Calculus is a field of mathematics that deals with the study of continuous change. It provides a framework for modeling systems in which there is change and a way to deduce the predictions of such models. Calculus is used to study functions and limits, and it is a collection of techniques for manipulating infinitesimals. The word calculus is Latin for "small pebble," which was used for counting out distances, tallying votes, and doing abacus arithmetic. Calculus is broadly classified into two different sections: differential calculus and integral calculus.

Differential calculus is the study of the definition, properties, and applications of the derivative of a function. The process of finding the derivative is called differentiation. Given a function and a point in the domain, the derivative at that point is a way of encoding the small-scale behavior of the function near that point.

Integral calculus, on the other hand, can be used to find areas, volumes, central points, and many useful things. It is used to determine the accumulation of quantities over time, such as distance, area, and volume.

Calculus is used in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modeled and an optimal solution is desired. It allows one to go from (non-constant) rates of change to the total change or vice versa, and many times in studying a problem we know one and are trying to find the other.

In summary, calculus is a branch of mathematics that deals with the study of continuous change and provides a framework for modeling systems in which there is change. It is used to study functions and limits, and it is a collection of techniques for manipulating infinitesimals. Calculus is used in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modeled and an optimal solution is desired.