Einige Funktionen in zwei Variablen: Höhenschichtlinien

z = 2  x - 3  y + 4

Show[
        GraphicsArray[{Plot3D[
              2  x - 3  y + 4, {x, -2, 2}, {y, -2, 2}, 
              PlotPoints -> 100, DisplayFunction -> Identity], 
            ContourPlot[2  x - 3  y + 4, {x, -2, 2}, {y, -2, 2}, 
              DisplayFunction -> Identity, Contours -> 20, 
              PlotPoints -> 100, ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]

z=(y^2)-(x^2)

Show[
        GraphicsArray[{Plot3D[y^2 - x^2, {x, -2, 2}, {y, -2, 2}, 
              PlotPoints -> 100, DisplayFunction -> Identity], 
            ContourPlot[y^2 - x^2, {x, -2, 2}, {y, -2, 2}, 
              DisplayFunction -> Identity, Contours -> 20, 
              PlotPoints -> 100, ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]

z=(x^2) + (y^2)

Show[
        GraphicsArray[{Plot3D[y^2 + x^2, {x, -2, 2}, {y, -2, 2}, 
              PlotPoints -> 100, DisplayFunction -> Identity], 
            ContourPlot[y^2 + x^2, {x, -2, 2}, {y, -2, 2}, 
              DisplayFunction -> Identity, Contours -> 20, 
              PlotPoints -> 100, ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]

z = (Sqrt[9 - (x^2) - (y^2)])

Show[
        GraphicsArray[{Plot3D[
              Sqrt[9 - x^2 - y^2], {x, -3, 3}, {y, -3, 3}, 
              PlotPoints -> 100, DisplayFunction -> Identity], 
            ContourPlot[
              Sqrt[Max[9 - x^2 - y^2, 0]], {x, -3, 3}, {y, -3, 3}, 
              DisplayFunction -> Identity, Contours -> 20, 
              PlotPoints -> 100, ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]

z = (e^(-(x^2) - (y^2)))

Show[
        GraphicsArray[{Plot3D[
              Exp[-x^2 - y^2], {x, -2, 2}, {y, -2, 2}, 
              PlotPoints -> 100, DisplayFunction -> Identity], 
            ContourPlot[Exp[-x^2 - y^2], {x, -2, 2}, {y, -2, 2}, 
              DisplayFunction -> Identity, Contours -> 20, 
              PlotPoints -> 100, ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]

z = sin x + cos y

Show[
        GraphicsArray[{Plot3D[
              Sin[x] + Cos[y], {x, -4 Pi, 4  Pi}, {y, -4 Pi, 4  Pi}, 
              PlotPoints -> 100, DisplayFunction -> Identity], 
            ContourPlot[
              Sin[x] + Cos[y], {x, -4 Pi, 4  Pi}, {y, -4 Pi, 4  Pi}, 
              DisplayFunction -> Identity, Contours -> 20, 
              PlotPoints -> 100, ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]

z=((x + y)/((x^2) + (y^2)))

Show[
        GraphicsArray[{Plot3D[(x + y)/(x^2 + y^2), {x, -2, 
                2}, {y, -2, 2}, PlotRange -> {-5, 5}, 
              PlotPoints -> 100, DisplayFunction -> Identity], 
            ContourPlot[(x + y)/(x^2 + y^2), {x, -2, 
                2}, {y, -2, 2}, DisplayFunction -> Identity, 
              Contours -> 20, PlotPoints -> 100, 
              ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]

z=((xy^2)/((x^2) + (y^2)))

Show[
        GraphicsArray[{Plot3D[(x y^2)/(x^2 + y^2), {x, -2, 
                2}, {y, -2, 2}, PlotPoints -> 100, 
              DisplayFunction -> Identity], 
            ContourPlot[(x y^2)/(x^2 + y^2), {x, -2, 
                2}, {y, -2, 2}, DisplayFunction -> Identity, 
              Contours -> 20, PlotPoints -> 100, 
              ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]

z=(sin 5  x) (e^(-y))

