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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 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.
      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.

Examples and Class Materials

Homework and Announcements

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Instructor: Br. David Carlson

Maintained by: Br. David Carlson
Last updated: January 21, 2020