Mechanics → Appendix: Mathematical Methods for Mechanics → Series Expansion
Series Expansion
Taylor Series
$$ f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \cdots $$
Example
$$ \sin x \approx x \quad (\text{for small } x) $$
$$ f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \cdots $$
$$ \sin x \approx x \quad (\text{for small } x) $$