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Swamp Thing said:Although "D" is not a number, it does take a function f(x) and give you f'(x), so in a sense we can think of D as a sort of number that represents thelocalvalue of f'(x)/f(x). If we plug that local ratio into a power series, then ##e^{Dh}## sort of makes sense. How far can we get if we try to run with this ball?

That's fine intuitively. You hit on the exact difference between applied and pure (or is that puerile ) math. In applied math degrees you still do some pure math simply as background (you should anyway). For example in the degree I did we did linear algebra as pure math before we did another subject Applied Linear Algebra. They don't tend to do that in Engineering and Physics courses so it makes following advanced pure math papers hard. Its actually a problem in applied math type degrees nowadays as well. My old alma mater doesn't even do the basic background pure math subjects because students thought it was just mind games. IMHO it's a big issue.

If you want to understand it you need a course in analysis, (colloquially called doing your epsilonics) which my alama mata once did but no longer does. A good reference and well written path into it for those already mathematically advanced is:

http://matrixeditions.com/5thUnifiedApproach.html

If you just have been exposed to basic calculus, and not gone deeper into applied math, I would suggest the following first:

https://www.amazon.com/dp/0691125333/?tag=pfamazon01-20

Thanks

Bill