CPSC 244 Project 6
Spring 2009
7 April 2009
Programming with Functions
ASSIGNED: 7 April 2009
DUE: 21 April 2009 (by the end of class.)
VALUE: 54 points
Overview: In this project you will complete programming problems related to Chapter 6
material. For ALL programs
•Use double precision reals by using REAL(KIND=8) when declaring variables. Also, print
out all real variables with six digits of precision.
•Test the input to ensure that the values are appropriate for the problem you are
solving. For example, for integration problems, you should at minimum require that
b > a. (Note: You may be required to check for other conditions given the specific
circumstances of the problem.)
Tasks:
1. (6 points each) The normal distribution is described by the function
1
σ√2πe−
1
2(x−µ
σ)2
,
where σis the standard deviation, and µis the mean. If we set z= (x−µ)/σ and let
σ= 1 we get a function (which we will integrate)
y(z) = 1
√2πe−
1
2z2(1)
which when integrated from −∞ to ∞should equal 1.
(a) Integrate Eqn. (1) using the trapezoid rule (as discussed in class). Use an internal
function to calculate needed values of y(z). Input values for a,b, and the number
of iterations n. Name this program Chap6_T1a.f90.
(b) Integrate the function y(x) = 1/x using the trapezoid rule. Use an internal func-
tion to calculate needed values of y(x). Input values for a,b, and the number of
iterations n. Also, compare your answer to the exact value of the integral (using
the intrinsic LOG(x) function). Name this program Chap6_T1b.f90.
1
