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## Other Plot Routines

There are other types of plot routines that are useful for analyzing functions of two variables:

contourplot
To plot the level sets or contours of a function on a domain in the plane:
```        contourplot(f(x,y),x=a..b,y=c..d);
```
For example,`contourplot(-x^4+2*x^2-y^2,x=-1.6..1.6,y=-1.6..1.6);` It is sometimes useful to tack an option like contours=40 onto the end of the contourplot command.

Note that smoother curves can be obtained by including a specification for the `grid` parameter of the form

```        contourplot(f(x,y),x=a..b,y=c..d,grid=[k,k]);
```
where k is an integer. The default value of k is 25.

Notice that a contour plot is a three dimensional plot of the level curves of the function viewed from above. You can see this by rotating the plot as you did with 3D graphics.

densityplot
To plot a density plot of a function on a domain in the plane, use:
```        densityplot(f(x,y),x=a..b,y=c..d);
```
In contrast with the contour plot, the density plot in Maple is a 2D object and cannot be rotated in space. For example, `densityplot(-x^4+ 2*x^2-y^2,x=-1.6..1.6,y=-1.6..1.6);`

display
This is a very powerful command because it allows you to combine two plots into one. It works with both plot and plot3d images. For example,
```	Plot1 := plot(cos(x),x=-Pi..Pi, color=red): #Note the suppressed output
Plot2 := plot(1 - x,x=-Pi..Pi, color=green):
display({Plot1, Plot2});
```

To plot the gradient vector field of a function over a domain, use
```        gradplot(f(x,y), x=a..b,y=c..d);
```
For example, the gradient vector field corresponding to the function is a vector field in which all vectors point radially outward from the origin: `gradplot(x^2+y^2, x=-1..1,y=-1..1);`

fieldplot
To plot a vector field over a domain, use
```        fieldplot([f1(x,y),f2(x,y)], x=a..b,y=c..d);
```
For example, the vector field corresponding to the differential equation for a simple harmonic oscillator is plotted by `fieldplot([y,-x], x=-1..1,y=-1..1);`

Bob Hesse
Wed Oct 23 21:17:40 CDT 1996