1.
Find all the real roots of
x4+3x3-1=0.
Can you find complex roots with your code? Show us how.
2. Calculate the first three positive roots of
x = 2 tan x.
This equation arises in calculating the exponential decay rates of certain modes of motions
(called eigenmodes) of an incompressible viscous fluid contained between two long
parallel walls.
3.
Compute 
as we did in class but this time using a series of ever finer polygons
on the outside of the circle. Your algorithm should be numerically stable,
we do not want to have the catastrophic roundoff error problems that we experienced
in class!