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)
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.
Using finite differences involves a considerable complication of the procedures of the calculus. Such an approach may be constructively more satisfactory but may not be appropriate for a first acquaintance with the subject. The technical complications of the epsilon-delta approach are involved enough, and it is how certain things are defined (and it is way easier to do things rigorously with) and furthermore it is the received way of doing things.