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  2. Euler–Maclaurin formula - Wikipedia

    en.wikipedia.org/wiki/Euler–Maclaurin_formula

    The remainder term arises because the integral is usually not exactly equal to the sum. The formula may be derived by applying repeated integration by parts to successive intervals [r, r + 1] for r = m, m + 1, …, n − 1. The boundary terms in these integrations lead to the main terms of the formula, and the leftover integrals form the ...

  3. Summation by parts - Wikipedia

    en.wikipedia.org/wiki/Summation_by_parts

    The formula for an integration by parts is () ′ = [() ()] ′ (). Beside the boundary conditions , we notice that the first integral contains two multiplied functions, one which is integrated in the final integral ( g ′ {\displaystyle g'} becomes g {\displaystyle g} ) and one which is differentiated ( f {\displaystyle f} becomes f ...

  4. Riemann sum - Wikipedia

    en.wikipedia.org/wiki/Riemann_sum

    In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician Bernhard Riemann . One very common application is in numerical integration , i.e., approximating the area of functions or lines on a graph, where it is also known as the rectangle rule .

  5. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.

  6. Discrete calculus - Wikipedia

    en.wikipedia.org/wiki/Discrete_calculus

    Discrete integral calculus is the study of the definitions, properties, and applications of the Riemann sums. The process of finding the value of a sum is called integration . In technical language, integral calculus studies a certain linear operator .

  7. Cantor (mathematics software) - Wikipedia

    en.wikipedia.org/wiki/Cantor_(mathematics_software)

    Typesetting of mathematical formulas using LaTeX; Backend-aware syntax highlighting; Plugin-based assistant dialogs for common tasks (like integrating a function or entering a matrix) Cantor was the first KDE project to implement upload to the GetHotNewStuff addon service, which is used to download or upload example worksheets. It provided ...

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