> There's a slant towards standardised EE-specific solutions for PDEs, but it's still much more abstract and mathematical than any field of CS, apart from maybe

> There's a slant towards standardised EE-specific solutions for PDEs, but it's still much more abstract and mathematical than any field of CS, apart from maybe cryptography and data science. Here's the thing, though: PDEs are NP-hard. There isn't a generalizable way to model dynamics. On the other hand, dynamics come up everywhere: - How is the pandemic going to evolve? - How will incentive structures skew cultures? - How do I build a suspension for my car? - How does heat leak from my house? - How does my understanding evolve with learning? ... and so on. What EE does -- and I think uniquely -- is given intuitive, graphical tools to think about differential equations, in tools like Laplace, Body, Nyquist, root-locus, and so on. They also give a lot of applied experience in applying those, including in contexts with nonlinearities. An op amp will clip on both sides, which you model as a linear differential equation (which is easy enough to reason about) and a memoryless, time-invariant nonlinearity. You squint. You kinda ask yourself how it would work if it /were/ linear, and the nonlinearity just cut gain. And at some point, after doing it enough, you have intuition for what it will do. With the EE-specific stuff, I can intuitively reason about these things think through to design. EE is all about modeling -- building simpler equations which approximate more complex ones in ways which give intuition -- so this is also usually correct or almost correct. Indeed, if you go onto grad level courses in control theory, you'll see formalizations of this intuition, where for example, a time-variant system or a nonlinear system is modeled as a linear time-invariant system, together with a bounded error. A lot of the mathy stuff -- which I've learned a fair bit of as well -- is in abstract more general, but in practice, gives much less intuition. My experience with the real world is that there are rarely actual differential equations handed to me. I kinda get that we've set up some pricing structure, or some incentive design, or whatnot, but I can't model it formally. I know which way things push, and whether those integrate or not. I can draw a block diagram and reason about how it will behave, in a way the math side doesn't let me do.