How to plot this function

Answer 1

[Star Strider]

Force the NaN value at (0,0) to be 0 —

[X,Y] = ndgrid(linspace(-5,5,50));
Z = (X.^3.*Y - X.*Y.^3)./(X.^2+Y.^2);
Z(isnan(Z)) = 0;

figure
surfc(X,Y,Z)
colormap(turbo)

.

[Dinh Le Dung]

It look fanstatic, thanks alot!!!

[Star Strider]

As always, my pleasure!

Answer 2

[Sam Chak]

Hi @Dinh Le Dung

Think it should look like this:

[X, Y] = meshgrid(-0.5:1/40:0.5);
Z = X.*Y.*(X.^2 - Y.^2)./(X.^2 + Y.^2);
surf(X, Y, Z), xlabel('x'), ylabel('y'), zlabel('f(x, y)')

[Dinh Le Dung]

but this graph doesnt cover the case f(0,0) =0 :(( Thanks for your help!!

[Walter Roberson]

[X, Y] = meshgrid(-0.5:1/40:0.5);
Z = X.*Y.*(X.^2 - Y.^2)./(X.^2 + Y.^2);

Z(X==0 & Y == 0) = 0;

surf(X, Y, Z), xlabel('x'), ylabel('y'), zlabel('f(x, y)')

[Dinh Le Dung]

Oh it look great!! Thanks a lot!!

Answer 3

[Abderrahim. B]

Hi!

Since you need to multiply by the truth, maybe this below:

f = @(x,y)((((x.^3).*y - x.*(y.^3)) ./ (x.^2 + y.^2) ).*( x ~= 0 & y~=0) + 0.*( x == 0 & y == 0))

f = function_handle with value:
    @(x,y)((((x.^3).*y-x.*(y.^3))./(x.^2+y.^2)).*(x~=0&y~=0)+0.*(x==0&y==0))

[X, Y] = meshgrid([1:.5:10], [0:.1:10]);
F = f(X, Y) ;
surf(X, Y, F)
colorbar

Hope this helps!

[Dinh Le Dung]

I try to zoom in the interval [-0.5, 0.5] but it seems like it does not cover the case f(0,0) = 0