Computer Science 1107
AN INTRODUCTION TO FORTRAN PROGRAMMING FOR SCIENTISTS AND ENGINEERS

Fall 2001

Objective: To explore writing FORTRAN 77 programs using functions and subroutines. All functions used should return a single value without changing argument values, and subroutines should only return values by changing the values of the arguments as discussed in class.

A. Text Problem 8, Page 364.

1. Use functions for all of the equations given in the problem. If you find it useful, you may use or modify portions of the trapezoid approximation program which we developed in class. Here is the trapezoid approximation program.

2. Create a hand-drawn flow chart for the entire program using the appropriately shaped boxes for start-stop, Input/Output, and computation as discussed in class OR write out the algorithm for the entire program using pseudocode which should be written out by hand, not typed.

3. Write the FORTRAN program, naming the source code file lab8a.f and including an explicit list of all variables as well as a short description of the problem in a documentation section using comment lines at the beginning of the program. Be careful to choose the types of your variables appropriately and to include the names and student numbers of all authors in the documentation section. If you use or modify the code provided above, be sure to note this in your documentation.

4. Check your results before creating your script file.

B. Dice Problem and Randomness.

1. Do not make a script file for the exploratory portions (1-5) of this problem.

2. Save the program dice.f into your itlabs account. Compile this and run it.

3. This program is designed to simulate a pair of dice rolling. With two fair dice, the expected probabilities are 1/36 for each of the following 36 outcomes:
   (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),
   (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),
   (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),
   (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),
   (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),
   (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6).
   This means that the probability of rolling a pair (or spot) that sums to 10 is 3/36 = 1/12 since the sum of 10 can be obtained by rolling (4, 6), (5, 5), or (6, 4).

4. Run dice.f sufficiently many times with sufficiently high numbers of rolls to discuss in a few paragraphs how "random" the random number generator is in this program. As you increase the numbers of rolls, do the probabilities seem to be approaching the expected probabilities?

5. Edit the program and comment out the PRINT line which prints each roll of the dice, and then recomplile the program.

6. For this problem, you do not need to include the program code or the compilation in your script file--just include the runs. Begin the script file and run your edited program sufficently many times to demonstrate the reasonableness of your conclusions.

C. Text Problem 22, page 464.

"Use your program to compute the voltage (not current) passing through the capacitor as described in Exercise 8 of Section 6.4." Use your program to find the voltage for a capacitance C of 5 F and a time interval T of 4 seconds.

In this problem, you may use subroutines and functions from either of the previous two problems, but it is required that you write at least one new subroutine to do the Monte Carlo integration.

1. Create a hand-drawn flow chart for the program using the appropriately shaped boxes for start-stop, Input/Output, and computation as discussed in class OR write out the algorithm for the entire program using pseudocode which should be written out by hand, not typed.

2. Write the FORTRAN program, naming the source code file lab8c.f and including an explicit list of all variables as well as a short description of the problem in a documentation section using comment lines at the beginning of the program. Be careful to choose the types of your variables appropriately and to include the names and student numbers of all authors in the documentation section.

3. Check your results before creating your script file.

   Then hand in the following for each of the three problems:

   • All required flow charts OR pseudocode.
   • A script file containing all of the following as required:
   • A printout of the source program obtained by using the UNIX cat command
   • A compilation of the program obtained by using the f77 command
   • Results of execution the program with the given data sets obtained by using a.out
   • The discussion from problem B.
   • A paragraph discussion regarding the utility of subprograms, namely functions and subroutines.

Recall: For this and all programming assignments you should follow good software engineering principles including using good structure, documenting your program with comments, and using meaningful names for variables. Failure to do this will lead to reduced credit.

For this and subsequent assignments, you have the option of working in teams of two people. In this case, turn in one copy of your results with both names and student numbers included on every page of every item submitted.