Vector Calculus

Linear Approximation

Analytic Linearization

Defined as the approximation of $f(x)$ by a first-order Taylor Series expansion about the point, $x=x_0$.

Therefore, we can approximate the function $f(x)$ by calculating the first $k$ terms of the Taylor Series.

• High $k$ means high approximation precision.

For the linear approximation, keep only the first two terms,

$$f(x)\approx f(x_0)+f^{\prime }(x_0)(x-x_0)$$