## differential equation

**Carola Schönlieb**explores how mathematicians use the heat equation to fill in the gaps.

**Angus Brown**looks at one of these, a simple model for option pricing, and explains how it takes us on the road to the famous Black-Scholes equation of financial mathematics, which won its discoverers the 1997 Nobel Prize in Economics.

**Peter Markowich**is a mathematician who likes to take pictures. At first his two interests seemed completely separate to him, but then he realised that behind every picture there is a mathematical story to tell.

*Plus*went to see him to find out more, and ended up with a pictorial introduction to partial differential equations.

*Plus*went to see him to find out more about his career.

**Chris Budd and Cathryn Mitchell**look at the maths that isn't only responsible for these medical techniques, but also for much of the digital revolution.

*Plus*spoke to

**Peter Wadhams**from the Polar Ocean Physics Group at the University of Cambridge to get a glimpse of the group's work.

Learn about the aerodynamics of footballs and perfect your free kick.