scitposting 4: so functions are really, really, really cool

I am only beginning to realize how crucial the interpretation of functions as vectors, or elements in a vector space, is to physics. This realization had widespread effects in classical mechanics, quantum mechanics, electromagnetics,…

Interpreting functions as vectors REALLY helped in the study of Fourier analysis and calculus of variations. And those fields of mathematics are really, really, really important in the study of mechanics. Basically when you do higher physics, you’re just playing around with the properties of functions. I think. Anyway, I’m not even in graduate school yet so I can’t say, but that’s probably how it works??

Long live f such that f is a continuous function. Long live differential operators!