Calculus

a large branch of mathematics concerned with quantities which are continuously variable. The many techniques of calculus were developed by the British scientist Isaac Newton (1643-1727) and the German philosopher Gottfried Wilhelm Leibniz (1646-1716).

Taken from Dictionary of Science

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Calculus (Latin, calculus, a small stone used for counting) is a branch in mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.

Historically, calculus was called "the calculus of infinitesimals", or "infinitesimal calculus". More generally, calculus (plural calculi) may refer to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, variational calculus, lambda calculus, pi calculus and join calculus.

Taken from Wikipedia

Factorial

the multiplication of a series of consecutive numbers from I to n inclusive, where n is a whole number. Thus, factorial 5, written as 5! = 1 x 2 x 3 x 4 x 5 = 120. Factorials of much larger numbers are not usually defined.

Taken from Dictionary of Science

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In mathematics, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example,

and

The notation n! was introduced by Christian Kramp in 1808.

The factorial function can also be defined for non-integer values, which involves more advanced mathematics, especially mathematical analysis.

Taken from Wikipedia