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  2. Calculus - Wikipedia

    en.wikipedia.org/wiki/Calculus

    Calculus is the mathematical study of continuous change, ... Latinized as Alhazen (c. 965 – c. 1040 AD) derived a formula for the sum of fourth powers.

  3. General Leibniz rule - Wikipedia

    en.wikipedia.org/wiki/General_Leibniz_rule

    In calculus, the general Leibniz rule, [1] ... This formula can be used to derive a formula that computes the symbol of the composition of differential operators.

  4. Fundamental theorem of calculus - Wikipedia

    en.wikipedia.org/.../Fundamental_theorem_of_calculus

    The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speaking, the two operations can be ...

  5. Integral - Wikipedia

    en.wikipedia.org/wiki/Integral

    The fundamental theorem of calculus is the statement that differentiation and ... and engineering involve integration where an explicit formula for the integral is ...

  6. Leibniz integral rule - Wikipedia

    en.wikipedia.org/wiki/Leibniz_integral_rule

    In calculus, the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Wilhelm Leibniz, states that for an integral of the form () (,), where < (), < and the integrands are functions dependent on , the derivative of this integral is expressible as (() (,)) = (, ()) (, ()) + () (,) where the partial derivative indicates that inside the integral, only the ...

  7. Glossary of calculus - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_calculus

    This formula summarizes the intuitive idea that the derivative of y with respect to x is the limit of the ratio of differences Δy/Δx as Δx becomes infinitesimal. differential calculus Is a subfield of calculus [30] concerned with the study of the rates at which quantities change.

  8. Product rule - Wikipedia

    en.wikipedia.org/wiki/Product_rule

    In calculus, the product rule (or Leibniz rule [1] or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions.For two functions, it may be stated in Lagrange's notation as () ′ = ′ + ′ or in Leibniz's notation as () = +.

  9. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [ l ] is defined as the linear part of the change in the functional, and the second variation [ m ] is defined as the quadratic part.

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