CIS Department > Br. David Carlson

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Introduction to Numerical Computation

Spring 2008

This course has two main goals: to teach the student the basics of programming in the Fortran 90/95 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.

Examples and Class Materials

Solving quadratic equations (especially in Fortran)
Solving quadratic equations with Mathematica.
Holistic Numerical Methods Institute

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.
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
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 /users/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 /users/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.
- 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.

Instructor: Br. David Carlson