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...

the endpoints of the path, and can be evaluated by the gradient theorem (the fundamental theorem of calculus for line integrals). Conversely, a (continuous)...

and a terminal point B {\displaystyle B} . Then the gradient theorem (also called fundamental theorem of calculus for line integrals) states that ∫ P v...

extensions of the fundamental theorem of calculus in higher dimensions are the divergence theorem and the gradient theorem. One of the most powerful generalizations...

div generalize immediately to other dimensions, as do the gradient theorem, divergence theorem, and Laplacian (yielding harmonic analysis), while curl and...

various names in physics such as the Generalized Stokes theorem or the Gradient theorem): for a function S {\textstyle S} analytical in a domain D {\textstyle...

Pierre Hohenberg in the framework of the two Hohenberg–Kohn theorems (HK). The original HK theorems held only for non-degenerate ground states in the absence...

is independent of the path, then the work done by the force, by the gradient theorem, defines a potential function which is evaluated at the start and end...

_{C}\nabla U'\cdot d\mathbf {x} ,} which can be evaluated using the gradient theorem to obtain W = U ′ ( x B ) − U ′ ( x A ) . {\displaystyle W=U'(\mathbf...

mathematics: Gradient descent, a first-order iterative optimization algorithm for finding the minimum of a function Gradient theorem, theorem that a line...

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

quantum scattering theory. Divergence theorem Gradient theorem Methods of contour integration Nachbin's theorem Line element Surface integral Volume element...

(\mathbf {p} )=\int _{P}\nabla \psi \cdot d{\boldsymbol {\ell }}} (gradient theorem) A | ∂ P = A ( q ) − A ( p ) = ∫ P ( d ℓ ⋅ ∇ ) A {\displaystyle \mathbf...

calculus) Gradient theorem (vector calculus) Green's theorem (vector calculus) Helly's selection theorem (mathematical analysis) Implicit function theorem (vector...

potential (conservative), then applying the gradient theorem (and remembering that force is the negative of the gradient of the potential energy) yields: W C...

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...

embodied by the integral theorems of vector calculus:: 543ff  Gradient theorem Stokes' theorem Divergence theorem Green's theorem. In a more advanced study...

mathematically as E = − ∇ ϕ . {\displaystyle \mathbf {E} =-\nabla \phi .} The gradient theorem can be used to establish that the electrostatic potential is the amount...

conditions represents the fundamental theorem of the gradient and is true for any vector field that is a gradient of a differentiable single valued scalar...

In mathematics, the gradient conjecture, due to René Thom (1989), was proved in 2000 by three Polish mathematicians, Krzysztof Kurdyka (University of Savoie...

{d} {\boldsymbol {s}}=0.} The last equality is obtained by applying gradient theorem. Since both terms are zero, we obtain the result D Γ D t = 0. {\displaystyle...

making V E {\textstyle V_{\mathbf {E} }} well-defined everywhere. The gradient theorem then allows us to write: E = − ∇ V E {\displaystyle \mathbf {E} =-\mathbf...

In mathematics, the mean value theorem (or Lagrange's mean value theorem) states, roughly, that for a given planar arc between two endpoints, there is...

In physics and mathematics, the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable vector...

Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e...

In mathematics, the inverse function theorem is a theorem that asserts that, if a real function f has a continuous derivative near a point where its derivative...

In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R...

with respect to x {\displaystyle x} and y {\displaystyle y} . The gradient theorem asserts that a 1-form is exact if and only if the line integral of...

In multivariable calculus, the implicit function theorem is a tool that allows relations to be converted to functions of several real variables. It does...

In calculus, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct...