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trapezoidal function

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  • Trapezoidal rule — This article is about the quadrature rule for approximating integrals. For the Explicit trapezoidal rule for solving initial value problems, see Heun s method. The function f(x) (in blue) is approximated by a linear function (in red). In… …   Wikipedia

  • Dickman function — The Dickman–de Bruijn function ρ(u) plotted on a logarithmic scale. The horizontal axis is the argument u, and the vertical axis is the value of the function. The graph nearly makes a downward line on the logarithmic scale, demonstrating that the …   Wikipedia

  • Dickman-de Bruijn function — In analytic number theory, Dickman s function is a special function used to estimate the proportion of smooth numbers up to a given bound.Dickman s function is named after actuary Karl Dickman, who defined it in his only mathematical publication …   Wikipedia

  • Stiff equation — In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small. It has proven difficult to formulate a precise …   Wikipedia

  • Clenshaw–Curtis quadrature — and Fejér quadrature are methods for numerical integration, or quadrature , that are based on an expansion of the integrand in terms of Chebyshev polynomials. Equivalently, they employ a change of variables x = cos θ and use a discrete… …   Wikipedia

  • Numerical integration — consists of finding numerical approximations for the value S In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also… …   Wikipedia

  • Simpson's rule — can be derived by approximating the integrand f (x) (in blue) by the quadratic interpolant P (x) (in red). In numerical analysis, Simpson s rule is a method for numerical integration, the numerical approximation of definite integrals.… …   Wikipedia

  • stringed instrument — a musical instrument having strings as the medium of sound production, played with the fingers or with a plectrum or a bow: The guitar, the harp, and the violin are stringed instruments. * * * Any musical instrument that produces sound by the… …   Universalium

  • Riemann sum — In mathematics, a Riemann sum is a method for approximating the total area underneath a curve on a graph, otherwise known as an integral. It may also be used to define the integration operation. The sums are named after the German mathematician… …   Wikipedia

  • Trapezium rule — In mathematics, the trapezium rule (the British term) or trapezoidal rule (the American term) is a way to approximately calculate the definite integral: int {a}^{b} f(x),dx. The trapezium rule works by approximating the region under the graph of… …   Wikipedia

  • Perfect number — In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum). Equivalently, a perfect… …   Wikipedia

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