While we can do some numerical integrations simply using only a few
points, or perhaps have only a few data points to base an integral off
of, frequently we will want to use 1000 subintervals -- and it gets a
little tedious entering all of those by hand!
So in lab we worked on using the Sum command in Mathematica to make our job easy.
Today I show off a number of examples, where we focus on the error
analysis.
- Given a fixed number of subintervals, what is the worst error
we could be making? And, perhaps more importantly,
- Given a tolerance, how do we choose the right number of
subintervals to make sure that our numerical estimates are good to
within that tolerance?
Finally I show that Simpson's gets cubic functions integrals exactly
right!