Numerical Methods, MAT 350
Autumn 2001

Homework: Some Integration

Due Wednesday, October 24, 2001 in class

Many important functions can be defined in terms of integrals. In this homework, you will write a subroutine to perform numerical integration and use this routine to calculate a function. Note that the first part of the assignment is due earlier.

Your first task is to write a subroutine that performs numerical integration. The boys in the class will use the Extended trapeziodal rule and the girls will use the Extended Simpson rule.

This part of the assignment is due Friday, October 12.

Students, as denoted by their initials, will look at different functions:

For your function, you need to do the following:
  1. Find a definition of your function in terms of an integral. The Geneva College library has:
  2. Look up the behavior of your function in the limits z goes to zero and z goes to infinity. Print out or photocopy a graph of the function.
  3. Write a subroutine (in the same file as your main program), for the function to be integrated. For some of the functions, you will need to use a global variable to specify the value of z in your subroutine; in FORTRAN, you would use a COMMON block statement.
  4. Evaluate the integral for various values of n at the example point given above. How large must n be to obtain an error of 1.0E-2? How large must n be to obtain an error of 1.0E-5? How large must n be to obtain an error of 1.0E-8?
  5. We have discussed the error associated with both integration techniques. Do your results agree with this? Explain.
  6. Graph your function versus z; a suggested domain is given above. Use at least n=50 when calculating the necessary integrals.