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...

field, the standard Stokes' theorem is recovered. The proof of the theorem consists of 4 steps. We assume Green's theorem, so what is of concern is how...

it is equivalent to the fundamental theorem of calculus. In two dimensions, it is equivalent to Green's theorem. Vector fields are often illustrated...

after the mathematician George Green, who discovered Green's theorem. This identity is derived from the divergence theorem applied to the vector field F...

solution is a sum of Green's functions as well, by linearity of L. Green's functions are named after the British mathematician George Green, who first developed...

theorems from vector calculus. In particular, the fundamental theorem of calculus is the special case where the manifold is a line segment, Green’s theorem...

introduced several important concepts, among them a theorem similar to the modern Green's theorem, the idea of potential functions as currently used in...

first occurs. Herein also his remarkable theorem in pure mathematics, since universally known as Green's theorem, and probably the most important instrument...

In number theory, the Green–Tao theorem, proven by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long...

geometry, developing such notions as similarity of shapes, the Pythagorean theorem (Proposition 47), equality of angles and areas, parallelism, the sum of...

the yellow and green areas, which is the area of ABCD. The operation of a linear planimeter can be justified by applying Green's theorem, though the design...

function are continuous, the Cauchy integral theorem can be proven as a direct consequence of Green's theorem and the fact that the real and imaginary parts...

with reproduction and death rates to model population changes.: 631  Green's theorem, which gives the relationship between a line integral around a simple...

theorem Goodstein's theorem Green's theorem (to do) Green's theorem when D is a simple region Heine–Borel theorem Intermediate value theorem Itô's lemma Kőnig's...

Gabriel's horn Jacobian matrix Hessian matrix Curvature Green's theorem Divergence theorem Stokes' theorem Vector Calculus Infinite series Maclaurin series,...

In two dimensions, the divergence and curl theorems reduce to the Green's theorem: Linear approximations are used to replace complicated functions with...

also in terms of radiometry. There is also an analogous theorem in electrostatics, known as Green's reciprocity, relating the interchange of electric potential...

Stokes' theorem simultaneously generalizes the three theorems of vector calculus: the divergence theorem, Green's theorem, and the Kelvin-Stokes theorem. The...

natural, metric-independent generalization of Stokes' theorem, Gauss's theorem, and Green's theorem from vector calculus. If a differential k-form is thought...

Cauchy–Riemann equations) for any smooth closed curve L. Correspondingly, by Green's theorem, the right-hand integrals are zero when F = f ( z ) ¯ {\displaystyle...

form of the area formula can be considered to be a special case of Green's theorem. The area formula can also be applied to self-overlapping polygons...

further refined by French mathematician Henri Dulac in 1923 using Green's theorem. Without loss of generality, let there exist a function φ ( x , y )...

Mathematics for her solution of the generic case of Green's conjecture in two papers. The case of Green's conjecture for generic curves had attracted a huge...

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

around D {\displaystyle D} . This follows easily, for example, from Green's theorem. As we will soon see, γ r {\displaystyle \gamma _{r}} is positively...

culmination of a long series of rhetorical moves, including (among others) Green's theorem, Gauss's potential theory and Faraday's lines of force – all of which...

reformulated as an application of Green's theorem in flux-divergence form (i.e. a two-dimensional version of the divergence theorem), in a way that avoids all...

Amsler-Laffon devised this entirely geometric method—independent of Green's theorem—long before the vector-analytic proof became standard; contemporaries...

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

segment of the polygon and two meridians, by a line integral with Green's theorem, or via an equal-area projection as commonly done in GIS. The other...