I'm teaching a course on multivariable calculus and we'll be spending a day on PDEs. Of course, a day is not enough to do this subject justice, so I'm looking for a short article or essay that I can give my students to read that will impress upon them the prevalence and utility of PDEs in the real world and hopefully motivate them to learn more. Ideally, this article would:
- Give and explain examples of PDEs not just from physics, but also from biology and economics. (These are the largest majors that are represented amongst my students.)
- Explain the "unreasonable effectiveness" of PDEs in modelling real-life situations. I'm not sure myself what the answer to this would be, but things like how PDEs arise from conservation laws and interconnected systems should be explained.
- Possibly give examples of how a mathematical understanding of these PDEs has led to breakthroughs about real world phenomena.
A similar question has been asked before, but my focus is more on PDEs than on differential equations in general. Also, since this is a course that is taught to college freshmen and sophomores who are typically STEM but non-math majors, I'm not really looking for as much mathematical formalism as the links in answers to that other question provided.