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  2. Riemann sum - Wikipedia

    en.wikipedia.org/wiki/Riemann_sum

    A Riemann sum of over [,] with partition is defined as = = () ... A generalized midpoint rule formula, also known as the enhanced midpoint integration, ...

  3. Trapezoidal rule - Wikipedia

    en.wikipedia.org/wiki/Trapezoidal_rule

    The trapezoidal rule may be viewed as the result obtained by averaging the left and right Riemann sums, and is sometimes defined this way. The integral can be even better approximated by partitioning the integration interval, applying the trapezoidal rule to each subinterval, and summing the results. In practice, this "chained" (or "composite ...

  4. Riemann integral - Wikipedia

    en.wikipedia.org/wiki/Riemann_integral

    One popular restriction is the use of "left-hand" and "right-hand" Riemann sums. In a left-hand Riemann sum, t i = x i for all i, and in a right-hand Riemann sum, t i = x i + 1 for all i. Alone this restriction does not impose a problem: we can refine any partition in a way that makes it a left-hand or right-hand sum by subdividing it at each t i.

  5. List of formulas in Riemannian geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    The Weyl tensor has the same basic symmetries as the Riemann tensor, but its 'analogue' of the Ricci tensor is zero: = = = = The Ricci tensor, the Einstein tensor, and the traceless Ricci tensor are symmetric 2-tensors:

  6. Numerical integration - Wikipedia

    en.wikipedia.org/wiki/Numerical_integration

    A quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration. Numerical integration methods can generally be described as combining evaluations of the integrand to get an approximation to the integral.

  7. Midpoint method - Wikipedia

    en.wikipedia.org/wiki/Midpoint_method

    The midpoint method computes + so that the red chord is approximately parallel to the tangent line at the midpoint (the green line). In numerical analysis , a branch of applied mathematics , the midpoint method is a one-step method for numerically solving the differential equation ,

  8. Famous Syrian activist Mazen Al-Hamada found dead in ... - AOL

    www.aol.com/famous-syrian-activist-mazen-al...

    After dedicating his life to fighting the regime of Assad, Mazen Al-Hamada did not live to see it fall. A symbol of resilience and courage, the famous Syrian activist was found dead in the ...

  9. Riemann–Stieltjes integral - Wikipedia

    en.wikipedia.org/wiki/Riemann–Stieltjes_integral

    The Riemann–Stieltjes integral admits integration by parts in the form () = () () ()and the existence of either integral implies the existence of the other. [2]On the other hand, a classical result [3] shows that the integral is well-defined if f is α-Hölder continuous and g is β-Hölder continuous with α + β > 1 .