This week's reading is rather low key. First, most if not all of the information you need is in the assignment text. Failing that, a keyword search on wikipedia is a good start.
Most of you have already started using functions in Python. For those of you who haven't, this week's set requires you to.
To learn about functions, ask a friend, work it out yourself, or refer to Guido van Rossum's Python Tutorial.
Pay attention in particular at how functions are primitive objects in Python (in fact, everything is an object in Python). Thus, we could define a function evalinzero(f) which returns the value of another function for x = 0:
def evalinzero(f):
return f(0)
we then have
import math evalinzero(math.exp)
1.0
which works also for home-grown functions,
def xplusone(x):
return x+1.0
evalinzero(xplusone)
1.0
and even for lambda functions,
evalinzero(lambda x: x+1.0)
1.0
It should now be reasonably straight forward how functions work in Python. Similar to C, Fortran, Mathematica, Matlab, etc, though the syntax varies a bit.
Have a look at Riemann sums, the trapezoidal rule, and Simpson's rule. Other, more sophisticated schemes exist, including Gaussian quadrature. Mathematica uses a series of methods, including various forms of quadrature, to perform precise numerical integration.