ruby_integrator
---------------

I. Introduction

This software provides an example for how to do numerical integration
with ruby and its math library.  It is coded to be a functional example
and is not necessarily designed for speed although it works well enough.
I wrote these classes to help learn the Ruby language.

Although I've checked my math against a couple of calculators and a
few on-line applets, this software comes with no guarantee and may
contain bugs.

A particularly good illustration of the estimation techniques used
herein is located at:

    http://www.math.ucla.edu/~ronmiech/Java_Applets/Riemann/index.html

II. Usage

There are two ways to use the estimator classes.  One is to initialize
them through a constructor, for example:

    require 'right_integral_estimator'
    r = RightIntegralEstimator.new(0, "pi", 100, Function.new("x","sin(x)"))
    print "Right: " + r.calculate.to_s + "\n"

The other is to instantiate the class and then set it up by having the
class interact on the user's terminal.  This is achieved by doing:

    require 'right_integral_estimator'
    r = RightIntegralEstimator.new
    r.interact
    print r.inspect + "\n"  # completely optional
    print "Right: " + r.calculate.to_s + "\n"

If using the latter method, an example interaction may look like:

    Please enter a function in terms of the variable x on the line below.
    For example: (pi*(sin(x^2)))^2

    You may use the constants e and pi in your function.

    Enter f(x) (type q to quit): sin(x^2)
    Enter start bound (type q to quit): 0
    Enter stop bound (type q to quit): 2*pi
    Enter number of sub-intervals (type q to quit): 100
    Shall I show evaluations (y/n) (type q to quit): n

    Using:

	a: 0.0
	b: 6.28318530717959
	n: 100
	function: f(x) = sin(x**2)

    Right: 0.672010534481375

III. Copyright Information

ruby_integrator is freely distributable
Copyright (C) 2005  Jordan Husney <jordan@husney.com>

ruby_integrator may be used by public or private entities for any
purpose.  ruby_integrator may be distributed in source or binary
form.

If changes are made to ruby_integrator the author will accept
patches via e-mail to Jordan Husney <jordan@husney.com> but this
is not required.