# Data Types for Differentiable Functions

We introduce a domain-theoretic computational model for multi-variable differential calculus, which for the first time gives rise to data types for differentiable functions. Differentiable functions of n variables are represented as sub-domain of the product of n+1 copies of the function space on the domain of intervals by tupling together consistent information about locally Lipschitz (piecewise differentiable) functions and their differential properties (partial derivatives). We discuss two applications of the model: A second-order method for obtaining exact solutions of ordinary differential equations and a domain-theoretic approach to the implicit function theorem, which allows for the robust construction of smooth surfaces.

**Tuesday 1st February 2005, 14:00**

Robert Recorde Room

Department of Computer Science