These are the vector fields for the examples in the lecture notes done by computer with Maple. 

>	with(plots);

 

>	fieldplot([-y,x],x=-5..5,y=-5..5,arrows=slim,anchor=tail,fieldstrength=maximal(3),grid=[10,10]);

 

>	fieldplot([x-1,-y/2],x=-5..5,y=-5..5,arrows=slim,anchor=tail,fieldstrength=maximal(3),grid=[10,10]);

 

>

 

>	vf:=fieldplot([8*x,-2*y],x=-5..5,y=-5..5,arrows=slim,anchor=tail,fieldstrength=maximal(1),grid=[10,10]):

 

>	cp:=contourplot(4*x^2-y^2,x=-5..5,y=-5..5):

 

>	display(vf,cp);

 

>	fieldplot3d([-x,z,y],x=0..3,y=0..3,z=0..3,arrows=SLIM,fieldstrength=maximal(1));

 

>