## MA/CS 371 - Lab 6

Even More Numerical Integration - Gaussian Quadrature

### Section 1: Introduction

In this lab you will verify the convergence behavior of the Gaussian
quadrature method by computing the integrals of a couple of functions.

If you have not already done so, create a directory for this lab and
copy the lab 6 files into it. If you start off in your home directory you
can do the following:

mkdir ~/cs371/lab6
cd ~/cs371/lab6
cp ~cs371/lab6/* .

and (as always) don't forget to type that last period.
### Section 2: Topics for Lecture

This week I'll talk about what happens when a function returns more
than one variable and briefly about the **nargin** and
**nargout** commands which count how many variables are actually
being passed into and out of a function.

### Section 3: The Gausspoints Function

This week I'm giving you a function which will give you the nodes and
weights for the Nth order Gaussian quadrature method. The format of
this subroutine is as follows: [x,a] = gausspoints(n);

The two variables on the left-hand side indicate that
**gausspoints** will return two vectors when called. The first
output variable will be a vector of the nodes, and the second output
variable will be a vector of the weights. For example, if your
program does
[x,a] = gausspoints(2);

then the variable x will be set to the vector
x = [ -0.7746 0.0000 0.7746 ]

and the variable a will be set to the vector
a = [ 0.5556 0.8889 0.5556 ]

as indicated in the table on page 213 of your book.
You should look through the code of **gausspoints.m** and make sure
you understand what it's doing.

### Section 4: Two Problems

Do Computer Problems 5.5.1 and 5.5.2 from the book. Approximate each
function with a first-order through sixth-order polynomial. Format
your output similarly to the way we did **trap.m** in previous
labs. Call the first program **prob1.m** and the second program
**prob2.m**.

### Section 5: Submitting Your Work

When you are ready, run
~cs371/submit lab6

to submit your **prob1.m** and **prob2.m** files. If you
call them something else then **submit** won't find them.

This
Week's Questions