area under the curve
David Kirschtel
dkirscht at moose.uvm.edu
Wed Apr 26 10:06:06 EST 1995
JF Neron (jfneron at fse.ulaval.ca) wrote:
>Is it possible to measure the area under the curve with excel or with some
>MACINTOSH shareware.
>This is a example of the data:
>Time TG
>15 80
>0 85
>5 220
>10 210
>15 200
....
There are a number of numerical integration techniques that would allow
you to do this and could be adapted to a spreadsheet. The simplest is
referred to as the Trapezoid Rule (may also be referred to as Eulers Method
in some books) which calculates the area of a trapezoid bounded by
adjacent sampling points:
sum across sampling intervals Area= 1/2*[TG(i1)  TG(i)]*[t(i1)  t(i)]
A more accurate and and slightly more complex method is Simpsons Rule
which fits a parabolic curve across three adjacent points (Best to cruise
through a Calculus text to get this one).
Also there are the RungeKutta algorithms but I don't think these will
readilty conform to a spreadsheet.
Hope this helps

David Kirschtel 
Dept. of Botany  What if the 'invisible hand' is
Univ. of Vermont 
Burlington, VT 054050086  guided by myopic eyes.

tel 802.656.0429 
email dkirscht at moose.uvm.edu 
More information about the Biosoft
mailing list