**Math.AP Analysis of PDE**

- Partial differential equations are used a lot for modelling systems in biology and medicine, and help describe e.g. animal coat pattern formation (zebras, leopards...), wound healing, tumor growth, spread of a virus in a population, predator-prey systems in ecology, predicting the variations of concentrations of chemicals (hormones, drugs...) within an organ over time...
- PDEs are used in climate modelling, from atmospheric dynamics to ocean currents. 
- Radar imaging is based on solving an inverse problem.  The recent buzz about metamaterials and invisibility is based on understanding variable-coefficient elliptic problems.