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...

areas, and calculation of gradients) are actually closely related. From the conjecture and the proof of the fundamental theorem of calculus, calculus as...

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

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

algorithm for finding the minimum of a function Gradient theorem, theorem that a line integral through a gradient field can be evaluated by evaluating the original...

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

_{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...

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...

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

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

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...

Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate...

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...

Gordon–Newell theorem (queueing theory) Gottesman–Knill theorem (quantum computation) Gradient theorem (vector calculus) Graph structure theorem (graph theory)...

{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...

expressed as the gradient of a scalar field that is a solution to Poisson's equation, and has a zero path integral. See gradient theorem. The integral equation...

Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law...

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

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

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...

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...

mathematics, specifically differential calculus, the inverse function theorem gives a sufficient condition for a function to be invertible in a neighborhood...

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

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...

\mathbf {u} } is path-independent. Finally, by the converse of the gradient theorem, a scalar function ψ ( x , y , t ) {\displaystyle \psi (x,y,t)} exists...

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