### 2.40 evaluate and plot a f(x,y) on 2D grid of coordinates

Evaluate $$x \exp ^{-x^2-y^2}$$ on 2D cartesian grid between $$x=-2 \cdots 2$$ and $$y=-4 \cdots 4$$ using $$h=0.2$$ for grid spacing.

Mathematica

f[x_,y_]:=x Exp[-x^2-y^2];
data = Table[f[x,y],{x,-2,2,.2},{y,-4,4,.2}];
ListPlot3D[data,
PlotRange->All,
ColorFunction->"Rainbow",
AxesLabel->{"x","y","z"},
LabelStyle->12,
Ticks->{Range[-2,2,1],Range[-4,4,1],Automatic},
DataRange->{{-2,2},{-4,4},Automatic},
ImageSize->400]



The above can also be done using Plot3D

f[x_,y_]:=x Exp[-x^2-y^2];
Plot3D[f[x,y],{x,-2,2},{y,-4,4},
PlotRange->All,
ColorFunction->"Rainbow",
AxesLabel->{"x","y","z"},
LabelStyle->12,
ImageSize->400]



I need to sort out the orientation diļ¬erence between the two plots above.

Matlab

[X,Y] = meshgrid(-2:.2:2, -4:.2:4);
Z = X .* exp(-X.^2 - Y.^2);
surf(X,Y,Z)
xlabel('x');
ylabel('y');
zlabel('z');



Maple

f:=(x,y)->x*exp(-x^2-y^2);
data:=[seq([seq(f(x,y),x=-2..2,.2)],y=-4..4,.2)]:
plots:-listplot3d(data)