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  2. Difference quotient - Wikipedia

    en.wikipedia.org/wiki/Difference_quotient

    Difference quotients may also find relevance in applications involving Time discretization, where the width of the time step is used for the value of h. The difference quotient is sometimes also called the Newton quotient [10] [12] [13] [14] (after Isaac Newton) or Fermat's difference quotient (after Pierre de Fermat). [15]

  3. Numerical differentiation - Wikipedia

    en.wikipedia.org/wiki/Numerical_differentiation

    The simplest method is to use finite difference approximations. A simple two-point estimation is to compute the slope of a nearby secant line through the points (x, f(x)) and (x + h, f(x + h)). [1] Choosing a small number h, h represents a small change in x, and it can be either positive or negative.

  4. Reciprocal rule - Wikipedia

    en.wikipedia.org/wiki/Reciprocal_rule

    Also, one can readily deduce the quotient rule from the reciprocal rule and the product rule. The reciprocal rule states that if f is differentiable at a point x and f(x) ≠ 0 then g(x) = 1/f(x) is also differentiable at x and ′ = ′ ().

  5. 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 â‹® ⋱ â‹® s 1 N − 1 ⋯ s N N − 1 ) ( a 1 â‹® a N ) = d !

  6. Algebraic number - Wikipedia

    en.wikipedia.org/wiki/Algebraic_number

    The sum, difference and product of algebraic integers are again algebraic integers, which means that the algebraic integers form a ring. The name algebraic integer comes from the fact that the only rational numbers that are algebraic integers are the integers, and because the algebraic integers in any number field are in many ways analogous to ...

  7. Differential of a function - Wikipedia

    en.wikipedia.org/wiki/Differential_of_a_function

    The quotient / is not infinitely small; rather it is a real number. The use of infinitesimals in this form was widely criticized, for instance by the famous pamphlet The Analyst by Bishop Berkeley. Augustin-Louis Cauchy ( 1823 ) defined the differential without appeal to the atomism of Leibniz's infinitesimals.

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