**Update**

Although we didn’t get to record it this is the material from the presentation. It was very interesting!

**Numerical computing with functions in Julia**

**Presenter:** John Wormell

**Bio:** PhD student at the University of Sydney interested in numerical methods for dynamical systems, chaos, spectral bases ( http://www.maths.usyd.edu.au/u/wormellj/ )

**Abstract:** While all we classically expect of a function in programming is that it produces outputs from inputs, knowledge of the function as a whole is really required for many operations: these include calculus operations, differential equation solving, root-finding and sampling from a distribution.

This talk will introduce some Julia packages that implement various kinds of natural, highly efficient “whole-function” manipulation. It will focus on ForwardDiff.jl, which performs efficient automatic differentiation, and ApproxFun, which represents functions very accurately as a sum of Chebyshev polynomials and then solves many problems using numerical linear algebra. We will discuss in particular how these packages make use of Julia’s capabilities, including multiple dispatch and the parametric type system.