November 1, 2007 --- Class 19 --- Numerical Integration in One Dimension

	Numerical Integration

	We talked about some of the standard methods for numerical
	integration in one dimension.  This is discussed in Section 11.1
	of CSM.  Additional material is available in Numerical Recipes
	or in Abramowitz and Stegun.  We compared the accuracy of
	various methods like the rectangle rule, trapezoid rule and
	Simpson's rule.  We indicated how Simpson's rule can simply
	be derived from removing the leading 1/N^2 error in the trapeziod
	rule with N and 2N points.  This technique can be extended in 
	the method known as Romberg integration.  The previous two points are
	expanded upon in Numerical Recipes.  Practical codes may be found
	there.