(function-approx)=
# Introduction to function approximation

```{dropdown} [Lagrange interpolation](fun-approx:lagrange-interp)
:open:

Useful, because derivatives and integrals of polynomial functions are easy to evaluate exactly. Used in:
* numerical methods for ODEs, e.g. [multi-step methods](ode:integration-schemes:common:multi-step)
* numerical methods for PDEs, e.g. base functions of [FEM](pde:fem).
  * Gaussian quadrature provides exact integration of integrals.
  * FEM uses **piece-wise** Lagrangian interpolation of the fields
* ...

```