CS 270 Home Page
Introduction to Numerical Computation
Spring 2010
This course has two main goals: to teach the student the basics of
programming in the Fortran 95 language and to use that language to find
numerical solutions to mathematical problems, especially problems of
interest in science and engineering. In order to do this, a good deal of time is spent on
studying elementary numerical analysis. Good software
engineering techniques are emphasized in the programming portions of the course.
Mathematica and hand calculators are used to help in solving several types of numerical analysis problems.
However, the Fortran work that forms the bulk of the course is done on the CIS department's Linux server.
You can access this server from any of the CIS lab PCs or from your PC in the dorms if you get appropriate
software (such as SecureCRT, TeraTerm, or PuTTY) as described on the
server usage page.
Off campus access is sometimes possible. See Br. David to investigate that possibility.
Meeting Times
- Tue, Thurs 8:30 - 9:45 am, Physics 01 (CIS lab)
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Further Information
- The Course Syllabus
- Tentative Course Schedule
- Grading Guidelines
- CIS Lab Schedule
See when you can use the lab to do your homework.
- mathworld.wolfram.com
Contains a wealth of resources,
including some on numerical methods.
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Dr. Botsko's Mathematica Web Page
- Wolfram Mathematica Learning Center
- Information on UNIX Editors
- For information on available commands on our Linux server, enter the following
at the comand prompt:
topic
topic 12
- See the Server Usage page
For information about our server and the software you can use to access it.
- The easiest way to compile a Fortran 90 program on our Linux system is as follows,
where we assume that the program is named
series.f90:
build90 series
The build90 script will link in the library of numerical subroutines if needed. It
will put the executable in a file with the name series (without the .f90).
You then run the program by entering ./series at the command prompt.
- Information on Well-known Series
- Power Series
- Of interest especially to engineering students:
- Fortran programs:
Anyone can copy these examples when viewing them in a browser. Students in this class
can also copy them at the commmand line as in the following two examples:
cp /home/cs270/trap1.f90 . (The dot is necessary. It represents the current directory.
Thus we will copy the file to the current directory. The filename will stay the same.)
cp /home/cs270/convert.f90 myconvert.f90 (This will copy to a new filename in
the current directory.)
- aboveavg.f90
Illustrates the use of a 1-dimensional array.
- arith1.f90
Prints the largest integer, the largest plus 1, etc.
- arith2.f90
Tries division by zero, etc.
- arith3.f90
Experiments with adding large and small numbers, as well as adding in different orders.
- arith4.f90
Reports on characteristics of integers and reals.
- arith5.f90
Reports on characteristics of integers
and reals of various kinds.
- average1.f90
Averages a list of numbers with 0 used to end data entry.
- average2.f90
Uses a WHILE loop to solve the same problem.
- bsectst1.f90
Uses bisection algorithm to find a zero of a function.
- bsectst2.f90
- bsectst3.f90
- convert.f90
Simple program to convert from Fahrenheit to Kelvin.
- deriv1.f90
Program to compute a derivative at a point.
- epsilon1.f90
Estimates the machine epsilon.
- epsilon2.f90
A minor variation on the previous program.
- epsilon3.f90
Shows how to use a subroutine.
- factorial.f90
Prints the factorial of each nonnegative integer entered.
- integ3.f90
Uses the numerical subroutine library to integrate sin(x) from 0 to pi.
- leqtest.f90
Uses Gaussian elimination with partial pivoting to solve a system of linear equations.
- leq.in
Input data file for the previous program.
- linear1.f90
Uses a library subroutine to solve a system of linear equations.
- linear2.f90
Solves a system of 3 linear equations in 3 variables via simple-minded elimination
and back substitution.
- looptest.f90
Finds the limits for integer and real loop control variables.
- machine1.f90
Looks up and prints the values of various machine constants.
- machine2.f90
Looks up and prints the values of some other machine constants.
- maxmin.f90
Finds where max and min are in a list of integers.
- multiply1.f90
Simply multiplies two numbers.
- multiply2.f90
Prints some products and quotients.
- newton3.f90
Uses Newton's method for finding a zero of a function.
- newraph3.f90
Uses Newton-Raphson method for finding a zero of a function.
- ode1.f90
Solves an ordinary differential equation via Euler's method.
- ode2.f90
Solves another ordinary differential equation via Euler's method.
- ode3.f90
Uses Taylor's series to solve an ordinary differential equation.
- ode4.f90
Uses Taylor's series to solve another ordinary differential equation.
- quadeq1.f90
Solves a quadratic equation via the quadratic formula.
- readfile.dat
Data file to accompany the following program.
- readfile.f90
Shows how to read numbers from a formatted file.
- series1.f90
Finds a partial sum of the series 1+ 1/2 + 1/4 + 1/8 +...
- series2.f90
Finds sin(x) for a particular value x by using the power series for sin(x).
- series3.f90
Uses an array so that terms can be added from smallest to largest.
- series8.f90
Program to investigate a Fourier series that converges to 1
on (-1, 1), to 0 at 1, to -1 on (1, 3), etc.
