Re: to first order ??


"Zinc Potterman" <zincnews@xxxxxxxxxxxxxxxxx (delete 123's to reply)> wrote in message
news:dhk4s7$h7e$1@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> My physics book says "
> to first order in delta x,
>
> delta f = (df/dx) delta x
>
> What does this mean please?

Abbreviating
delta x to dx
and
delta f to df

See
http://mathworld.wolfram.com/TaylorSeries.html
x --> x + dx
a --> x
x-a --> dx

df = f(x + dx) - f(x) by definition
= f(x) + f'(x) dx + 1/2 f''(x) dx^2 + 1/6 f'''(x) dx^3 + ....
- f(x) by Taylor expansion
= f'(x) dx + 1/2 f''(x) dx^2 + 1/6 f'''(x) dx^3 + .... by simplification
= f'(x) dx by throwing away higher powers of dx
because too small.

hth

Dirk Vdm


.

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