Why isn't finite calculus more popular?

I'm reading through Concrete Math, and learning about finite calculus. I've never heard of it anywhere else, and a Google search found very few relevant sources. It seems to me an incredibly powerful tool for evaluating sums, essentially a systematization of the use of telescoping sums. Why isn't it more widely known and used? (Related question)

Solution 1:

I'm reading through Concrete Math, and learning about finite calculus. I've never heard of it anywhere else, and a Google search found very few relevant sources.

The name "finite calculus" is unusual. The traditional term is calculus of finite differences or variants such as difference calculus. A search for those terms will be more productive.

It seems to me an incredibly powerful tool for evaluating sums, essentially a systematization of the use of telescoping sums. Why isn't it more widely known and used?

It is widely known and used, most obviously in numerical analysis, but also in many other subjects.

Solution 2:

All formulas of discrete calculus will depend on $\Delta x$ (and $\Delta y,\Delta z$, etc.). After $\Delta x\to 0$, the formulas will inevitably become simpler. Those more cumbersome formulas may be the main turn-off, especially for the people who already know calculus well. On the other hand, the limits themselves seem to be an even bigger turn-off, especially for the people who don't know calculus yet.