4. Contour Plots

Drawing the graph of a function $f(x,y)$

1. Take a point $(x,y)$ in the domain of $f$
2. Calculate $z=f(x,y)$
3. Plot all points $(x,y,z)$

Constructing a contour plot of a function $f(x,y)$

• Take a level on the 3 dimensional graph and your contour is there.

Level curves and contour maps

Definition

A level curve of a function $f$ of two variables is a curve in $R^2$ with equation $f(x,y)=K$, where $K$ is a constant (in the range of $f$). A plot with several level curves is called a contour map.