Python versions of what we have been doing:
New library: SciPy (Scientific Python)
Builds off Numpy
Contains lots of data analysis functions
Most of the functions in this library are translations of very old
Fortran functions.
Python (and MATLAB) allows you to write a function in one language
(Fortran, C, C++, etc.) and call it from Python.
Goal
Estimate the value of a definite integral
The approach taken depends on what we know about the function
If we know the function, using the integral function is
generally going to be the best approach becase we don't need
to worry about whether the table of values has enough points
to gurantee a desired accuracy.
If we only have a table of values, we have options, but the
simplest approach would be to create the spline and integrate
that.
funints.py
Demonstrates how to estimate integrals using the quad function
when you know the function.
tableints.py
Assumes you only know a table of values
Demonstrates how to use the trapezoidal and Simpson's rule
functions in the SciPy library.
splineints.py
Demonstrates how to build a spline, evaluate the spline at a given
number of points, integrate the spline.
There are also routines for derivatives and roots of splines to estimate
these for the function in the table.