What is noise in an image? How do we detect it, and how can we use tools from analysis to remove noise?
Given a series of pictures from a CAT scan, how can we mathematically reconstruct the original (3d) object?
What happens to the temperature of a heated object over time? Can we predict how fast the cooling will occur?
How does a tsunami wave travel? When will it hit land? Can we model the wave front with a differential equation?