Math 171 Spring 2005, Lab 15 (double lab)

Due Thursday, April 7, 11:59 P.M.

The purpose of this lab is to give you additional practice using functions in in Fortran, and to introduce you to using modules.

Write a program called newtmeth that implements Newton's method. Your program should be structured as follows:

You should implement Newton's method in a function called newt that takes as its arguments an initial guess for the root, the name of the function to which Newton's method should be applied, and the name of its derivative. The return value of the function should be the approximated root.
You should test your function by using it to approximate pi and the square root of two by solving for zeros of the appropriate functions.
You should return from your function when two successive approximations to a root differ by less than a specified cutoff value stored in a parameter variable called tol. You will need to experiment with various values for tol to determine the smallest value that for which convergence still occurs.
The tol variable and all your functions should be contained inside a module used by your main program.

When passing the names of functions contained in a module used by your main program, you should not redeclare the functions using the EXTERNAL keyword. This is redundant with the definition you have given in the module.
When passing the names of Fortran intrinsic functions, you should declare the function names using INTRINSIC rather than EXTERNAL.