Why are some functions denoted by capital letters? For example, an ODE is represented by the equation $F(t, y, y',\ldots, y^n) = 0$. Here, what I understand is that F is actually a multivariate function. Similarly, for $dy/dx=f(x,y)$ if we consider $f(x,y)=-M(x,y)/N(x,y)$ we get separable equation. Why represent $M$ and $N$ with capital letters? Are they different from the functions represented by small letters?
Capital and small letter function notations
1
$\begingroup$
notation
-
1@Gerry: Yes, of course; the joke someone proposed once was to just use "the next letter" any time you needed a symbol, and as an example wrote the definition of continuity that way. It was nigh unreadable. But the point is that it's just symbols, and while we tend to select certain symbols for context, that context is entirely created "outside" the mathematical objects in question. We are used to certain symbols "signaling" certain kinds of objects, but that's mere social convention, not a mathematical difference inherent in the chosen symbols (though I know I'm preaching to the choir). – 2012-06-27