# Calculus

Mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.

- Calculus500 related topics

## Infinitesimal

Infinitesimal or infinitesimal number is a quantity that is closer to 0|zero than any standard real number, but that is not zero.

Infinitesimals are a basic ingredient in calculus as developed by Leibniz, including the law of continuity and the transcendental law of homogeneity.

## Function (mathematics)

Called the domain of the function and the set Y is called the codomain of the function.

Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).

## Isaac Newton

English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher") widely recognised as one of the greatest mathematicians and physicists of all time and among the most influential scientists.

Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for developing infinitesimal calculus.

## Mathematical analysis

Branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions.

Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis.

## Gottfried Wilhelm Leibniz

German polymath active as a mathematician, philosopher, scientist and diplomat.

As a mathematician, his greatest achievement was the development of the main ideas of differential and integral calculus, independently of Isaac Newton's contemporaneous developments, and mathematicians have consistently favored Leibniz's notation as the conventional and more exact expression of calculus.

## Mathematics

Mathematics is an area of knowledge that includes such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and the spaces in which they are contained (geometry), and quantities and their changes (calculus and analysis).

## Algebra

Quadratic formula.svg expresses the solution of the equation

Even though some methods, which had been developed much earlier, may be considered nowadays as algebra, the emergence of algebra and, soon thereafter, of infinitesimal calculus as subfields of mathematics only dates from the 16th or 17th century.

## Area

Quantity that expresses the extent of a region on the plane or on a curved surface.

For shapes with curved boundary, calculus is usually required to compute the area.

## Differential calculus

In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change.

## Derivative

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

Derivatives are a fundamental tool of calculus.