known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval... 41 KB (5,356 words) - 02:48, 5 May 2024 |
In mathematics, the Riemann–Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes.... 19 KB (2,871 words) - 15:21, 22 April 2024 |
In mathematics, the Riemann–Liouville integral associates with a real function f : R → R {\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} } another... 16 KB (2,611 words) - 18:33, 13 January 2024 |
Lebesgue integration (redirect from Lebesgue integral) mathematicians attempted to put integral calculus on a firm foundation. The Riemann integral—proposed by Bernhard Riemann (1826–1866)—is a broadly successful... 40 KB (5,660 words) - 12:07, 25 February 2024 |
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... 21 KB (3,414 words) - 18:44, 4 May 2024 |
Henstock–Kurzweil integral or generalized Riemann integral or gauge integral – also known as the (narrow) Denjoy integral (pronounced [dɑ̃ˈʒwa]), Luzin integral or Perron... 18 KB (2,768 words) - 12:02, 12 April 2024 |
the integrals at hand are Lebesgue integrals, we may use the bounded convergence theorem (valid for these integrals, but not for Riemann integrals) in... 52 KB (11,107 words) - 03:32, 30 April 2024 |
he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex... 26 KB (2,927 words) - 17:10, 8 May 2024 |
integral is constructed using Darboux sums and is one possible definition of the integral of a function. Darboux integrals are equivalent to Riemann integrals... 16 KB (2,512 words) - 11:34, 23 February 2024 |
the Riemann integral in n dimensions will be called the multiple integral. Multiple integrals have many properties common to those of integrals of functions... 44 KB (8,008 words) - 22:17, 8 May 2024 |
Gustav Lejeune Dirichlet, and Bernhard Riemann. Lebesgue presents six conditions which it is desirable that the integral should satisfy, the last of which... 18 KB (2,082 words) - 07:05, 6 May 2024 |
Antiderivative (redirect from General integral) of the Riemann integral defined as the limit of left-hand or right-hand Riemann sums over regular partitions, one will obtain that the integral of such... 21 KB (3,294 words) - 15:06, 25 March 2024 |
the animation to the right. For a line integral over a scalar field, the integral can be constructed from a Riemann sum using the above definitions of f... 20 KB (3,090 words) - 06:11, 29 April 2024 |
Contour integration (redirect from Contour integral) partition of an interval and the Riemann integral. In both cases the integral over a contour is defined as the sum of the integrals over the directed smooth curves... 45 KB (9,631 words) - 04:26, 8 May 2024 |
that if f is a function having a Riemann integral in the interval [a, b], then its integral is the limit of Riemann sums taken by sampling the function... 21 KB (2,394 words) - 18:48, 9 November 2022 |
Fubini's theorem (redirect from An elegant rearrangement of a conditionally convergent iterated integral) {\text{d}}x\right){\text{d}}y.} Here all integrals are Lebesgue integrals. Fubini's theorem is not true as stated for the Riemann integral, but it is true if the function... 41 KB (7,888 words) - 12:45, 10 May 2024 |
The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined... 68 KB (10,287 words) - 11:24, 5 May 2024 |
Wikipedia page. Length Area Volume Probability Moving average Riemann sum Riemann–Stieltjes integral Bounded variation Jordan content Cauchy principal value... 2 KB (221 words) - 02:51, 2 May 2022 |
of discontinuous functions in Riemann's sense. In this work, while giving a rigorous definition of the Riemann integral as well as explicit rigorous proofs... 17 KB (1,930 words) - 06:51, 6 May 2024 |
Calculus (redirect from Differential and Integral Calculus) called "infinitesimal calculus". Bernhard Riemann used these ideas to give a precise definition of the integral. It was also during this period that the... 73 KB (8,575 words) - 02:33, 6 May 2024 |
expression as the norm of the partitions approaches zero, we arrive at the Riemann integral. We know that this limit exists because f was assumed to be integrable... 31 KB (4,886 words) - 00:07, 5 May 2024 |
integral Riemann multiple integral Riemann invariant Riemann mapping theorem Measurable Riemann mapping theorem Riemann problem Riemann solver Riemann sphere... 4 KB (287 words) - 19:15, 29 November 2023 |
Derivative (redirect from Inverse integral) Press, ISBN 978-0-691-15995-9 Roussos, Ioannis M. (2014), Improper Riemann Integral, CRC Press, ISBN 978-1-4665-8807-3 Rychlík, Karel (1923), Über eine... 55 KB (7,184 words) - 21:07, 17 April 2024 |
Fractional calculus (redirect from Fractional integral) operators. The classical form of fractional calculus is given by the Riemann–Liouville integral, which is essentially what has been described above. The theory... 57 KB (7,149 words) - 08:43, 30 April 2024 |
Real analysis (section Riemann integration) compared to the Riemann integral, the Lebesgue integral was defined with similar basic ideas in mind. Compared to the Riemann integral, the more sophisticated... 49 KB (7,673 words) - 19:10, 25 December 2023 |