# Thread: Vector calculus question

1. ## 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

2. 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