Darstellungsformen Funktionen mehrerer Veränderlicher (created with Mathematica 9)

Analytische Darstellung

f=x^2+y^2

g=Sin[x*y]

p=T/V  (* Konstante n R auf eins gesetzt! *)

Funktionstafel

Table[f,{x,0,3},{y,0,3}] // MatrixForm

Graphisch als Fläche im Raum

Plot3D[f,{x,-3,3},{y,-3,3},AxesLabel->{"x","y","f"}]

Plot3D[f,{x,-3,3},{y,-3,3},AxesLabel->{"x","y","f"},RegionFunction->Function[{x,y,z},x^2+y^2≤9]]

Plot3D[g,{x,-3,3},{y,-3,3},AxesLabel->{"x","y","g"},Mesh->False,PlotPoints->20]

Plot3D[p,{T,0,3},{V,0,3},AxesLabel->{"T","V","p"},PlotRange->{0,20},PlotPoints->100]

Höhenliniendiagramm

ContourPlot[f,{x,-2,2},{y,-2,2},Contours->{1,2,3,4},FrameLabel->{"x","y"},ContourLabels->Function[{x,y,z},Text[Framed[z],{x,y},Background->White]]]

ContourPlot[g,{x,-3,3},{y,-3,3},Contours->Table[c,{c,-1,1,0.1}],FrameLabel->{"x","y"},ColorFunction->"BlueGreenYellow"]

ContourPlot[p,{T,0,3},{V,0,3},FrameLabel->{"T","V"},ContourLabels->True]

Dichtediagramm

DensityPlot[f,{x,-2,2},{y,-2,2},FrameLabel->{"x","y"}]

DensityPlot[g,{x,-3,3},{y,-3,3},FrameLabel->{"x","y"},PlotPoints->50]

DensityPlot[p,{T,0,3},{V,0,3},FrameLabel->{"T","V"},PlotPoints->50]

Schnittkurvendiagramm

cuts = {0,1,2,3};

fc=f /. y->cuts

Plot[fc ,{x,-3,3},
AxesLabel->{"x","f"},PlotLegends->Map[("y="<>ToString[#])&,cuts],ImageSize->400]

gc=g /. y->cuts

Plot[gc ,{x,-3,3},
AxesLabel->{"x","g"},PlotLegends->Map[("y="<>ToString[#])&,cuts],ImageSize->400]

pc=p /. T->cuts

Plot[pc ,{V,0,3},
AxesLabel->{"V","p"},PlotLegends->Map[("T="<>ToString[#])&,cuts],ImageSize->400,AspectRatio->1]

Darstellung Funktionen dreier Veränderlicher (Beispiel: 3D ContourPlot)

ContourPlot3D[x^2+y^2+z^2,{x,-3,3},{y,-3,3},{z,-3,3}]