Discrete calculus

Summary

Discrete calculus studies change and accumulation for functions on discrete sets, such as the integers or the vertices and cells of a grid. Difference quotients take the place of derivatives, and finite sums take the place of integrals. Its results mirror those of ordinary calculus, often with exact formulas instead of limits, and it includes the calculus of finite differences. It is used in difference equations, numerical analysis, combinatorics, and in discrete models of geometry and physics.