How to plot discontinous function f(x,y)

Please, how do I plot discontinous function of two variables: f(x,y)

z = f(x,y) = x-.8193318913*sin(x)*cos(x)/(cos(x)^2+sinh(y)^2)-(0.2931044702e-2*(0.7500000000e-3*x^2-0.7500000000e-3*y^2+0.1622336517e-1))*sin(x)*cos(x)/(((0.7500000000e-3*x^2-0.7500000000e-3*y^2+0.1622336517e-1)^2+0.2250000000e-5*x^2*y^2)*(cos(x)^2+sinh(y)^2))-0.4396567053e-5*x*y*sinh(y)*cosh(y)/(((0.7500000000e-3*x^2-0.7500000000e-3*y^2+0.1622336517e-1)^2+0.2250000000e-5*x^2*y^2)*(cos(x)^2+sinh(y)^2));

[Torsten]

Why discontinuous ?

[University Glasgow]

I just wanna use this function as an example.

[Sam Chak]

It's a bit mathematically strange. Even if you want use this equation as an example, are the insignificant numbers necessary? I mean, why didn't you remove the insignificant zeros from the equation as you typed and then checked the equation?

By the way, can you point out the discontinuity in the equation? It probably makes the plotting easier.

[University Glasgow]

Sorry about that... I copied it from maple directly

[Torsten]

The usual way to plot a function z = f(x,y) is a surface plot.

Look up

https://de.mathworks.com/help/matlab/ref/surf.html

for examples.

[University Glasgow]

Thank you for this. I know about this. I just wanna find out how plot f(x,y) that has discontinuity. For instance,

f(x,y) = 1/(x+1) + 1/(y-1)

[Torsten]

This function has no discontinuities. It is not defined for x = -1 and y = 0 and y = 1. Discontinuities can only appear in the domain where the function is defined.

To plot a function with singularities (like the one above), you must choose x and y such that they don't contain such singularities. Or you must return NaN from the function for those values of x and/or y where f has singularities. NaN values are not plotted.

[University Glasgow]

Please, how do I do that?

[Torsten]

f = @(x,y) 1./(x+1)+1./(y-1);
x = -2:0.05:2;
y = -2:0.05:2;
[X,Y] = meshgrid(x,y);
Z = f(X,Y);
Z(abs(Z)>1e2) = NaN;
surf(X,Y,Z)

[University Glasgow]

Thank you

Answer 1

[Chunru]

syms x y z
f(x, y) = x-.8193318913*sin(x)*cos(x)/(cos(x)^2+sinh(y)^2)-(0.2931044702e-2*(0.7500000000e-3*x^2-0.7500000000e-3*y^2+0.1622336517e-1))*sin(x)*cos(x)/(((0.7500000000e-3*x^2-0.7500000000e-3*y^2+0.1622336517e-1)^2+0.2250000000e-5*x^2*y^2)*(cos(x)^2+sinh(y)^2))-0.4396567053e-5*x*y*sinh(y)*cosh(y)/(((0.7500000000e-3*x^2-0.7500000000e-3*y^2+0.1622336517e-1)^2+0.2250000000e-5*x^2*y^2)*(cos(x)^2+sinh(y)^2));
ezplot(f)

[University Glasgow]

Thank you