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  2. Symbolab - Wikipedia

    en.wikipedia.org/wiki/Symbolab

    Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]

  3. Exponential integral - Wikipedia

    en.wikipedia.org/wiki/Exponential_integral

    For real non-zero values of x, the exponential integral Ei(x) is defined as ⁡ = =. The Risch algorithm shows that Ei is not an elementary function.The definition above can be used for positive values of x, but the integral has to be understood in terms of the Cauchy principal value due to the singularity of the integrand at zero.

  4. Integration by parts - Wikipedia

    en.wikipedia.org/wiki/Integration_by_parts

    This visualization also explains why integration by parts may help find the integral of an inverse function f −1 (x) when the integral of the function f(x) is known. Indeed, the functions x(y) and y(x) are inverses, and the integral ∫ x dy may be calculated as above from knowing the integral ∫ y dx.

  5. Photomath - Wikipedia

    en.wikipedia.org/wiki/Photomath

    Photomath is an educational technology mobile app, owned by Google.It features a computer algebra system with an augmented optical character recognition system, designed for use with a smartphone's camera to scan and recognize mathematical equations; the app then displays step-by-step explanations onscreen.

  6. Matrix exponential - Wikipedia

    en.wikipedia.org/wiki/Matrix_exponential

    It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group. Let X be an n×n real or complex matrix. The exponential of X, denoted by e X or exp(X), is the n×n matrix given by the power series = =!

  7. Taylor's theorem - Wikipedia

    en.wikipedia.org/wiki/Taylor's_theorem

    for α ∈ N n and x ∈ R n. If all the k {\textstyle k} -th order partial derivatives of f : R n → R are continuous at a ∈ R n , then by Clairaut's theorem , one can change the order of mixed derivatives at a , so the short-hand notation

  8. Wronskian - Wikipedia

    en.wikipedia.org/wiki/Wronskian

    In mathematics, the Wronskian of n differentiable functions is the determinant formed with the functions and their derivatives up to order n – 1.It was introduced in 1812 by the Polish mathematician Józef Wroński, and is used in the study of differential equations, where it can sometimes show the linear independence of a set of solutions.

  9. Equation solving - Wikipedia

    en.wikipedia.org/wiki/Equation_solving

    In the simple case of a function of one variable, say, h(x), we can solve an equation of the form h(x) = c for some constant c by considering what is known as the inverse function of h. Given a function h : A → B, the inverse function, denoted h −1 and defined as h −1 : B → A, is a function such that