CS 270 Home Page
Introduction to Numerical Computation
Spring 2020
This course has two main goals: to teach the student the basics of
programming in a modern version of the Fortran language and to use that language to find
numerical solutions to mathematical problems, especially problems of
interest in mathematics, 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 new Linux server, in part due
to its speed. You can access this server most easily from any of the CIS lab PCs.
You can also access this server from another computer on the campus network if you are not connected via wirelss and get appropriate
software (such as SecureCRT, TeraTerm, or PuTTY) as described on the
server usage page.
Contact Br. David if you want to try connecting to this server from the dorms or from off-campus.
You will need to supply your computer's IP address (external IP address if you are on a home network).
Then we will grant access to that IP address. For some unknown reason, access via wireless in Dupre and possible elsewhere does
not work.
Further Information
- The Course Syllabus
- Grading Guidelines
- Hidden Figures
the book and movie show early computers -- people -- who calculated orbits and learned to program -- in Fortran.
- Documents, homilies, and speeches of Pope Francis
- Poverty, Hunger, and Social Justice in America
In honor of Martin Luther King, Jr.
- Wolfram Mathematica Documentation Center
- Wolfram Learning Center
- Wolfram MathWorld
Contains a wealth of resources,
including some on algebra and number theory.
- Wolfram Functions
- Wolfram Library
- Wolfram Demonstrations
- Education web site by Texas Instruments
Includes manuals and tutorials for many TI calculators and links to math web sites.
- 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:
- ACM Code of Ethics
- Fortran programs:
Anyone can copy these examples when viewing them in a browser. Students in this class
can also copy them at the command line as in the following two examples:
cp /home/cs270/trap1.f90 . (The dot is needed and means the current directory.
Thus we copy the file to the current directory and keep the same filename.)
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.
- arith0.f90
Does a division, multiplies the quotient by the denominator, and sometimes does not get the numerator exactly.
- 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 find a good approximation for a definite integral.
- 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.
- matrices1.f90
Adds 2-dimensional matrices using a couple of methods.
- matrices2.f90
Finds a matrix product as well as the product of a matrix and a column vector.
- max.f90
Finds the maximum number in a list of real inputs and finds the location of that maximum.
- 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.
- quadeq1a.f90
Solves a quadratic equation via the quadratic formula.
- quadeq2.f90
Solves a quadratic equation, but adds the scaling of the coefficients and the avoidance
of possible catastrophic cancellation that blind application of the quadratic formula can give.
- 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).
- series2dbl.f90
A version of the previous example, but using double precision reals.
- 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 power series approximation to find an approximate value for a definite integral.
- SeriesToFile.f90
Program to get partial sums of the geometric series using data read from a file.
Output goes to a file.
- sort.f90
An insertion sort for data in a linear array.
- 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 find an approximate value for a definite integral.
- trap2.f90
Double precision version of trap1.f90.
- trebuchet.f90
Given a starting speed and a user input for the angle of elevation, this program finds
how long a rock hurled by a trebuchet would be in the air and how far it would travel
horizontally. Air resistance is ignored.
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