Taylor Series
An infinite polynomial series representation of a smooth function expressed in terms of its higher-order derivatives evaluated at a single point a.
Governing formula
f(x) = ∑_(n=0)^(∞) (f^(n)(a) / n!) (x - a)^n
SI unit
Infinite Polynomial Expansion
In depth
Essential for linearizing non-linear physics equations near equilibrium. Truncating Taylor series after first or second-order terms yields local linear or quadratic approximations.
Examples in the real world
Approximating simple pendulum motion sin θ ≈ θ for small angle oscillations.