15.1, 15.2 Level curves. Limits

You can generate the level curves of a function using Maple. Note that the command is "contourplots".

Here is an example that we discussed in class: the function .

> with(plots):

Warning, the name changecoords has been redefined

> contourplot(arctan(y/x),x=0.0001..1,y=0..2,contours=15);

One can also understand why the limit of the same function does not exist at (0,0) by looking at its graph.

> F:=plot3d([x,y,arctan(y/x)],x=0.001..2,y=0..2,style=wireframe,color=blue,numpoints=1000): display(F,axes=frame,labels=[x,y,z]);