Level Curves and Surfaces The graph of a function of two variables is a surface in space Pieces of graphs can be plotted with Maple using the command plot3dFor example, to plot the portion of the graph of the function f(x,y)=x 2 y 2 corresponding to x between 2 and 2 and y between 2 and 2, type > with (plots);LEVEL CURVES The level curves (or contour lines) of a surface are paths along which the values of z = f(x,y) are constant;In your last example, if $z$ is constant then so is $x^2y^2$ This should look familiar, as the level curves for that are hyperbolas If you want to improve, first get comfortable with the conic sections (points, lines, double lines, circles, ellipses, parabolas, and hyperbolas) You could then move on to more complicated ones
Calculus Iii Functions Of Several Variables
