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  2. John Wallis - Wikipedia

    en.wikipedia.org/wiki/John_Wallis

    He shows that the areas are, respectively, 1, 1/6, 1/30, 1/140, etc. He next considered curves of the form y = x 1/ m and established the theorem that the area bounded by this curve and the lines x = 0 and x = 1 is equal to the area of the rectangle on the same base and of the same altitude as m : m + 1.

  3. History of calculus - Wikipedia

    en.wikipedia.org/wiki/History_of_calculus

    The ancient period introduced some of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way. . Calculations of volumes and areas, one goal of integral calculus, can be found in the Egyptian Moscow papyrus (c. 1820 BC), but the formulas are only given for concrete numbers, some are only approximately true, and they are not ...

  4. Limit (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Limit_(mathematics)

    In mathematics, a limit is the value that a function (or sequence) approaches as the argument (or index) approaches some value. [1] Limits of functions are essential to calculus and mathematical analysis , and are used to define continuity , derivatives , and integrals .

  5. Timeline of calculus and mathematical analysis - Wikipedia

    en.wikipedia.org/wiki/Timeline_of_calculus_and...

    [1] 3rd century BC - Archimedes develops a concept of the indivisibles—a precursor to infinitesimals—allowing him to solve several problems using methods now termed as integral calculus. Archimedes also derives several formulae for determining the area and volume of various solids including sphere, cone, paraboloid and hyperboloid. [2]

  6. Calculus - Wikipedia

    en.wikipedia.org/wiki/Calculus

    Henri Lebesgue invented measure theory, based on earlier developments by Émile Borel, and used it to define integrals of all but the most pathological functions. [42] Laurent Schwartz introduced distributions, which can be used to take the derivative of any function whatsoever. [43] Limits are not the only rigorous approach to the foundation ...

  7. Mathematical analysis - Wikipedia

    en.wikipedia.org/wiki/Mathematical_analysis

    Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. [1] [2] These theories are usually studied in the context of real and complex numbers and functions.

  8. Gottfried Wilhelm Leibniz - Wikipedia

    en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz

    Gottfried Wilhelm Leibniz (or Leibnitz; [a] 1 July 1646 [O.S. 21 June] – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to many other branches of mathematics, such as binary arithmetic and statistics.

  9. List of limits - Wikipedia

    en.wikipedia.org/wiki/List_of_limits

    In these limits, the infinitesimal change is often denoted or .If () is differentiable at , (+) = ′ ().This is the definition of the derivative.All differentiation rules can also be reframed as rules involving limits.