- series15.f90
Uses a Taylor's series approximation to integrate sin(x) from 0 to pi.
- sqroot.f90
Prints a table of square roots. More importantly, it shows
how to use a 1-dimensional array.
- subroutines.f90
Illustrates how to write and use subroutines. Really short subroutines
are used in this and the next two examples in order to keep the examples simple.
- subroutines2.f90
Illustrates how to write and use subroutines. This one has a subroutine
with an INOUT parameter.
- subroutines3.f90
Illustrates how to write and use subroutines. This one replaces one of the
subroutines in the previous two examples with a function.
- trap1.f90
Uses the trapezoidal rule to integrate sin(x) from 0 to pi.
- trap2.f90
Double precision version of trap1.f90.
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Examples and Class Materials
Help is Available
Note on Flu
Because of the possibility of H1N1 and other types of flu affecting us on campus, please practice good
hand washing, etc.
If you get the flu, please notify me by phone or e-mail and stay home for 24 hours after the fever has gone.
Check with me about what you miss. You will not be penalized for missing class in this situtation.
It is better to stay away from class and not spread the flu when you are ill.
Homework, Labs, etc.
- Lab 0 will be done in class on Thurs, Jan 14.
- Homework 1: Do problem 2-15 in the text by writing a Fortran program under the name hw1.f90.
Due anytime Tue, Jan 26.
Hint: the correct answer should be about 0.140 kilograms = 140 grams. Use the senddc script to
send me your program as follows:
senddc hw1.f90
- Homework 2: Do problem 2-26 in the text by writing a Fortran program under the name hw2.f90.
You may do this problem either individually or in pairs. In the latter case, just submit one
homework for both students, but be sure both names are in the comment section at the top.
Due anytime Tue, Feb 2. Use the senddc script to send me your program as follows:
senddc hw2.f90
- Homework 3: Do problem 3-12 in the text by writing a Fortran program under the name hw3.f90.
Do this one individually, please.
Due anytime Tue, Feb 9. Use the senddc script to send me your program as follows:
senddc hw3.f90
Note that the text has a typo. They meant to reverse the values of n1 and n2 between the two sets of data.
Thus, use this test data:
a) n1 = 1.0, n2 = 1.7, theta = 45 degrees
b) n1 = 1.7, n2 = 1.0, theta = 45 degrees
It sounds like they want you to run your program twice to
get the two results. Thus, they don't want the above
numbers to be hard-coded; they should be entered by the
user when running the program.
- Since 8:30 classes are cancelled on Thurs, Feb 11, read chapter 4 on your own.
- Homework 4:
Do problem 4-22 on page 178. Name your program hw4.f90.
You may do it individually or in pairs. If you do the problem in a group of 2,
put both names in the comment section and just have one of you submit the program. Send it to me with:
senddc hw4.f90
The program is due by Wed, Feb 16 (anytime that day) -- as long as more bad weather does not delay things further!
- Homework 5:
This is a set of small group problems on series. The work will be
presented by the groups in class on Thurs, Feb 18 and Thurs, Feb 25. The two people in each group should check with
each other in person, by email, phone, etc. as needed. If you get stuck or are unsure if you have adequately answered
your problem, check with Br. David. If your problem involves writing a Fortran program, use senddc to send it to me.
- For Thurs, Mar 11, read chapter 5.
- For Tue, Mar 16, do the second small group problems on series.
See the handout given in class (or follow the link) for the problems and
who works on what. The presentations are to be done in class on Mar 16.
- Homework 6: For Tue, Mar 23, do the following problem individually.
Copy the hw6.f90 program from the Mar15Examples folder on the course network drive. Then modify the program so that
it prints out partial sums for the geometric series 1 + x + x^2 + x^3 + x^4 + ....
The program should read its input from the text file hw6.in and write its output to the file hw6.out (except that
any error messages should be written to the screen). The hw6.in file should contain any number of lines of the form:
x-value number_of_terms
For example, hw6.in might contain:
0.5 4
0.5 20
0.7 22
The program should then find and print to hw6.out
the first 4 partial sums of the geometric series when x = 0.5, next the first 20 terms
for x = 0.5, and finally the first 22 terms when x = 0.7. Each of these 3 reports should be preceded by a header like this
one for the first report:
For x value 0.5 the first 4 partial sums are:
Between reports there should be a blank line to separate them.
If either hw6.in or hw6.out fails to open, print an error message on the screen. Also, if a read fails, print an error
on the screen. You may skip checking to see if a write fails to work. Use our efficient method to compute x^k from the previous
term; do not use x ** k. For the above input file data, the output would look something like this:
For x value 0.5 the first 4 partial sums are:
0.10000000E+01
0.15000000E+01
0.17500000E+01
0.18750000E+01
For x value 0.5 the first 20 partial sums are:
(20 lines of numbers appear here)
For x value 0.7 the first22 partial sums are:
(22 lines of numbers appear here)
Send your hw6.f90 program to me with:
senddc hw6.f90
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Exams
- Final Exam: Thurs, May 6, 8:30 - 10:30 am
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Maintained by: Br. David Carlson
Last updated: March 15, 2010
Disclaimer
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