A new approach to the calculus is introduced using the calculus of finite differences and finite sums, both as motivation and as useful tools. The main reason for this development is to create an ideal context in which the computer can be naturally incorporated into calculus courses. Most topics are first developed in the discrete setting and then extended to the continuous case by applying the limit. This provides a constant review of all topics, a definite aid to most students. Furthermore, the numerical techniques used by computers are all within the scope of the finite calculus. Moreover, by starting with the finite calculus, a wider range of topics can be naturally included in the calculus course, including discrete models based on difference equations (especially useful for non‐science majors) and various approximation and interpolation techniques which make calculus usable in practical situations.