| Ordinary (continuous) calculus | Discrete calculus |
|---|---|
| Functions R-->R | Sequences N-->R or N-->Z or ... |
| Derivatives | Differences |
| Derivative rules | Rules for differences |
| Derivative formulas
for powers, etc. | Difference formulas
for factorial powers, etc. |
| Definite integrals | Definite sums |
| Antiderivatives | Antidifferences |
| Fundamental Theorem of Calculus | Telescoping Sum Formula |
| Integral formulas | Formulas for sums |
| Taylor polynomials | Interpolating polynomials |
| Taylor series | Newton's advancing difference formula |
| Differential equations | Difference equations/recurrence relations |