29 November 2007

Derivatives/Differentiation

One of my collegues asked me, what differentiation was. I said the same old thing.
"Ratio of change in an dependent variable to a small change in a independent variable. "

He asked me, don't you think it is a complicated way of saying something simpler?
I started breaking my head.

if a line is y = mx+c
dy/dx = m

Y
| /> y= mx + c
| /
| /
| /
| /
| /
| /
|/_______________________> y=m
/
_|_______________________> x
|


For eg 4/2 => 4-2-2=0 thus answer is 2.
similaly change in y/change in x = change in y - m * change in x = 0

Because m is the derivative of mx+c wrt y, we can say that;
"change in y is constant".

More generally, "what is the change in terms of the independent variable required to see the change we see in dependent variable".
It is nothing more than fancy way of saying "rate of change"!

Someone told me even this is complicated way of saying subtracting the previous number in the series from the current. Discrete version is called "The First Difference".

Bhaskara II knew the stuff, then he did not publish his research in Nature! That is obviously his fault.

~rAGU

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