Examples of Contour Plots (Level Curves)

Dr. K. G. TeBeest

> with( plots ) :

Warning, the name changecoords has been redefined

Plot the paraboloid

> f := x^2 + y^2 ;

> plot3d( f, x = -4 .. 4, y = -4 .. 4, style = patchcontour, axes = framed ) ;

Plot the contour plot (level curves) of the same paraboloid. Let's plot the level curves

> contourplot( f, x = -4 .. 4, y = -4 .. 4, contours = [0,1,2,3,4,5,6], scaling = constrained, color = blue ) ;

Plot the hyperbolic paraboloid

> f := y^2 - x^2 ;

> plot3d( f, x = -4 .. 4, y = -4 .. 4, style = patchcontour, axes = framed ) ;

Plot the contour plot (level curves) of the same hyperbolic paraboloid.

> contourplot( f, x = -4 .. 4, y = -4 .. 4, scaling = constrained ) ;

Plot the function

> f := - x * y * exp(-x^2-y^2) ;

> plot3d( f, x = -3 .. 3, y = -3 .. 3, axes = framed, grid = [41,41] ) ;

Plot the contour plot (level curves) of the same surface with the number of contours set to 12.

> contourplot( f, x = -3 .. 3, y = -3 .. 3, scaling = constrained, grid = [51,51], color = blue, contours = 12 ) ;

Plot the function

> f := exp( -(x^2+y^2) / 10 ) * cos( x^2+y^2 ) ;

> plot3d( f, x = -3 .. 3, y = -3 .. 3, axes = framed, grid = [41,41] ) ;

Plot the contour plot (level curves) of the same surface with the number of contours set to 8.

> contourplot( f, x = -3 .. 3, y = -3 .. 3, scaling = constrained, grid = [51,51], color = blue, contours = 8 ) ;

Dr. K. G. TeBeest
Applied Mathematics
Kettering University