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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 ) bounded by C.It is the two-dimensional special case of Stokes' theorem (surface in ).
Herein also his remarkable theorem in pure mathematics, since universally known as Green's theorem, and probably the most important instrument of investigation in the whole range of mathematical physics, made its appearance. We are all now able to understand, in a general way at least, the importance of Green's work, and the progress made since ...
In mathematics, Green's identities are a set of three identities in vector calculus relating the bulk with the boundary of a region on which differential operators act. They are named after the mathematician George Green , who discovered Green's theorem .
In particular, the fundamental theorem of calculus is the special case where the manifold is a line segment, Green’s theorem and Stokes' theorem are the cases of a surface in or , and the divergence theorem is the case of a volume in . [2] Hence, the theorem is sometimes referred to as the fundamental theorem of multivariate calculus.
Great orthogonality theorem (group theory) Green–Tao theorem (number theory) Green's theorem (vector calculus) Grinberg's theorem (graph theory) Gromov's compactness theorem (Riemannian geometry) Gromov's compactness theorem (symplectic topology) Gromov's theorem on groups of polynomial growth (geometric group theory)
The title page to Green's original essay on what is now known as Green's theorem. In 1828, Green published An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism, which is the essay he is most famous for today. It was published privately at the author's expense, because he thought it would be ...
There is also an analogous theorem in electrostatics, known as Green's reciprocity, relating the interchange of electric potential and electric charge density. Forms of the reciprocity theorems are used in many electromagnetic applications, such as analyzing electrical networks and antenna systems. [ 1 ]
In mathematics, Green formula may refer to: Green's theorem in integral calculus; Green's identities in vector calculus; Green's function in differential equations; the Green formula for the Green measure in stochastic analysis