Copyright © 1997 by James F. Hurley, University of Connecticut, Department of Mathematics, U-9, Storrs CT 06269-3009. All rights reserved.

*Mathematica*'s built-in Plot3D command is a good tool for plotting a surface that is the graph of *z = f(x, y)*, for a continuous function *f*. The following short routine illustrates this for the graph of *z = *+ 4. As usual, to generate the plot, position the cursor at the end of the last blue line, and press the Enter key, or depress the Shift key and the Return key simultaneously.

**(* ***Mathematica*** Routine to plot graph of a surface **

Plot3D[ F[x, y], {x, -3, 3}, {y, -3, 3},

AxesLabel -> {"x", "y", "z"} ]

The following more elaborate routine first generates the same plot that the above routine produces, and then gives a second plot with coordinate axes (in red). In using this routine to make your own plots, some adjustment of the input intervals [*a, b*] along the *x*-axis, [*c, d*] along the *y*-axis, and [*e, f*] along the *z*-axis may be necessary to produce a good plot and worthwhile axes. To do that, change the part of the routine that draws the coordinate axes.

**(* ***Mathematica*** Routine to plot graph of a surface **

b := 3;

c := -3;

d := 7;

e := -9;

f := 10;

plainplot = Graphics3D[

Plot3D[ F[x, y], {x, -3, 3}, {y, -3, 3},

AxesLabel -> {"x", "y", "z"} ]

];

coordaxes = Graphics3D[{

{RGBColor[1, 0, 0],

Line[{{a, 0, 0}, {b, 0, 0}}],

Text["x", {b + .3, 0, 0}]},

{RGBColor[1, 0, 0],

Line[{{0, c, 0}, {0, d, 0}}],

Text["y", {0, d + 1, 0}]},

{RGBColor[1, 0, 0],

Line[{{0, 0, e}, {0, 0, f}}],

Text["z", {0, 0, f + 5}]}

}];

Show[plainplot, coordaxes]

Converted by