Please use some easy to understand examples, I’m not very smart.
In: Mathematics
Pretty much everything? They’re used to predict how fluids flow, how heat propagates, how solids deform under pressure, how pretty much anything to do with electricity or magnetism behaves (including light and other EM radiation), and even how financial markets behave.
Basically any time you have something that depends on multiple variables – e.g. something that varies in both time and space, or in two different dimensions of space – and which is governed by rules that involve rates of change with respect to those variables, PDEs are useful.
Most electronic and magnetic circuits are characterized by PDEs. Solving these formulas allows engineers to make electronic parts the right size to do their job; too small and they would burn out too fast and too large and they would cost too much.
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