Copyright © 1997, 2001 by James F. Hurley, University of Connecticut, Department of Mathematics, Unit 3009, Storrs CT 06269-3009. All rights reserved.

*Mathematica* has a built-in command to generate plots of the *level curves* of a function *f* of two variables. The basic form of the command is

ContourPlot[F[x, y], {x, xmin, xmax}, {y, ymin, ymax}]

where F[x, y] is an expression in the variables *x* and *y*, which range over the respective intervals [*xmin, xmax*] and [*ymin, ymax*]. For the function *f* with formula *f(x, y) = * + , with *x* and *y* each varying between --4 and 4, executing the following command produces curves corresponding to equally-spaced values of *z = f(x, y)*. (Recall to execute a command, position the cursor after the command and hit Enter at the lower right corner of the keyboard, or press the Shift and Enter keys together.)

** (* Command to plot level curves of ***f (x, y) = x^2* + *y*^2 *)

ContourPlot[x^2 + y^2, {x, -4, 4}, {y, -4, 4}]

The default output plots 10 level curves in shaded gray scale, with lighter shades corresponding to larger values of *z*. The following more detailed command plots five level curves without shading. Try it!

**(* ***Mathematica*** Routine to plot level curves of ***f (x, y) = x^*

Contours -> 5, ContourShading -> False]

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