CS 270 Home Page
Introduction to Numerical Computation
Spring 2018
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 get appropriate
software (such as SecureCRT, TeraTerm, or PuTTY) as described on the
server usage page.
Access from off campus or the dorms is more difficult. Contact
Br. David if you wish to try this.
Further Information
 Documents, homilies, and speeches of Pope Francis
 Poverty, Hunger, and Social Justice in America
In honor of Martin Luther King, Jr.
 The Course Syllabus
 Tentative Course Schedule
 Grading Guidelines
 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 Wellknown 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 1dimensional 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 simpleminded 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 2dimensional 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 NewtonRaphson 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 1dimensional 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
Help is Available
Note on Flu
Because of the possibility of the flu affecting us on campus, please practice good hand washing, etc.
If a doctor will prescribe Tamiflu or similar for you, it is said that it reduces the length and the severity of the flu.
If you get the flu, please notify me by phone or email and stay home for 24 hours after the symptoms are over.
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 and Announcements
 See Schoology for homework.

Exams
 First Exam:
 Fri, Feb 16
 May cover almost anything that we have done thus far. This includes chapters 1 to 4 in the text, the limitations
of integers and reals on the computer, and how to solve quadratic equations accurately on a computer.
Power series will NOT be on this exam.
 Openbook, open notes exam. You may bring anything on paper that you wish.
Be sure to bring to bring your notes from class, handouts, homework solutions, and example programs.
 Also bring a hand calculator, as you are likely to need it to answer some of the questions.
Calculators may not be shared by students.
 Cell phones and pagers should be turned off and put away.
 No phones, laptops, or other computers may be used.
 Second Exam:
 Mon, Mar 26
 May cover almost anything that we have done thus far, but emphasizing topics done since exam 1.
This includes chapters 5 and 6 in the text, as well as power series, Taylor's series, ratio test, formatting of output,
files, and arrays. Userdefined subroutines and functions will not be on this exam.
 Openbook, open notes exam. You may bring anything on paper that you wish.
Be sure to bring to bring your text, notes from class, handouts, homework solutions, and example programs.
 Also bring a hand calculator, as you are likely need it to answer some of the questions.
Calculators may not be shared by students.
 Cell phones and pagers should be turned off and put away.
 No laptops or other computers may be used.
 Final Exam:
 Tues, May 8, 4:00 pm  6:00 pm

