The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every...

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'...

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

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...

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

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

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...

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

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...

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

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...

case of Stokes' theorem (surface in R 3 {\displaystyle \mathbb {R} ^{3}} ). In one dimension, it is equivalent to the fundamental theorem of calculus. In...

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

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...

generalization of the product rule Leibniz integral rule The alternating series test, also called Leibniz's rule The Fundamental theorem of calculus, also called...

decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable vector fields can be resolved into the sum of an irrotational...

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

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...

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

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

is now known as Rolle's theorem, and was proved only for polynomials, without the techniques of calculus. The mean value theorem in its modern form was...

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

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

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

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

of derivatives and integrals in alternative calculi List of equations List of fundamental theorems List of hypotheses List of inequalities Lists of integrals...

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

theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls, or simply the curl theorem,...

Derivative Fundamental theorem of calculus Integral Limit Non-standard analysis Partial derivative Infinite Series Sir Isaac Newton Gottfried Leibniz List of calculus...

} . The fundamental theorem of vector calculus states that, under some regularity conditions, any vector field can be expressed as the sum of a conservative...