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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 โ€ฆ See more

    The 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 โ€ฆ See more

    The notion of a differential motivates several concepts in differential geometry (and differential topology).
    โ€ข See more

    17th century CE
    Calculus evolved into a distinct branch of mathematics.
    20th century
    Several new concepts in multivariable calculus, differential geometry, seemed to encapsulate the intent of the old terms.
    17th century CE
    Cauchy and others gradually developed the Epsilon, delta approach to continuity, limits and derivatives, giving a solid conceptual foundation for calculus.
    17th century CE
    Calculus evolved into a distinct branch of mathematics.
    17th century CE
    The presentations of, e.g., Newton, Leibniz, were marked by non-rigorous definitions of terms like differential, fluent and "infinitely small".
    17th century CE
    Infinitesimal quantities played a significant role in the development of calculus.
    17th century CE
    The use of differentials in this form attracted much criticism, for instance in the famous pamphlet The Analyst by Bishop Berkeley.
    17th century CE
    Isaac Newton referred to them as fluxions.
    17th century CE
    It was Gottfried Leibniz who coined the term differentials for infinitesimal quantities and introduced the notation for them which is still used today.
    17th century CE
    Archimedes 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 โ€ฆ

    There are several approaches for making the notion of differentials mathematically precise.
    1. Differentials โ€ฆ See more

    The 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 โ€ฆ See more

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