Show[
        GraphicsArray[{Plot3D[
              Sin[5  x]*Exp[-y], {x, -2, 2}, {y, -2, 2}, 
              PlotRange -> {-Exp[2], Exp[2]}, 
              PlotPoints -> 100, DisplayFunction -> Identity], 
            ContourPlot[
              Sin[5  x]*Exp[-y], {x, -2, 2}, {y, -2, 2}, 
              DisplayFunction -> Identity, Contours -> 20, 
              PlotPoints -> 100, ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]

z=(((sin x) (sin y))/(1 + (x^2) + (y^2)))

Show[
        GraphicsArray[{Plot3D[
              Sin[x]*Sin[y]/(1 + x^2 + y^2), {x, -Pi, 
                Pi}, {y, -Pi, Pi}, PlotPoints -> 100, 
              DisplayFunction -> Identity], 
            ContourPlot[
              Sin[x]*Sin[y]/(1 + x^2 + y^2), {x, -Pi, 
                Pi}, {y, -Pi, Pi}, DisplayFunction -> Identity, 
              Contours -> 20, PlotPoints -> 100, 
              ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]

z=|x|-|y|

Show[
        GraphicsArray[{Plot3D[
              Abs[x] - Abs[y], {x, -2, 2}, {y, -2, 2}, 
              PlotPoints -> 100, DisplayFunction -> Identity], 
            ContourPlot[Abs[x] - Abs[y], {x, -2, 2}, {y, -2, 2}, 
              DisplayFunction -> Identity, Contours -> 20, 
              PlotPoints -> 100, ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]

z=(ln x) (ln y)

Show[
        GraphicsArray[{Plot3D[Log[x] Log[y], {x, 0.01, 1}, {y, 0.01, 1}, 
              PlotPoints -> 100, PlotRange -> {0, 10}, 
              DisplayFunction -> Identity], 
            ContourPlot[Log[x] Log[y], {x, 0.01, 1}, {y, 0.01, 1}, 
              DisplayFunction -> Identity, Contours -> 20, 
              PlotPoints -> 100, ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]

z=sin((e^x) + (e^y))

Show[
        GraphicsArray[{Plot3D[
              Sin[Exp[x] + Exp[y]], {x, -3, 3}, {y, -3, 3}, 
              PlotPoints -> 100, PlotRange -> {-1, 1}, 
              DisplayFunction -> Identity], 
            ContourPlot[Sin[Exp[x] + Exp[y]], {x, -3, 3}, {y, -3, 3}, 
              DisplayFunction -> Identity, Contours -> 20, 
              PlotPoints -> 100, ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]

z=tan(x+(y/2))

Show[
        GraphicsArray[{Plot3D[
              Tan[x + y/2], {x, -Pi, Pi}, {y, -Pi, Pi}, 
              PlotPoints -> 100, PlotRange -> {-10, 10}, 
              DisplayFunction -> Identity], 
            ContourPlot[Tan[x + y/2], {x, -Pi, Pi}, {y, -Pi, Pi}, 
              DisplayFunction -> Identity, Contours -> 20, 
              PlotPoints -> 100, ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]

z=(((cos (10  x)) y)/((e^y) - (x^2)))

Show[
        GraphicsArray[{Plot3D[(Cos[10  x]*y)/(Exp[y] - 
                    x^2), {x, -2, 2}, {y, -2, 2}, 
              PlotPoints -> 200, PlotRange -> {-25, 25}, 
              DisplayFunction -> Identity], 
            ContourPlot[(Cos[10  x]*y)/(Exp[y] - x^2), {x, -2, 
                2}, {y, -2, 2}, DisplayFunction -> Identity, 
              Contours -> 20, PlotPoints -> 100, 
              ColorFunction -> (Hue[#/4] &)]}], 
        ImageSize -> 1200]