Math 3 --- Fortran

Homework Assignments

Instructor: David Arnold

Homework Assignments

Assignments and activities will be accumulated on this page as we progress through the semester.

Spring 2003

Here are the homework assignments for the Spring semester, 2003.

Assignment #1

Bring a CD to my office in order that I might burn on the CD all the software needed for this course.
After installing Emacs on your home computer, or working in the lab at school, work through the Emacs tutorial while sitting at the computer.
Use Emacs to make a copy of the program file sieve.f90 passed out in class. Obtain a printout and hand in.
I strongly encourage you to work through the Linux tutorial found at http://www.ee.surrey.ac.uk/Teaching/Unix/. From time to time throughout the semester, peck away at this tutorial.

Assignment #2

This week's assignment is to write a program to compute the roots of a quadratic equation using the quadratic formula. You can download the activity and a complete description of the assignment at: http://online.redwoods.cc.ca.us/instruct/darnold/fortran/activities/Project1QuadraticFormula/project1.pdf I am extremely curious how this pdf file will print on a variety of different systems. If you experience any weird font difficulties, either onscreen or when printing, please report them to me immediately at David-Arnold@Eureka.redwoods.cc.ca.us. LaTeX source code for this project is also available at: http://online.redwoods.cc.ca.us/instruct/darnold/fortran/activities/Project1QuadraticFormula/project1.tex

Assignment #3

This assignment uses Newton's Method to find the zeros of a function. You can download the activity at http://online.redwoods.edu/instruct/darnold/fortran/activities/newtonsmethod/newton.pdf. Latex source code is available at http://online.redwoods.edu/instruct/darnold/fortran/activities/newtonsmethod/newton.tex. The Metapost file to create the graphics in this document are also available. http://online.redwoods.edu/instruct/darnold/fortran/activities/newtonsmethod/newton.mp. Gnuplot was used to export Figure 3 of the document as Metapost code. The resulting graphics needed to compile the document follow.
This document was compiled using pdflatex with the command pdflatex newton.

Assignment #4

This assignment builds on the previous assignment #3. In this activity, we code Newton's Method as a subroutine. This is a useful technique for storing important pieces of code for reuse in larger programs. You can download the activity at: http://online.redwoods.edu/instruct/darnold/fortran/activities/NewtonSubroutine/newton.pdf
Latex code is available at:
http://online.redwoods.edu/instruct/darnold/fortran/activities/NewtonSubroutine/newton.tex
This document was compiled with the command pdflatex newton.tex

Assignment #5

This assignment uses the bisection method to find the roots of a polynomial. You can download the activity at: http://online.redwoods.edu/instruct/darnold/fortran/Activities/BisectionMethod/bisect.pdf
Latex code is also available: http://online.redwoods.edu/instruct/darnold/fortran/Activities/BisectionMethod/bisect.tex
Graphics files are also available:
The file was compiled using pdflatex

Assignment #6

This assignment uses Newton's Method to find the basin of attraction for the root z=1 of z=1. The assignment then calls for the student to color three basins of attraction, one in red for initial guesses that converge to one root of z³=1, in green for initial guesses that converge to the second root of z³=1, and in blue for initial guesses that converge to the third root of unity. Matlab is used to create the final image. http://online.redwoods.edu/instruct/darnold/fortran/Activities/NewtonCubeRootUnity/cuberoot.pdf
Latex code is also available: http://online.redwoods.edu/instruct/darnold/fortran/Activities/NewtonCubeRootUnity/cuberoot.tex
Graphics files are also available:
The file was compiled using pdflatex

Assignment #7

This assignment requires the student to write subroutines that will solve upper and lower triangular systems. http://online.redwoods.edu/instruct/darnold/fortran/Activities/TriangularSystems/TriangularSystems.pdf
Latex code is also available: http://online.redwoods.edu/instruct/darnold/fortran/Activities/TriangularSystems/TriangularSystems.tex
The file was compiled using pdflatex

Assignment #8

This assignment requires the student to write subroutines that will solve systems using Gaussian elimination with partial pivoting. http://online.redwoods.edu/instruct/darnold/fortran/Activities/LinearSystemsII/LinearSystemsII.pdf
Latex code is also available: http://online.redwoods.edu/instruct/darnold/fortran/Activities/LinearSystemsII/LinearSystemsII.tex
The file was compiled using pdflatex

Assignment #9

This assignment works with matrix operations and requires the writing of a subroutine to perform matrix multiplication. http://online.redwoods.edu/instruct/darnold/fortran/Activities/MatrixOps/MatrixOps.pdf
Latex code is also available: http://online.redwoods.edu/instruct/darnold/fortran/Activities/MatrixOps/MatrixOps.tex
The file was compiled using pdflatex

Assignment #10

This assignment solves diagonally dominant systems using Jacobi iteration. http://online.redwoods.edu/instruct/darnold/fortran/Activities/JacobiIteration/JacobiIteration.pdf
Latex code is also available: http://online.redwoods.edu/instruct/darnold/fortran/Activities/JacobiIteration/JacobiIteration.tex
The file was compiled using pdflatex

