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Differential (mathematics) - Wikipedia
Basic notions. In calculus, the differential represents a change in the linearization of a function . The total differential is its generalization for functions of multiple variables. In traditional approaches to calculus, the differentials (e.g. dx, dy, dt, etc.) are interpreted as infinitesimals. See more
In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions.
The term is used in โฆ See moreThe term differential is used nonrigorously in calculus to refer to an infinitesimal ("infinitely small") change in some varying quantity. For example, if x is a variable, then a change in โฆ See more
The notion of a differential motivates several concepts in differential geometry (and differential topology).
โข See more17th century CECalculus evolved into a distinct branch of mathematics.20th centurySeveral new concepts in multivariable calculus, differential geometry, seemed to encapsulate the intent of the old terms.17th century CECauchy and others gradually developed the Epsilon, delta approach to continuity, limits and derivatives, giving a solid conceptual foundation for calculus.17th century CECalculus evolved into a distinct branch of mathematics.17th century CEThe presentations of, e.g., Newton, Leibniz, were marked by non-rigorous definitions of terms like differential, fluent and "infinitely small".17th century CEInfinitesimal quantities played a significant role in the development of calculus.17th century CEThe use of differentials in this form attracted much criticism, for instance in the famous pamphlet The Analyst by Bishop Berkeley.17th century CEIsaac Newton referred to them as fluxions.17th century CEIt was Gottfried Leibniz who coined the term differentials for infinitesimal quantities and introduced the notation for them which is still used today.17th century CEArchimedes used them, even though he did not believe that arguments involving infinitesimals were rigorous.Infinitesimal quantities played a significant role in the development of calculus. Archimedes used them, even though he did not believe that arguments โฆ
There are several approaches for making the notion of differentials mathematically precise.
1. Differentials โฆ See moreThe term differential has also been adopted in homological algebra and algebraic topology, because of the role the exterior derivative plays in de Rham cohomology: in a cochain complex $${\displaystyle (C_{\bullet },d_{\bullet }),}$$ the โฆ See more
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webJan 1, 2021 · 1) The simplest problems, solved by the mathematicians of Ancient Greece by the method of exhaustion (cf. Exhaustion, method of ), in which infinitesimal quantities are used merely to prove that two given โฆ
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