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Math Help - Vector calculus question

  1. #1
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    Vector calculus question

    I'm given this
    \frac{\phi{(x + \delta{x})} - \phi{x}}{\delta{x}} \approx \frac{d\phi}{dx}\mid_x + O(\delta{x})
    Hence
    \delta{x} = \phi{(x + \delta{x})} - \phi{x} = \frac{d\phi}{dx}\mid_x\delta{x} + O(\delta{x}^2)

    I dont really understand either of these statements especially where O comes from and why you need it. Anyone have any ideas or know anywhere to point me where i could get an explaination
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  2. #2
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    The \displaystyle O(\delta x) means that all the remaining "stuff" is bounded by a scalar multiple of \displaystyle |\delta x|.

    i.e. if \displaystyle f(x) = O(\delta x) then \displaystyle f(x) \leq M|\delta x| for some \displaystyle M \in \mathbf{R}.


    http://en.wikipedia.org/wiki/Order_notation
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