Chebfun is a Matlab-based system for numerical computing
with functions as opposed to just numbers in 1D and 2D;
it is also the most convenient tool available for 1D and 2D
rootfinding and for ODE boundary-value problems. This talk
will describe some of the algorithms behind Chebfun and
demonstrate it in action, including the extension to two
dimensions known as Chebfun2.