I had him for second term calculus, which was the first math course I took in college. So I get to listen to him speak it in my minds eye —- his voice is unforgettable. He was a great teacher.
2. I have an interesting take on this subject. I became an engineer at 50. Out of personal choice. What I found was that engineering had changed and what mattered was your savvy in manipulating expensive programs on the computer. In those programs, differential equations were solved numerically. No one even thinks about solving them any other way. There isn’t any time.
Aren't most DEs not solvable analytically? i.e. only a tiny subset are neatly solvable - like precisely manufactured puzzles. In general, for any real problem you encounter "in the wild", numerical methods are the only way to find solutions (which are approximate).
DE theory is still useful for designing frameworks within which numerical methods can operate.
I, too, had Rota for his "exploring higher mathematics" seminar. What a remarkable human being! I retain excitement for hierarchies of infinity to this day.
As to your second point - yes, programs solve DE's numerically. I suppose it's still nice to know a bit about how they were solved in the 'olden days'?
