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  2. Euler–Maclaurin formula - Wikipedia

    en.wikipedia.org/wiki/Euler–Maclaurin_formula

    In mathematics, the Euler–Maclaurin formula is a formula for the difference between an integral and a closely related sum. It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the machinery of calculus. For example, many asymptotic expansions are derived from the ...

  3. Summation by parts - Wikipedia

    en.wikipedia.org/wiki/Summation_by_parts

    A summation-by-parts (SBP) finite difference operator conventionally consists of a centered difference interior scheme and specific boundary stencils that mimics behaviors of the corresponding integration-by-parts formulation. [3][4] The boundary conditions are usually imposed by the Simultaneous-Approximation-Term (SAT) technique. [5] The ...

  4. Lists of mathematics topics - Wikipedia

    en.wikipedia.org/wiki/Lists_of_mathematics_topics

    Lists cover aspects of basic and advanced mathematics, methodology, mathematical statements, integrals, general concepts, mathematical objects, and reference tables. They also cover equations named after people, societies, mathematicians, journals, and meta-lists. The purpose of this list is not similar to that of the Mathematics Subject ...

  5. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    More detail may be found on the following pages for the lists of integrals: Gradshteyn, Ryzhik, Geronimus, Tseytlin, Jeffrey, Zwillinger, and Moll 's (GR) Table of Integrals, Series, and Products contains a large collection of results. An even larger, multivolume table is the Integrals and Series by Prudnikov, Brychkov, and Marichev (with ...

  6. Fundamental theorem of calculus - Wikipedia

    en.wikipedia.org/wiki/Fundamental_theorem_of...

    The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speaking, the two operations can be ...

  7. Calculus - Wikipedia

    en.wikipedia.org/wiki/Calculus

    The definite integral inputs a function and outputs a number, which gives the algebraic sum of areas between the graph of the input and the x-axis. The technical definition of the definite integral involves the limit of a sum of areas of rectangles, called a Riemann sum. [47]: 282 A motivating example is the distance traveled in a given time.

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