Taylor expansion
Polynomial function approximation
A Taylor expansion is a mathematical representation of a function as an infinite sum of terms, each calculated from the function's derivatives at a single point.
It allows complex functions to be approximated by polynomials: The Taylor expansion of sine around zero begins x − x³/6 + x⁵/120.
When centered at zero, it's called a Maclaurin series.
Taylor expansions are fundamental in calculus, physics, and engineering for approximating functions that would otherwise be difficult to compute.
- seriesOrdered set of related items
- infinite seriesSum with unlimited terms
- polynomialExpression with variable terms
- approximationNear but inexact value
- derivativeFunction's rate of change
second derivative · convergence · infinite · coefficients · calculus · remainder · terms · function · limit · radius · analytic · truncation · linearization · higher-order · tangent · power · sum · factorial
- DecompositionsLU decomposition, QR decomposition, eigendecomposition, diagonalization, prime factorization
- limit methods
- perturbation methodsfirst-order, second-order, higher-order, time-dependent, time-independent
- Autodiffbackpropagation, chain rule, gradients, partial derivative, derivative
- Simplificationsideal gas, frictionless, point source, rigid body, blackbody
Taylor, expand, expands, expanded, expanding, expandable, expansion, expansions, expansive