14.1: Functions of Several Variables

Example: f(x,y)=1-x-y

f[x_,y_]:=1-x-y;
Plot3D[f[x,y],{x,-3,3},{y,-3,3}]
ContourPlot[f[x,y],{x,-3,3},{y,-3,3}]

Example: g(x,y)=((x^2)+3(y^2))(e^(-((x^2)+(y^2))))

g[x_,y_]:=((x^2)+3(y^2))(E^(-((x^2)+(y^2))));
Plot3D[g[x,y],{x,-3,3},{y,-3,3}]
ContourPlot[g[x,y],{x,-3,3},{y,-3,3}]

Manipulate[Plot3D[g[x,y],{x,-3,3},{y,-3,3},Ticks->False,Mesh->False,ViewPoint->{2.123,t, 1.767}],{t,-π,π,0.1}]

Example: h(x,y)=((sin(x)sin(y))/(x y))

h[x_,y_]:=((Sin[x]Sin[y])/(x y));
Off[Power::"infy",∞::"indet",Plot3D::"plnc",Plot3D::"gval"];
Plot3D[h[x,y],{x,-6,6},{y,-6,6},PlotPoints->100,Mesh->False,PlotRange->{-.3,1}]

Manipulate[Plot3D[h[x,y],{x,-6,6},{y,-6,6},Ticks->False,PlotPoints->100,Mesh->False,PlotRange->{-.3,1},ViewPoint->{2.123,t, 1.767}],{t,-π,π,0.1}]