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^C^1INTERPOLATION
^Cby Thierry G. Lombry

   Interpolation is the mathematical art of fitting a curve to a set of 
points.  This is what you must do if you have a whole set of data, such as 
scientific observations, and wish to find a mathematical function that best 
describes it.

   This program accepts input of the x and y coordinates of a set of data 
points.  For instance, if you are conducting an experiment regarding rate of 
rainfall, x might be the number of days since the start of the experiment, 
while y is the cumulative number of inches of rain measured since the 
experiment began.  Or if you're tracking political results, x could be the 
year of a Presidential election and y the number of votes a particular party 
received.  Each data point consists of these two coordinates.

   Once the data has been entered, a polynomial function will be computed to 
fit the data as closely as possible.  A polynomial is a sum of various powers 
of x, like 1, x, x^^2 (x squared), x^^3 (x cubed), etc.  Each power is multiplied
by a constant known as a coefficient.  The value of y for a given x is found 
by plugging the value of x into the equation and solving for y; there is one 
unique value of y for each x.  If a good fit is reached, the value of y for a 
particular x will be close to the originally-input coordinates of a point 
involving the same x.

   After the polynomial is shown, its derivative and integral are also given; 
this will make some sense to you if you've taken some calculus, but is likely 
to mystify you otherwise.  In simple terms, the derivative is the rate at 
which the original function changes as you increase x; the integral is the 
area underneath the curve of the function between the lower and upper limits 
of x that are charted.

   Once all of this math is over with, if you have a color graphics adapter 
you will be shown a graph of the original points and the polynomial function.  
You can see from this how well the function fits your points, and get an idea 
what the curve looks like.

   To run this program outside ^1Big Blue Disk^0, type:  ^1INTERPOL^0.

DISK FILES THIS PROGRAM USES:
^FINTERPOL.EXE
^FBRUN30.EXE
^FRETURN30.EXE