Due Fri 6 Nov

This project has 5 parts. All plots need your name as part of the title.
Each plot is of one or more 2d vector fields F = <P(x,y),Q(x,y)>, and
the equation of the Vector Field needs to be in the title also. If
not otherwise given use the range -2..2 for both x and y.
Make sure to stable your pages.

Part 1. This part has several plots, but only one of the plots is to be
printed. Here P = k * y and Q = k * x for the three values of k = 1, 2, 8.
(Print the one that looks the best.)

Part 2. Minor changes in P or Q can make major changes in the "global look"
of the Vector Fields plot. Take P = -y, Q = x which just negates the P
term from part 1. 

Part 3. Take the vector field from part 2 and normalize the F an each point
and plot it. (that is replace F by F/|F| where |F| = length of F.)

Part 4. Actually most of any vector field looks very boring. Plot the
vector field of part 2 over some ranges like x=k..k+2,y=m..m+2 for 
(k,m)=(100,100), (200,100) and (100,200). Only print one of the three
plots, the one where the arrows are "most pointed up".

Part 5. The interesting parts of a vector field are near points where
the vector field is zero. (We have seen this before, y=f(x) does its
interesting things where f'(x) is zero.) There are only a certain number
of behaviors near a zero, we have seen two above. Look at F=<x,y>,
F=<-x,-y>, F=<-x,y>, F=<-x,0> and print the one that looks most like
an explosion.

The following are example maple commands.
with(plots);
p:=y:q:=-sin(x)-y/10:
fieldplot([p,q],x=-10..10,y=-3..3);