# A report onCalculus      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.

- Calculus ## 77 related topics with Alpha ## Mathematics                   Mathematics is an area of knowledge that includes such topics as numbers (arithmetic, 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). ## Integral

Integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.

Integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data.    Along with differentiation, integration is a fundamental, essential operation of calculus, and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. ## Mathematical analysis

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

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. ## Infinitesimal

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

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. ## Gottfried Wilhelm Leibniz

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

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. ## Geometry

Geometry is, with arithmetic, one of the oldest branches of mathematics.

Geometry is, with arithmetic, one of the oldest branches of mathematics.                This was a necessary precursor to the development of calculus and a precise quantitative science of physics. ## 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).

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. ## 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.

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. ## Archimedes

Approximation of pi; defining and investigating the spiral that now bears his name; and devising a system using exponentiation for expressing very large numbers.

Approximation of pi; defining and investigating the spiral that now bears his name; and devising a system using exponentiation for expressing very large numbers.              Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including: the area of a circle; the surface area and volume of a sphere; area of an ellipse; the area under a parabola; the volume of a segment of a paraboloid of revolution; the volume of a segment of a hyperboloid of revolution; and the area of a spiral. ## Differential calculus 