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.