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Eh, most diffEQ classes are taught at a super introductory level, and if there is much difficulty, it's actually because they're taught at a super introductory level, in the style of, "You just need to memorize these various magic tricks," which is supremely unhelpful to building intuition. There's a more significant jump when going to something like differentiable manifolds, because that's generally only targeted at math grad students, so they often go into the other ditch in terms of rigor.
Understanding diffEQ is nearly essential for the sciences. Honestly, I don't know how one would survive physics for physics majors without it; generally it's the super introductory versions of physics that skip the differential equations and again require you to just memorize a bunch of magical formulas that seem to come from magic. It's the physics for physics majors that show how all the typical super simplified problems are just pretty easy differential equations. It even came up in some neuroscience classes I took (scared the pants off the bio majors, but was unsurprisingly the easiest part of the material for me). One can't hide even in CS, at least not today. I mean, even just the extremely rudimentary concept of gradient descent. Even manifold stuff; I still see manifold learning stuff popping up here and there. I guess if you want CS for web design, sure, but if you're thinking CS for cutting edge tech, you need a pretty large chunk of math these days.
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