This namespace contains implementations of various approaches to [numerical
differentiation](https://en.wikipedia.org/wiki/Numerical_differentiation).

Each of these methods uses [Richardson
extrapolation](https://en.wikipedia.org/wiki/Richardson_extrapolation) to
accelerate convergence, and roundoff error estimation to bail out of the
computation when roundoff error threatens to overwhelm the calculation.

For an implementation of [forward-mode automatic
differentiation](https://en.wikipedia.org/wiki/Automatic_differentiation),
see [[emmy.dual]] (for the backing implementation)
and [[emmy.calculus.derivative]] (for the [[emmy.operator/Operator]]
instances that make it pleasant to use this method.)

Entrypoint for univariate and multivariate minimization routines.

ODE solvers for working with initial value problems.

Implements utilities shared by all integrators, for example:

- code to wrap a sequence of progressively better estimates in a common `integrator` interface
- data structures implementing various integration intervals.

### U Substitution and Variable Changes

This namespace provides implementations of functions that accept an
`integrator` and perform a variable change to address some singularity, like
an infinite endpoint, in the definite integral.

The strategies currently implemented were each described by Press, et al. in
section 4.4 of ['Numerical
Recipes'](http://phys.uri.edu/nigh/NumRec/bookfpdf/f4-4.pdf).

Trapezoid method.

This namespace contains implementations of a number of methods for root-finding
on real-valued functions of one argument.

NOTE: This namespace is not yet stable: Expect these functions to change as
new root-finding methods are added. 

This namespace contains an implementation of Brent's method for finding the
minimum of a real-valued function.