Department of Computer Science

Numerical Calculus

Spring Semester 2012

Dr. Maury Eggen

For the fifth programming assignment of the semester we require tools which will assist us with numerical integration. Write functions which will implement the following methods:

1. Rectangles, left endpoints
2. Rectangles, right endpoints
3. Rectangles, midpoints
4. Rectangles, random points
5. Trapezoidal rule
6. Simpson's 1/3 rule
7. Simpson's 3/8 rule
8. Parallel versions of rectangles and trapezoidal rule.
9. Monte-Carlo integration

Each of the above assume that the function is known (we have a closed form formula for the function which we can evaluate). Each also assumes that we have equal subintervals over which the function is evaluated.

If the function is given in closed form, provide a general Monte Carlo integration method. Find a general way of putting the function in a box, and throwing darts at the box.

Work on your user interface and think about the integration of the packages provided so far into a working numerical methods software project. Be prepared to demonstrate in class.

You may test your programs on functions for which you know the value of the integral, but also test your programs on functions for which the value of the integral is unknown.