CSC270S, 1997, St. George Campus
 
Assignment 1

Due Friday, January 30, 1998 at BEGINNING of tutorial


A Numerical Integration Program 

You are to implement three methods of numerical integration: Riemann,
trapezoid, and Simpson's.  The methods are quite similar, so most of
the code you write for one method can be used for the other two.
You'll be provided with a `skeleton program' and will have to write
code for the bodies of three functions, one for each integration
method.

Make a directory in your account and copy the skeleton file into it:

  % cd
  % mkdir a1
  % cd a1
  % cp ~jstewart/270/hwk1/integrate.c .
                                      ^ Note the period.  Don't forget it!
  
Compile and test the skeleton program:

  % gcc integrate.c -o integrate
  % integrate

  usage: integrate method a b n coefficients
       - `method' is one of: r (Riemann), t (trapezoid), or s (Simpson)
       - `a' and `b' define the interval of integration
       - `n' is the number of intervals
       - `coefficients' define the polynomial to integrate, list in order
       -                of decreasing power (e.g. t^2, then t^1, then t^0)

  % integrate s 1 4 100 12.3 -4.7 0 1 0

  method:     SIMPSON
  range:      [1,4]
  intervals:  100
  polynomial: 12.3 t^4 + -4.7 t^3 + 0 t^2 + 1 t^1 + 0 t^0
  computed integral = 0

Note that the computed integral is 0.  That's because the integration
code still has to be written in the program.

Programming

Read and understand the complete program, integrate.c.  Implement the
three integration methods by adding code to the three corresponding
functions in integrate.c.  You do not need to add code outside those
functions, but you may do so if you wish and if you document your
additions.

Provide good comments in your code, including a comment above each
of the three functions.

Read the newsgroup and POST ALL OF YOUR QUESTIONS TO THE NEWSGROUP.
 
Testing 
 
Test all three integrations methods with the two functions provided on
the Web page.  Test all three integration methods with one other
function that you choose.  Each of these nine tests should be run with
10, 100, and 1000 intervals.

For each of the nine tests, provide one separate page of program
output (captured from the screen).  On that page, calcluate the exact
value of the integral and, for each of 10, 100, and 1000 intervals,
the absolute error and the relative error.

Report

Write a short report (at most one page long) comparing the three
methods.  From your test results, discuss their relative speed and
their relative accuracies.  Do certain methods performs very
accurately for certain classes of polynomials?  For each method, how
does the accuracy increase as the number of intervals increases by a
factor of 2, 4, 8, and so on?  Discuss any other interesting things
that you discovered.

For the function that you chose for testing, write one or two
sentences explaining what interesting characteristic of numerical
integration is demonstrated by that function.  You should have chosen
an interesting function.
 
Hand-in details
 
Hand in the following:
 - the cover page (included below)
 - a hardcopy printout of your program, 
 - nine pages, one for each of the test functions
 - a one-page report

Put this into an ENVELOPE.  Write the following on the outside of the
envelope:
 - your CDF account name
 - your name (with surname underlined)
 - your tutorial
 - your student number
 
Your programs must also be submitted electronically by the deadline.
You must submit your integrate.c program by executing EXACTLY THIS
COMMAND:

   % submit -N a1 csc270h integrate.c

You may, if you wish, also submit a README file that the tutor will
read.  For more information on the submit command, type `man submit'
on CDF.

The tutors will compile and run your program.  MAKE SURE that the
following command works with the program that you submit:

   % gcc -o integrate integrate.c
   % integrate ...
   
YOU WILL LOSE MARKS if you don't follow these submission instructions
exactly.  This is because the tutors will be marking more than 300 of
these assignments and any deviations from these instructions will cost
them time and frustration.  Please help to keep the tutors happy.
 


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COVER SHEET FOR ASSIGNMENT 1


    CDF account name:

    Surname:

    Given Name(s):

    Student Number:

    TA's name:

    Tutorial location:

 
I declare that this assignment is my own work and is submitted in
accordance with the University of Toronto Code of Behavior on Academic
Matters, the Code of Student Conduct, and the guidelines for avoiding
plagiarism described in the course syllabus.
 
I discussed this assignment with the following people:





 
Signature

------------------------------------------------------------------------

GRADING
 
Program

        Correctness                                    / 20

        Style (including comments)                     / 5

        Test output (nine pages)                       / 5
 
Report

        Content                                        / 10

        Style and readability                          / 5

                                                ----------- 

Total                                                  / 45