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  2. Antiderivative - Wikipedia

    en.wikipedia.org/wiki/Antiderivative

    The slope field of () = +, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a continuous function f is a differentiable function F whose derivative is equal to the original function f.

  3. Five-point stencil - Wikipedia

    en.wikipedia.org/wiki/Five-point_stencil

    An illustration of the five-point stencil in one and two dimensions (top, and bottom, respectively). In numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is a stencil made up of the point itself together with its four "neighbors".

  4. Nonelementary integral - Wikipedia

    en.wikipedia.org/wiki/Nonelementary_Integral

    In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function. [1] A theorem by Liouville in 1835 provided the first proof that nonelementary antiderivatives exist. [2]

  5. Derivation (differential algebra) - Wikipedia

    en.wikipedia.org/wiki/Derivation_(differential...

    If ε = 1, this definition reduces to the usual case. If ε = −1, however, then = + | | | | for odd | D |, and D is called an anti-derivation. Examples of anti-derivations include the exterior derivative and the interior product acting on differential forms.

  6. Inverse function rule - Wikipedia

    en.wikipedia.org/wiki/Inverse_function_rule

    In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the derivative of f. More precisely, if the inverse of f {\displaystyle f} is denoted as f − 1 {\displaystyle f^{-1}} , where f − 1 ( y ) = x {\displaystyle f^{-1}(y)=x} if and only if f ...

  7. Liouville's theorem (differential algebra) - Wikipedia

    en.wikipedia.org/wiki/Liouville's_theorem...

    Other examples include the functions ⁡ and . Liouville's theorem states that elementary antiderivatives, if they exist, are in the same differential field as the function, plus possibly a finite number of applications of the logarithm function.

  8. Antiderivative (complex analysis) - Wikipedia

    en.wikipedia.org/wiki/Antiderivative_(complex...

    However, this formal similarity notwithstanding, possessing a complex-antiderivative is a much more restrictive condition than its real counterpart. While it is possible for a discontinuous real function to have an anti-derivative, anti-derivatives can fail to exist even for holomorphic functions of a complex variable.

  9. Finite difference coefficient - Wikipedia

    en.wikipedia.org/wiki/Finite_difference_coefficient

    For arbitrary stencil points and any derivative of order < up to one less than the number of stencil points, the finite difference coefficients can be obtained by solving the linear equations [6] ( s 1 0 ⋯ s N 0 ⋮ ⋱ ⋮ s 1 N − 1 ⋯ s N N − 1 ) ( a 1 ⋮ a N ) = d !

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