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...

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...

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'...

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...

algebra Fundamental theorem of calculus Fundamental theorem of calculus for line integrals Fundamental theorem of curves Fundamental theorem of cyclic...

function at that point. Differential calculus and integral calculus are connected by the fundamental theorem of calculus. This states that differentiation...

century with the independent discovery of the fundamental theorem of calculus by Leibniz and Newton. The theorem demonstrates a connection between integration...

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...

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...

(by the fundamental theorem of calculus) in the framework of Riemann integration, but with absolute continuity it may be formulated in terms of Lebesgue...

integration Linearity of integration Arbitrary constant of integration Cavalieri's quadrature formula Fundamental theorem of calculus Integration by parts...

Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables:...

related to definite integrals through the second fundamental theorem of calculus: the definite integral of a function over a closed interval where the function...

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...

(variational form) integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation...

allows expressing the fundamental theorem of calculus, the divergence theorem, Green's theorem, and Stokes' theorem as special cases of a single general result...

(roughly speaking) measures precisely the extent to which the fundamental theorem of calculus fails in higher dimensions and on general manifolds. — Terence...

curl is a form of differentiation for vector fields. The corresponding form of the fundamental theorem of calculus is Stokes' theorem, which relates the...

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...

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...

be derived using the fundamental theorem of calculus. The (first) fundamental theorem of calculus is just the particular case of the above formula where...

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...

physics and mathematics, the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that any sufficiently smooth, rapidly decaying...

follows at once from the fundamental theorem of calculus, together with the mean value theorem for derivatives. Since the mean value of f on [a, b] is defined...

integrates this picture, which corresponds to applying the fundamental theorem of calculus, one obtains Cavalieri's quadrature formula, the integral ∫...

applications, the Riemann integral can be evaluated by the fundamental theorem of calculus or approximated by numerical integration, or simulated using...

time. It may be seen as a stochastic generalization of the (second) fundamental theorem of calculus. It is named after the Russian mathematician Eugene...

generalize the fundamental theorem of calculus to higher dimensions: In two dimensions, the divergence and curl theorems reduce to the Green's theorem: Linear...

development of infinitesimal calculus; in particular, for proof of the fundamental theorem of calculus. His work centered on the properties of the tangent;...

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...