790

UwU brat mathematician behavior (lemmy.nz)

submitted 1 year ago by fossilesque@mander.xyz to c/science_memes@mander.xyz

135 comments fedilink hide all child comments

you are viewing a single comment's thread
view the rest of the comments

[-] Phoenix3875@lemmy.world 22 points 1 year ago

I think rather d/dx is the operator. You apply it to an expression to bind free occurrences of x in that expression. For example, dx²/dx is best understood as d/dx (x²). The notation would be clear if you implement calculus in a program.

[-] bhamlin@lemmy.world 18 points 1 year ago

If not fraction, why fraction shaped?

[-] Amir@lemmy.ml 2 points 1 year ago

If you use exterior calculus notation, with d = exterior derivative, everything makes so much more sense

[-] yetAnotherUser@discuss.tchncs.de 4 points 1 year ago

I just think of the definition of a derivative.

d is just an infinitesimally small delta. So dy/dx is literally just lim (∆ -> 0) ∆y/∆x. which is the same as lim (x_1 -> x_0) [f(x_0) - f(x_1)] / [x_0 - x_1].

Note: ∆ -> 0 isn't standard notation. But writing ∆x -> 0 requires another step of thinking: y = f(x) therefore ∆y = ∆f(x) = f(x + ∆x) - f(x) so you only need ∆x approaching zero. But I prefer thinking d = lim (∆ -> 0) ∆.