t], {t, 0, 20  Pi}];

v[t_] := 5  { Sin[t], Cos[t]};
par1 = 
        ParametricPlot[v[t], {t, 0, 2  Pi}, 
          AspectRatio -> Automatic];

v[t_] := 
        5  { Sin[t], Cos[t]} +  { Sin[10  t], 
            Cos[10  t]};
par2 = 
        ParametricPlot[v[t], {t, 0, 2  Pi}, 
          AspectRatio -> Automatic];

Show[par1, par2]

v[t_] := 
        5  { Sin[t], Cos[t]} +  { Sin[E t], 
            Cos[E t]};
par2 = 
        ParametricPlot[v[t], {t, 0, 200  Pi}, 
          AspectRatio -> Automatic];

v[t_] := 
        5  { Sin[t], Cos[t]} +  { Sin[E t], 
            Cos[E t]};
par2 = 
        ParametricPlot[v[t], {t, 0, 4000  Pi}, AspectRatio -> Automatic, 
          PlotPoints -> 400];

v[t_, u_] := {t  Sin[t], Cos[t], 
          Sin[u]};
ParametricPlot3D[
        v[t, u], {t, 0, 4  Pi}, {u, 0, 4  Pi}];

v[t_, u_] := {Sin[t], Cos[t], Sin[u]};
ParametricPlot3D[
        v[t, u], {t, 0, 4  Pi}, {u, 0, 4  Pi}];

v[t_, u_] := {Sin[t], Cos[2  t], 
          Sin[u]};
ParametricPlot3D[
        v[t, u], {t, 0, 4  Pi}, {u, 0, 4  Pi}];

v[t_,u_]:={Sin[t],Cos[u+t],Sin[u]};
ParametricPlot3D[v[t,u],{t,0,4Pi},{u,0,4Pi},PlotPoints->15];

vec[u_,v_]:={Sin[u] Cos[v],Sin[u] Sin[v],Cos[u]};
ParametricPlot3D[vec[u,v],{u,0,2Pi},{v,0,Pi}];

Zeit! Time! Temps!

v[t_, u_] := {Sin[t], Cos[u + t], 
          Sin[u]};
ParametricPlot3D[v[t, u], {t, 0, 4  Pi}, {u, 0, 4  Pi}, 
        PlotPoints -> 20];