%%  Graphs of a function of 2 variables - simple cases

%% EZ ways
% You can plot the graph of a function of 2 variables using *ezsurf*.
% For example, here's plot the graph of 
%%
% 
% $$f(x,y) = \sin(x)\cos(y).$$
% 

syms x y
f = sin(x)*cos(y)
ezsurf(f)

%%
% If you want to specify the ranges of values of x and y instead of letting
% MaTLAB choose, you can.  Here x goes from -10 to 10 and y goes from -3 to
% 3.  (For this particular function, it's actually better to use the same
% range for x and y.)

ezsurf(f,[-10,10,-3,3])

%%
% You can use *ezcontour* to get a contour or level curve plot.

ezcontour(f)

%%
% or if you want to specify the ranges of values for x and y

ezcontour(f,[-10,10,-3,3])

%% A more complicated way
% This is useful if you want more control over the plots or don't have 
% access to the syms command
%
% First, define the coordinate grid.  Be sure to put the ; at the end of
% the command.  Otherwise MATLAB will print the list of all of the x and y
% values for points in the grid.

[X1,Y1] = meshgrid(-2*pi:0.2:2*pi,-2*pi:0.2:2*pi);

%%
% Now define the function.  Remember you have to use .* for multiplication
% because you are working with vectors.
 
Z1 = sin(X1).*cos(Y1);

%%
 

surf(X1,Y1,Z1)

%%

contour(X1,Y1,Z1)