Assignment #11
- Adjust the program of Assignment #10 so as to use Gauss-Seidel iteration. Save this program in assign11/gauss_seidel_iteration.f90. Your program should accomplish this goal by writing a subroutine called gauss_seidel and including it in a module.
Assignment #12

This assignment uses numerical routines to approximate a definite integral. Routines used are left endpoint, right endpoint, and midpoint methods. http://online.redwoods.edu/instruct/darnold/fortran/activities/integration/integration.pdf
The Latex source file is available. http://online.redwoods.edu/instruct/darnold/fortran/activities/integration/integration.tex
Metapost code for the figures are available. Figures were changed to pdf with the mptopdf program.
The Latex file was compiled with pdflatex using these figures.
Add two new functions to the integration module, one for the trapezoid method and one for Simpson's method. Explanation of these techniques are given in the following links.
- http://online.redwoods.edu/instruct/darnold/Math50B/CalculatorPrograms/trap.pdf
- http://online.redwoods.edu/instruct/darnold/Math50B/CalculatorPrograms/simp.pdf

Assignment #13

This assignment shows the technique for finding an interpolating polynomial for a given set of data points. http://online.redwoods.edu/instruct/darnold/fortran/activities/interpolatingpolynomial/interpolating.pdf
The Latex source file is available. http://online.redwoods.edu/instruct/darnold/fortran/activities/interpolatingpolynomial/interpolating.tex
The Latex source code was compiled using pdflatex and these figures.

Assignment #14

Sir William Rowan Hamilton presented his paper On Quaternions to the Royal Irish Academy in 1843. Since then, the quaternions have played an instrumental role in abstract algebra and physics, to name a few subjects. This week's assignment is to write a program that performs Quaternion arithmetic, scalar multiplication, addition, subtraction, multiplication, conjugation, and division. http://online.redwoods.edu/instruct/darnold/fortran/activities/Quaternions/Quaternions.pdf

Assignment #15

This week's assignment uses a numerical technique to solve the boundary value problem y''=y, y(0)=1, y(1)=-1. Using the central difference formula for the second derivative, a partition on the interval [0,1] results in a triangular system of n equations in n unknowns. The system is solved using one of the LAPACK routines, sgtsv, which is available in the LAPACK repository located at http://www.netlib.org/lapack/. You will want to download the file sgtsv.f and its dependencies at http://www.netlib.org/lapack/single/. Alternatively, you can download the files from our server at nelibfiles.zip. After downloading the files, extract them to the folder fortran/assign15>.
Download the activity at the following url. http://online.redwoods.edu/instruct/darnold/fortran/activities/make/Makefiles.pdf
Source code for the activity is available.
The file Makefiles.tex was compiled using pdflatex.

Spring 2002

Assignment #1

Bring me a CD and I will copy the software needed for Fortran onto the CD. This will save immense downloading times. Also, there are instructions on the CD for installing the software. After that, complete the Emacs tutorial on the help menu.

Assignment #2

Install Emacs on your home system. Use the Emacs software to make a copy of the handout distributed in class. I would strongly urge you to first visit the info files on Fortran-mode. Press C-h i to open info. Select the Emacs menu and hit Enter. Scroll down (immense) to the Fortran menu and hit Enter. Try some of the suggestions given in the help for Fortran mode. You will not understand nor will you need everything that is here. Use the parts that make sense and help you accomplish what you need to do. Emacs is a lifelong learning process, so don't try to learn it all at once.
Download http://www.star.le.ac.uk/~cgp/prof77.ps . Read pages 1-30. You'll need to open this in GSView, so first install Ghostscript, then GSView from the software CD.

Assignment #3

Another excellent resource for Fortran programmers is:

http://www.kcl.ac.uk/kis/support/cit//fortran/f77book.pdf

This week's assignment is to write a program to compute the roots of a quadratic equation using the quadratic formula. You can download the activity and a complete description of the assignment at:

http://online.redwoods.cc.ca.us/instruct/darnold/fortran/activities/Project1QuadraticFormula/project1.pdf.

David-Arnold@Eureka.redwoods.cc.ca.us

http://online.redwoods.cc.ca.us/instruct/darnold/fortran/activities/Project1QuadraticFormula/project1.tex.

Assignment #4

This week's assignment is to create an amortization table to track the progress of a homeowners mortgage. You can download the activity at:

http://online.redwoods.cc.ca.us/instruct/darnold/fortran/activities/AmortizationTable/AmortizationTable.pdf.

http://online.redwoods.cc.ca.us/instruct/darnold/fortran/activities/AmortizationTable/AmortizationTable.tex.

Assignment #5

This week's assignment uses subroutines to swap integers. You can download the activity at:

http://online.redwoods.cc.ca.us/instruct/darnold/fortran/activities/ModularProgramming/modular.pdf.

http://online.redwoods.cc.ca.us/instruct/darnold/fortran/activities/ModularProgramming/modular.tex.

