I need to plot the following functions but I receive this error "Invalid indexing or function definition. When defining a function ensure that the arguments are symbolic variables ...."

x = 2:30;

y = 40:60;

u = @(x,y) 10*sin(200*x)+0.1*cos(10*y)+(100*x)./y;           

v = @(x,y) 10*cos(200*x)+0.1*sin(10*y)-100*(x./y);

syms x y

ex =  diff(u,x);

ey = diff(v,y);

Gxy = diff(v,x)+diff(u,y);

[X,Y] = meshgrid(x,y);

Z = ex(X,Y);

figure(1)

mesh(X, Y, Z)

[X,Y] = meshgrid(x,y);

Z = ey(X,Y);

figure(2)

mesh(X, Y, Z)

[X,Y] = meshgrid(x,y);

Z = Gxy(X,Y);

figure(3)

mesh(X, Y, Z)

Answer 1

[Walter Roberson]

You have defined

 x = 2:30;
 y = 40:60;

but then you have

syms x y

That is equivalent to

x = sym('x');
y = sym('y');

which is to say that it overwrites x and y, and afterwards they are no longer numeric. But afterwards you sometimes treat them as symbols and sometimes treat them as numeric. In particular,

 [X,Y] = meshgrid(x,y);

attempts to treat them as numeric.

You also have

u = @(x,y) 10*sin(200*x)+0.1*cos(10*y)+(100*x)./y;           
v = @(x,y) 10*cos(200*x)+0.1*sin(10*y)-100*(x./y);

ex =  diff(u,x);
ey = diff(v,y);

The two diff() lines attempt to take the symbolic differentiation of a MATLAB function handle. You probably cannot do that. You can differentiate a symbolic expression, and you might be able to differentiate a symbolic function, but probably not a function handle.

ex = diff(u(x,y), x);
ey = diff(v(x,y), y)

would invoke the function handles on the symbolic parameters x and y, giving a symbolic expression as a result, and that symbolic expression can be differentiated.

[mohsen]

I removed the syms x y

and replaced the diff with

ex = diff(u(x,y), x);

ey = diff(v(x,y), y);

but I still get an error what else I should change?

[Walter Roberson]

With x and y numeric and u a function handle, u(x,y) would be numeric, so diff(u(x,y),x) would be a numeric difference rather than a symbolic difference. When you request a numeric difference, the second parameter must be the number of times the difference is to be taken, not a variable indicating a direction. That is not going to be what you want. You need to be using symbolic expressions and to have x and y being symbolic. What you should be doing is renaming your numeric uses of x and y.

Note: you do not need to define x or y before defining a function handle that uses those names as parameters in @(x,y) . Your first need for your numeric x and y is in your meshgrid(). You also do not need to recalculate the meshgrid() since you are not changing X or Y or the numeric x or y between your meshgrid() calls. So you could just eliminate your use of x and y as numeric and directly call

[X, Y] = meshgrid(2:30, 40:60);