The Taylor series is a way of representing a function as an infinite sum of terms based on its derivatives at a single point. It allows us to approximate complicated functions using polynomials, which are easier to work with. Each term in the series involves a derivative of the function evaluated at a chosen point, usually called “a,” and is multiplied by a power of (x - a). The more terms we include, the better the approximation becomes, especially when x is close to a. This method is commonly

MML 17. Higher Order Derivatives - Linearization - Multivariate Taylor Series

Taylor Series Method To Solve First Order Differential Equations (Numerical Solution)