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Level curves.

It is generally hard to draw a picture of the graph of a function of two variables. Sometimes, we need to draw level curves; just remember the level curves on a map, in geography.

Take a function f of two variables x and y, defined on a doamin D. For a real number k, the curve of level k, denoted $\mathcal{C}(k)$ is the set of all the points in D such that f(x,y)=k.

Example 4.3   Let f(x,y)= x2+y2.

Figure 2: Cylinders.
\mbox{\subfigure[the graph]{\epsfig{file=Paraboloid.eps,height=4c...
...igure[level curves]{\epsfig{file=LevelCurves1.eps,height=4cm} }

Noah Dana-Picard