Differential (infinitesimal) and Integral

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Difference between Differential (infinitesimal) and Integral

Differential (infinitesimal) vs. Integral

The term differential is used in calculus to refer to an infinitesimal (infinitely small) change in some varying quantity. In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

Archimedes

Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.

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Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the 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.

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Derivative

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).

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Differential form

In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates.

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Exterior derivative

On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree.

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Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.

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Hyperreal number

The system of hyperreal numbers is a way of treating infinite and infinitesimal quantities.

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Infinitesimal

In mathematics, infinitesimals are things so small that there is no way to measure them.

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Isaac Newton

Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.

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Limit (mathematics)

In mathematics, a limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value.

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Linear combination

In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).

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Long s

The long, medial, or descending s (ſ) is an archaic form of the lower case letter s. It replaced a single s, or the first in a double s, at the beginning or in the middle of a word (e.g. "ſinfulneſs" for "sinfulness" and "ſucceſsful" for "successful").

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Non-standard analysis

The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Variable (mathematics)

In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.

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Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

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