eigen values graphing
imaginary:
theta > 0 spiral OUT, unstable
theta <0 spiral IN, asymptotically stable
if only the imaginary, its in the center, and its stable
r1 and r2 both positive = node unstable
r1 and r2 both negative = node, asymptotic ally stable
1 positive and 1 negative = saddle point, unstable
r1=r2>0, unstable, node
r1=r2<0, asmptotically stable
section 9.3.
let dx/dt=F(x,y) dy/dt=G(x,y)
find crit. pts. set dy/dt=0 and dx/dt=0
then use linear approx. (dF/dx dF/dy )
( dG/dx dG.dy )
plug in the crit. pts,
then find the eigen values and vectors
and do the same thing for all the crit. pts.
then graph it, and move the graph according to the crit. pts.