why are differential equations so difficult? it would seem even smart people struggle with understanding them. Is the problem is how they are taught or is the concept inherently hard/ It should not be that hard given that we're taking 'rates of change' broadly speaking, yet it is.
Even among the engineering-oriented lower division math courses, material in differential equations courses is both antiquated and presented like a laundry list. This essay is more than 20 years old now, but the complaints are basically as relevant today.[1]
Both. They are taught, generally speaking, by giving a series of techniques to solve problems without the underlying mathematics (i.e why those techniques work on those problems). Calculus generally takes some time to grok, which typically doesn't have unless your really into it. Think how many people fail to grasp exponential growth (the simplest ODE).
