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> the concept of a function shouldn't depend on what your favourite letter is On the other hand, you can also argue that the concept of a function shouldn't de
by enriquto 3y ago
> the concept of a function shouldn't depend on what your favourite letter is
On the other hand, you can also argue that the concept of a function shouldn't depend on your favourite ordering of its variables. Thus, if you have a potential that oscillates in time, such as:
V = (1 + sin(t))/sqrt(x^2+y^2)
You may want to take derivatives with respect to each variable, such as dV/dt, dV/dx and so on. Their meaning is clear. What does D_2(V) mean, though? It does depend on your favourite ordering of the letters!
Even if you prefer positional notation for derivatives (à la Spivak), it must be recognized that the naming-based notation has its merits, and sometimes is clearer.
- BruceEel 3y agoah, interesting dark corner there. Also, I was thinking there must be merit in allowing for some discrepancies in use of different notations when dealing with "read" use, as in learning a new concept, vs. "write" use, as in working on something, like the SO OP..
- xigoi 3y agoIn what you have written, V is not a function, but a value calculated from some other values, so it does not make sense to differentiate it. If you instead write: V : ℝ³ → ℝ V(t,x,y) = (1 + sin(t))/sqrt(x^2+y^2) then it’s clear what D_2(V) means.
- archgoon 3y ago[dead]
- enriquto 3y ago> not a function, but a value calculated from some other values The term of art is "an expression" [0]. And you can also differentiate expressions with respect to their variables. It's a perfectly supported construction in all symbolic computer algebra packages. No need to assign an (arbitrary) ordering to your variables in order to differentiate with respect to them. [0] https://en.wikipedia.org/wiki/Expression_(mathematics) https://en.wikipedia.org/wiki/Expression_(mathematics)