Debugging Activity

This is not a homework assignment. Rather, this is an activity that we will perform in class tonight using the GNU debugger. This is a short tutorial on how to use the GNU debugger, which is useful for finding run-time errors in programs that compile successfully, but produce unexpected results at run-time.

Debugging activity in pdf format.

Debugging activity in tex format.

Assignment #6

In Interactive Fortran 77, by Chivers and Sleightholme, read chapters 7 and 8 on arrays and do loops.
Write a program to find the average of the 100 integer scores in the file scores.txt. Use modular programming to construct this project; that is, break the project up into small subroutines to accomplish each task. You will find a full description of the assignment in the activity:

http://online.redwoods.cc.ca.us/instruct/darnold/fortran/activities/SortingLists/SortingLists.pdf.

http://online.redwoods.cc.ca.us/instruct/darnold/fortran/activities/SortingLists/SortingLists.tex.

There are a number of nice refinements you can make to this program. For example, can you assign letter grades based on the test score and print them out in a column next to the test score?

Assignment #7

This week's assignment is called counting characters. You will find a full description of the activity at:

Activities/CountingCharacters/CountingCharacters.pdf

You will also need the data in this file:

Activities/CountingCharacters/raven.txt

Assignment #8

This week's assignment is an introduction to the F compiler. You are also going to write a program that will find the integral of a function. You will find a full description of the assignent in the activity:

http://online.redwoods.cc.ca.us/instruct/darnold/Fortran/activities/Fortran90/Fortran90.pdf

You can also find a link to compile.el here:

http://online.redwoods.cc.ca.us/instruct/darnold/Fortran/Resources/compile.el

Assignment #9

http://online.redwoods.cc.ca.us/instruct/darnold/Fortran/actvities/Fortran90subroutines/anatomy.pdf

http://online.redwoods.cc.ca.us/instruct/darnold/Fortran/actvities/Fortran90subroutines/anatomy.tex

Assignment #10

This week's assignment uses Euclid's Algorithm to find the greatest common divisor of two integers. Once that is accomplished, it is a simple matter to find a common denominator and add two fractions.

http://online.redwoods.cc.ca.us/instruct/darnold/fortran/activities/gcd/gcd.pdf

The tex file can also be downloaded.

http://online.redwoods.cc.ca.us/instruct/darnold/fortran/activities/gcd/gcd.tex

Assignment #11

This week's assignment is to write a program to estimate an infinite series. You will be given the exact solution and will be asked to report the absolute and relative error of the approximation.

http://online.redwoods.edu/instruct/darnold/fortran/activities/kindparameters/kind.pdf

The tex file can also be downloaded.

http://online.redwoods.edu/instruct/darnold/fortran/activities/kindparameters/kind.tex

Assignment #12

This week's assignment is to write a program to estimate an an integral using a Monte Carlo Simulation. This involves generating random numbers and throwing darts at a target in a random fashion. This is a work in progress at the moment.

http://online.redwoods.edu/instruct/darnold/fortran/activities/RandomNumbers/monte_carlo.pdf

The tex file can also be downloaded.

http://online.redwoods.edu/instruct/darnold/fortran/activities/RandomNumbers/monte_carlo.tex

Assignment #13

This week's assignment is to write a program to solve an upper triangular system of equations using Back Substitution.

http://online.redwoods.edu/instruct/darnold/fortran/activites/LinearSystems/linearsystems.pdf

The tex file can also be downloaded.

http://online.redwoods.edu/instruct/darnold/fortran/activites/LinearSystems/linearsystems.tex

You will also need to download the data files containing system1.dat and system2.dat.

http://online.redwoods.edu/instruct/darnold/fortran/activites/LinearSystems/system1.dat

http://online.redwoods.edu/instruct/darnold/fortran/activites/LinearSystems/system2.dat

Assignment #14

This week's assignment is to write a program to play an arbitrary system in upper triangular form, using Gaussian elimination both with and without pivoting.

http://online.redwoods.edu/instruct/darnold/fortran/activites/LinearSystemsII/linearsystemsII.pdf

The tex file can also be downloaded.

http://online.redwoods.edu/instruct/darnold/fortran/activites/LinearSystemsII/linearsystemsII.tex

Assignment #15

Sir William Rowan Hamilton presented his paper On Quaternions to the Royal Irish Academy in 1843. Since then, the quaternions have played an instrumental role in abstract algebra and physics, to name a few subjects. This week's assignment is to write a program that performs Quaternion arithmetic, scalar multiplication, addition, subtraction, multiplication, conjugation, and division.

http://online.redwoods.edu/instruct/darnold/fortran/activites/Quaternions/Quaternions.pdf

The tex file can also be downloaded.

http://online.redwoods.edu/instruct/darnold/fortran/activites/Quaternions/Quaternions.tex