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  2. Calculus - Wikipedia

    en.wikipedia.org/wiki/Calculus

    Calculus 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. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.

  3. Symmetry of second derivatives - Wikipedia

    en.wikipedia.org/wiki/Symmetry_of_second_derivatives

    A modern approach to classical theorems of advanced calculus, W. A. Benjamin Tao, Terence (2006), Analysis II (PDF) , Texts and Readings in Mathematics, vol. 38, Hindustan Book Agency, doi : 10.1007/978-981-10-1804-6 , ISBN 8185931631

  4. Chain rule - Wikipedia

    en.wikipedia.org/wiki/Chain_rule

    In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g.More precisely, if = is the function such that () = (()) for every x, then the chain rule is, in Lagrange's notation, ′ = ′ (()) ′ (). or, equivalently, ′ = ′ = (′) ′.

  5. Glossary of calculus - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_calculus

    Is a subfield of calculus [30] concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus, the study of the area beneath a curve. [31] differential equation Is a mathematical equation that relates some function with its derivatives. In applications ...

  6. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    The calculus of variations may be said to begin with Newton's minimal resistance problem in 1687, followed by the brachistochrone curve problem raised by Johann Bernoulli (1696). [2] It immediately occupied the attention of Jacob Bernoulli and the Marquis de l'Hôpital , but Leonhard Euler first elaborated the subject, beginning in 1733.

  7. Curl (mathematics) - Wikipedia

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

    2) = ⁠ 1 / 2 ⁠ n(n − 1) dimensions, and allows one to interpret the differential of a 1-vector field as its infinitesimal rotations. Only in 3 dimensions (or trivially in 0 dimensions) we have n = ⁠ 1 / 2 ⁠ n(n − 1), which is the most elegant and common case. In 2 dimensions the curl of a vector field is not a vector field but a ...

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