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... 32 KB (5,125 words) - 17:26, 26 April 2024 |
The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated... 20 KB (3,001 words) - 18:43, 3 April 2024 |
vector calculus. In particular, the fundamental theorem of calculus is the special case where the manifold is a line segment, Green’s theorem and Stokes'... 35 KB (4,830 words) - 19:24, 11 April 2024 |
accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. They make... 73 KB (8,575 words) - 20:40, 25 April 2024 |
algebra Fundamental theorem of calculus Fundamental theorem of calculus for line integrals Fundamental theorem of curves Fundamental theorem of cyclic... 5 KB (553 words) - 02:58, 16 December 2023 |
Integral (redirect from Integral calculus) century with the independent discovery of the fundamental theorem of calculus by Leibniz and Newton. The theorem demonstrates a connection between integration... 67 KB (9,153 words) - 08:32, 20 March 2024 |
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through... 44 KB (7,506 words) - 12:02, 23 April 2024 |
version of the second fundamental theorem of calculus, that integrals can be computed using any of a function's antiderivatives. The first full proof of the... 48 KB (5,968 words) - 05:46, 24 April 2024 |
Absolute continuity (redirect from Fundamental theorem of Lebesgue integral calculus) (by the fundamental theorem of calculus) in the framework of Riemann integration, but with absolute continuity it may be formulated in terms of Lebesgue... 19 KB (2,686 words) - 16:49, 8 March 2024 |
integration Linearity of integration Arbitrary constant of integration Cavalieri's quadrature formula Fundamental theorem of calculus Integration by parts... 4 KB (389 words) - 12:14, 10 February 2024 |
Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables:... 19 KB (2,375 words) - 15:38, 29 April 2024 |
(variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation... 8 KB (1,354 words) - 15:53, 25 May 2023 |
Antiderivative (category Integral calculus) related to definite integrals through the second fundamental theorem of calculus: the definite integral of a function over a closed interval where the function... 21 KB (3,294 words) - 15:06, 25 March 2024 |
Differential form (redirect from Exterior calculus) allows expressing the fundamental theorem of calculus, the divergence theorem, Green's theorem, and Stokes' theorem as special cases of a single general result... 66 KB (9,950 words) - 14:18, 10 February 2024 |
These two points of view are related to each other by the fundamental theorem of discrete calculus. The study of the concepts of change starts with... 38 KB (6,491 words) - 00:53, 28 February 2024 |
De Rham cohomology (redirect from De Rham theorem) (roughly speaking) measures precisely the extent to which the fundamental theorem of calculus fails in higher dimensions and on general manifolds. — Terence... 19 KB (2,921 words) - 03:10, 13 August 2023 |
Curl (mathematics) (redirect from Curl (vector calculus)) curl is a form of differentiation for vector fields. The corresponding form of the fundamental theorem of calculus is Stokes' theorem, which relates the... 34 KB (4,932 words) - 18:46, 29 April 2024 |
the fundamental theorem of calculus. Laisant proved that if F{\displaystyle F} is an antiderivative of f{\displaystyle f}, then the antiderivatives of f−1{\displaystyle... 10 KB (1,647 words) - 02:59, 19 March 2024 |
in X to g(f(x)) in Z. fundamental theorem of calculus The fundamental theorem of calculus is a theorem that links the concept of differentiating a function... 88 KB (10,913 words) - 11:59, 19 April 2024 |
Leibniz integral rule (redirect from Derivative of Riemann integral) be derived using the fundamental theorem of calculus. The (first) fundamental theorem of calculus is just the particular case of the above formula where... 52 KB (11,107 words) - 03:32, 30 April 2024 |
In calculus, Taylor's theorem gives an approximation of a k {\textstyle k} -times differentiable function around a given point by a polynomial of degree... 54 KB (9,621 words) - 12:42, 27 March 2024 |
Helmholtz decomposition (redirect from Fundamental theorem of vector calculus) physics and mathematics, the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that any sufficiently smooth, rapidly decaying... 42 KB (6,710 words) - 15:02, 23 March 2024 |
integrates this picture, which corresponds to applying the fundamental theorem of calculus, one obtains Cavalieri's quadrature formula, the integral ∫... 35 KB (6,249 words) - 08:28, 22 April 2024 |
Riemann integral (category Definitions of mathematical integration) applications, the Riemann integral can be evaluated by the fundamental theorem of calculus or approximated by numerical integration, or simulated using... 41 KB (5,354 words) - 21:23, 11 November 2023 |
Dynkin's formula (category Probability theorems) time. It may be seen as a stochastic generalization of the (second) fundamental theorem of calculus. It is named after the Russian mathematician Eugene... 5 KB (639 words) - 23:12, 27 January 2023 |
Isaac Barrow (category Vice-Chancellors of the University of Cambridge) development of infinitesimal calculus; in particular, for proof of the fundamental theorem of calculus. His work centered on the properties of the tangent;... 21 KB (2,220 words) - 15:59, 15 January 2024 |
Cantor function (section Lack of absolute continuity) pointed out that it was a counterexample to an extension of the fundamental theorem of calculus claimed by Harnack. The Cantor function was discussed and... 21 KB (3,375 words) - 20:14, 30 March 2024 |
generalize the fundamental theorem of calculus to higher dimensions: In two dimensions, the divergence and curl theorems reduce to the Green's theorem: Linear... 21 KB (2,078 words) - 17:06, 19 April 2024 |