Example 10.1.1
Define    as a Maple function and sketch its graph.

>	f:=(x, y)->x^2*sin(y);

>	plot3d(f(x, y), x=-2..2, y=-10..10, style=patch, labels=[x,y,z], grid=[20,80]);

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Example 10.1.2
Sometimes graphing routines have difficulties with surfaces that have vertical tangent planes.  For instance try to plot the graph of .

>	f:=(x,y)->sqrt(5-2*x+3*y);

>	plot3d(f(x,y), x=-3..3, y=-3..3, orientation=[-20,60], labels=[x,y,z]);

A way to remedy this problem is to parametrize this surface in such a way that one of the parameters is constant along the line , where the vertical tangent plane occurs.  For instance let    and use x and s as parameters.

>	eq:=op(1, f(x,y))=s; rr:=isolate(eq, y);

>	plot3d(subs(rr, [x,y,f(x,y)]), x=-3..3, s=0..10, orientation=[-20,60], labels=[x,y,z]);

Example 10.1.3
Define  as a Maple function and evaluate .

>	g:=(x, y, z)->x+y^2+z^3;

>	g(sqrt(2), Pi, exp(1));

Example
Create a contourplot for the function , first by using contourplot , then by using contourplot3d .

>	f:=(x, y)->x^2*sin(y);

>	contourplot(f(x, y), x=-2..2, y=-10..10, numpoints=3600);

The advantages of using contourplot3d instead of contourplot are that the contourplot3d is faster and allows for more detailed color control.  the color control allows the user to identify high levels (red) and low levels (purple).

>	contourplot3d(f(x, y), x=-2..2, y=-10..10, shading=ZHUE, axes=boxed, orientation=[-90, 0], numpoints=2500);

A similar picture can be obtained by using the plot3d   command with a style=patchcontour  option.

>	plot3d(f(x, y), x=-2..2, y=-10..10, shading=ZHUE, style=patchcontour, axes=boxed, orientation=[-90, 0], numpoints=2500);

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