Visualizing differential equations
Whenever I read a physics article, I try to visualize the quantities that the author is talking about. I do this by ASSOCIATING the quantity with some REAL thing. Example – if the article talks about FREQUENCY, I think of a wave – specifically either a string waving (standing wave) or a water wave (moving wave). Now , FREQUENCY is no longer mysterious, but a PROPERTY of my Water Wave.
I try to do this whenever I can. However, I get stuck when the article suddenly throws an EQUATION on the board. What exactly IS the real thing that one associates with the equation? Consider BESSEL’s equation? Or any Differential Equation. WHAT real object are we talking about?
The truth is that the equation applies to MULTIPLE possible physical scenarios (and in some cases, to NO real world scenarios). So – trying to associate it with something real is a bit of a challenge.
I am open to ideas about how people get around this. The best I can do is think of the differential equation as belonging to a MATHEMATICAL object – maybe a sort of space (vector space?).
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